Week_21-A2_1NN_Implementing_Locality_Sensitive_Hashing.ipynb

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    "colab": {
      "name": "A2_1NN-Implementing Locality Sensitive Hashing_CLU02-NB02.ipynb",
      "provenance": []
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7iR0ByhZg-IS"
      },
      "source": [
        "# Locality Sensitive Hashing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A4Wop5Nag-In"
      },
      "source": [
        "Locality Sensitive Hashing (LSH) provides for a fast, efficient approximate nearest neighbor search. The algorithm scales well with respect to the number of data points as well as dimensions.\n",
        "\n",
        "In this assignment, you will\n",
        "* Implement the LSH algorithm for approximate nearest neighbor search\n",
        "* Examine the accuracy for different documents by comparing against brute force search, and also contrast runtimes\n",
        "* Explore the role of the algorithm’s tuning parameters in the accuracy of the method"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5WWMun3_g-Is"
      },
      "source": [
        "## Import necessary packages"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "_NCPs3eexBcR",
        "outputId": "dfaadf80-ac08-4250-e29f-272d2ba8fb3d"
      },
      "source": [
        "pip install turicreate"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting turicreate\n",
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            "Building wheels for collected packages: prettytable, resampy, gast\n",
            "  Building wheel for prettytable (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for prettytable: filename=prettytable-0.7.2-py3-none-any.whl size=13714 sha256=f443a11b12fb472bd1621c313ed4c2348b82470130b985aab5918f2189cfe0ff\n",
            "  Stored in directory: /root/.cache/pip/wheels/b2/7f/f6/f180315b584f00445045ff1699b550fa895d09471337ce21c6\n",
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            "  Created wheel for gast: filename=gast-0.2.2-py3-none-any.whl size=7554 sha256=90dd5a15d97d4f601d1f9e14699806866b04d51c862f4e30be0304a1cc5136e8\n",
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            "Successfully built prettytable resampy gast\n",
            "Installing collected packages: numpy, llvmlite, h5py, tensorflow-estimator, tensorboard, numba, keras-applications, gast, tensorflow, resampy, prettytable, coremltools, turicreate\n",
            "  Attempting uninstall: numpy\n",
            "    Found existing installation: numpy 1.19.5\n",
            "    Uninstalling numpy-1.19.5:\n",
            "      Successfully uninstalled numpy-1.19.5\n",
            "  Attempting uninstall: llvmlite\n",
            "    Found existing installation: llvmlite 0.34.0\n",
            "    Uninstalling llvmlite-0.34.0:\n",
            "      Successfully uninstalled llvmlite-0.34.0\n",
            "  Attempting uninstall: h5py\n",
            "    Found existing installation: h5py 3.1.0\n",
            "    Uninstalling h5py-3.1.0:\n",
            "      Successfully uninstalled h5py-3.1.0\n",
            "  Attempting uninstall: tensorflow-estimator\n",
            "    Found existing installation: tensorflow-estimator 2.6.0\n",
            "    Uninstalling tensorflow-estimator-2.6.0:\n",
            "      Successfully uninstalled tensorflow-estimator-2.6.0\n",
            "  Attempting uninstall: tensorboard\n",
            "    Found existing installation: tensorboard 2.6.0\n",
            "    Uninstalling tensorboard-2.6.0:\n",
            "      Successfully uninstalled tensorboard-2.6.0\n",
            "  Attempting uninstall: numba\n",
            "    Found existing installation: numba 0.51.2\n",
            "    Uninstalling numba-0.51.2:\n",
            "      Successfully uninstalled numba-0.51.2\n",
            "  Attempting uninstall: gast\n",
            "    Found existing installation: gast 0.4.0\n",
            "    Uninstalling gast-0.4.0:\n",
            "      Successfully uninstalled gast-0.4.0\n",
            "  Attempting uninstall: tensorflow\n",
            "    Found existing installation: tensorflow 2.6.0\n",
            "    Uninstalling tensorflow-2.6.0:\n",
            "      Successfully uninstalled tensorflow-2.6.0\n",
            "  Attempting uninstall: resampy\n",
            "    Found existing installation: resampy 0.2.2\n",
            "    Uninstalling resampy-0.2.2:\n",
            "      Successfully uninstalled resampy-0.2.2\n",
            "  Attempting uninstall: prettytable\n",
            "    Found existing installation: prettytable 2.1.0\n",
            "    Uninstalling prettytable-2.1.0:\n",
            "      Successfully uninstalled prettytable-2.1.0\n",
            "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
            "tensorflow-probability 0.13.0 requires gast>=0.3.2, but you have gast 0.2.2 which is incompatible.\n",
            "librosa 0.8.1 requires resampy>=0.2.2, but you have resampy 0.2.1 which is incompatible.\n",
            "datascience 0.10.6 requires folium==0.2.1, but you have folium 0.8.3 which is incompatible.\n",
            "albumentations 0.1.12 requires imgaug<0.2.7,>=0.2.5, but you have imgaug 0.2.9 which is incompatible.\u001b[0m\n",
            "Successfully installed coremltools-3.3 gast-0.2.2 h5py-2.10.0 keras-applications-1.0.8 llvmlite-0.33.0 numba-0.50.1 numpy-1.18.5 prettytable-0.7.2 resampy-0.2.1 tensorboard-2.0.2 tensorflow-2.0.4 tensorflow-estimator-2.0.1 turicreate-6.4.1\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.colab-display-data+json": {
              "pip_warning": {
                "packages": [
                  "numpy"
                ]
              }
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c2Nh5B9wg-Iv"
      },
      "source": [
        "from __future__ import print_function # to conform python 2.x print to python 3.x\n",
        "import numpy as np\n",
        "import turicreate\n",
        "from scipy.sparse import csr_matrix\n",
        "from sklearn.metrics.pairwise import pairwise_distances\n",
        "import time\n",
        "from copy import copy\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "'''compute norm of a sparse vector\n",
        "   Thanks to: Jaiyam Sharma'''\n",
        "def norm(x):\n",
        "    sum_sq=x.dot(x.T)\n",
        "    norm=np.sqrt(sum_sq)\n",
        "    return(norm)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k3it2ieBg-I2"
      },
      "source": [
        "## Load in the Wikipedia dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2rs2LX0wxzst",
        "outputId": "44270c90-dece-4498-bb0e-b7d422f79e60"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount ('/content/gdrive')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/gdrive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z-Taph0-g-I3"
      },
      "source": [
        "#wiki = turicreate.SFrame('people_wiki.sframe/')\n",
        "\n",
        "wiki = turicreate.SFrame('/content/gdrive/My Drive/Turicreate/Week 21/people_wiki.sframe/')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NhWp_N9fg-I6"
      },
      "source": [
        "For this assignment, let us assign a unique ID to each document."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Um52e7Fng-JB"
      },
      "source": [
        "wiki = wiki.add_row_number()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "s_04OZrFyEVf",
        "outputId": "bf73685d-b296-463e-c604-828b5213cdd1"
      },
      "source": [
        "wiki"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Digby_Morrell&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Digby Morrell</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">digby morrell born 10<br>october 1979 is a former ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Alfred_J._Lewy&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Alfred J. Lewy</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">alfred j lewy aka sandy<br>lewy graduated from ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Harpdog_Brown&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Harpdog Brown</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">harpdog brown is a singer<br>and harmonica player who ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Franz_Rottensteiner&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Franz Rottensteiner</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">franz rottensteiner born<br>in waidmannsfeld lower ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/G-Enka&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">G-Enka</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">henry krvits born 30<br>december 1974 in tallinn ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Sam_Henderson&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Sam Henderson</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">sam henderson born<br>october 18 1969 is an ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Aaron_LaCrate&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Aaron LaCrate</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">aaron lacrate is an<br>american music producer ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Trevor_Ferguson&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Trevor Ferguson</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">trevor ferguson aka john<br>farrow born 11 november ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Grant_Nelson&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Grant Nelson</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">grant nelson born 27<br>april 1971 in london  ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Cathy_Caruth&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Cathy Caruth</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">cathy caruth born 1955 is<br>frank h t rhodes ...</td>\n",
              "    </tr>\n",
              "</table>\n",
              "[59071 rows x 4 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
              "</div>"
            ],
            "text/plain": [
              "Columns:\n",
              "\tid\tint\n",
              "\tURI\tstr\n",
              "\tname\tstr\n",
              "\ttext\tstr\n",
              "\n",
              "Rows: 59071\n",
              "\n",
              "Data:\n",
              "+----+-------------------------------+---------------------+\n",
              "| id |              URI              |         name        |\n",
              "+----+-------------------------------+---------------------+\n",
              "| 0  | <http://dbpedia.org/resour... |    Digby Morrell    |\n",
              "| 1  | <http://dbpedia.org/resour... |    Alfred J. Lewy   |\n",
              "| 2  | <http://dbpedia.org/resour... |    Harpdog Brown    |\n",
              "| 3  | <http://dbpedia.org/resour... | Franz Rottensteiner |\n",
              "| 4  | <http://dbpedia.org/resour... |        G-Enka       |\n",
              "| 5  | <http://dbpedia.org/resour... |    Sam Henderson    |\n",
              "| 6  | <http://dbpedia.org/resour... |    Aaron LaCrate    |\n",
              "| 7  | <http://dbpedia.org/resour... |   Trevor Ferguson   |\n",
              "| 8  | <http://dbpedia.org/resour... |     Grant Nelson    |\n",
              "| 9  | <http://dbpedia.org/resour... |     Cathy Caruth    |\n",
              "+----+-------------------------------+---------------------+\n",
              "+-------------------------------+\n",
              "|              text             |\n",
              "+-------------------------------+\n",
              "| digby morrell born 10 octo... |\n",
              "| alfred j lewy aka sandy le... |\n",
              "| harpdog brown is a singer ... |\n",
              "| franz rottensteiner born i... |\n",
              "| henry krvits born 30 decem... |\n",
              "| sam henderson born october... |\n",
              "| aaron lacrate is an americ... |\n",
              "| trevor ferguson aka john f... |\n",
              "| grant nelson born 27 april... |\n",
              "| cathy caruth born 1955 is ... |\n",
              "+-------------------------------+\n",
              "[59071 rows x 4 columns]\n",
              "Note: Only the head of the SFrame is printed.\n",
              "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aJZ1nPsLg-JF"
      },
      "source": [
        "## Extract TF-IDF matrix"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QPPRxzlGg-JJ"
      },
      "source": [
        "We first use Turi Create to compute a TF-IDF representation for each document."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 415
        },
        "id": "xUC3a3pfg-JL",
        "outputId": "31ca5d18-e6dc-4292-c89d-5bb450c115c3"
      },
      "source": [
        "wiki['tf_idf'] = turicreate.text_analytics.tf_idf(wiki['text'])\n",
        "wiki.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Digby_Morrell&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Digby Morrell</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">digby morrell born 10<br>october 1979 is a former ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;melbourne&#x27;:<br>3.8914310119380633, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Alfred_J._Lewy&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Alfred J. Lewy</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">alfred j lewy aka sandy<br>lewy graduated from ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;time&#x27;:<br>1.3253342074200498, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Harpdog_Brown&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Harpdog Brown</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">harpdog brown is a singer<br>and harmonica player who ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;society&#x27;:<br>2.4448047262085693, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Franz_Rottensteiner&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Franz Rottensteiner</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">franz rottensteiner born<br>in waidmannsfeld lower ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;kurdlawitzpreis&#x27;:<br>10.986495389225194, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/G-Enka&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">G-Enka</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">henry krvits born 30<br>december 1974 in tallinn ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;curtis&#x27;:<br>5.299520032885375, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Sam_Henderson&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Sam Henderson</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">sam henderson born<br>october 18 1969 is an ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;asses&#x27;:<br>9.600201028105303, &#x27;s ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Aaron_LaCrate&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Aaron LaCrate</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">aaron lacrate is an<br>american music producer ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;streamz&#x27;:<br>10.986495389225194, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Trevor_Ferguson&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Trevor Ferguson</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">trevor ferguson aka john<br>farrow born 11 november ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;concordia&#x27;:<br>6.250296940830698, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Grant_Nelson&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Grant Nelson</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">grant nelson born 27<br>april 1971 in london  ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;heavies&#x27;:<br>8.907053847545358, &#x27;n ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Cathy_Caruth&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Cathy Caruth</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">cathy caruth born 1955 is<br>frank h t rhodes ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;2002&#x27;:<br>1.8753125887822302, ...</td>\n",
              "    </tr>\n",
              "</table>\n",
              "[10 rows x 5 columns]<br/>\n",
              "</div>"
            ],
            "text/plain": [
              "Columns:\n",
              "\tid\tint\n",
              "\tURI\tstr\n",
              "\tname\tstr\n",
              "\ttext\tstr\n",
              "\ttf_idf\tdict\n",
              "\n",
              "Rows: 10\n",
              "\n",
              "Data:\n",
              "+----+-------------------------------+---------------------+\n",
              "| id |              URI              |         name        |\n",
              "+----+-------------------------------+---------------------+\n",
              "| 0  | <http://dbpedia.org/resour... |    Digby Morrell    |\n",
              "| 1  | <http://dbpedia.org/resour... |    Alfred J. Lewy   |\n",
              "| 2  | <http://dbpedia.org/resour... |    Harpdog Brown    |\n",
              "| 3  | <http://dbpedia.org/resour... | Franz Rottensteiner |\n",
              "| 4  | <http://dbpedia.org/resour... |        G-Enka       |\n",
              "| 5  | <http://dbpedia.org/resour... |    Sam Henderson    |\n",
              "| 6  | <http://dbpedia.org/resour... |    Aaron LaCrate    |\n",
              "| 7  | <http://dbpedia.org/resour... |   Trevor Ferguson   |\n",
              "| 8  | <http://dbpedia.org/resour... |     Grant Nelson    |\n",
              "| 9  | <http://dbpedia.org/resour... |     Cathy Caruth    |\n",
              "+----+-------------------------------+---------------------+\n",
              "+-------------------------------+-------------------------------+\n",
              "|              text             |             tf_idf            |\n",
              "+-------------------------------+-------------------------------+\n",
              "| digby morrell born 10 octo... | {'melbourne': 3.8914310119... |\n",
              "| alfred j lewy aka sandy le... | {'time': 1.325334207420049... |\n",
              "| harpdog brown is a singer ... | {'society': 2.444804726208... |\n",
              "| franz rottensteiner born i... | {'kurdlawitzpreis': 10.986... |\n",
              "| henry krvits born 30 decem... | {'curtis': 5.2995200328853... |\n",
              "| sam henderson born october... | {'asses': 9.60020102810530... |\n",
              "| aaron lacrate is an americ... | {'streamz': 10.98649538922... |\n",
              "| trevor ferguson aka john f... | {'concordia': 6.2502969408... |\n",
              "| grant nelson born 27 april... | {'heavies': 8.907053847545... |\n",
              "| cathy caruth born 1955 is ... | {'2002': 1.875312588782230... |\n",
              "+-------------------------------+-------------------------------+\n",
              "[10 rows x 5 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iY1cRYIDg-JM"
      },
      "source": [
        "For the remainder of the assignment, we will use sparse matrices. Sparse matrices are matrices) that have a small number of nonzero entries. A good data structure for sparse matrices would only store the nonzero entries to save space and speed up computation. SciPy provides a highly-optimized library for sparse matrices. Many matrix operations available for NumPy arrays are also available for SciPy sparse matrices.We first convert the TF-IDF column (in dictionary format) into the SciPy sparse matrix format."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MuOuLXmng-JO"
      },
      "source": [
        "def sframe_to_scipy(x, column_name):\n",
        "    '''\n",
        "    Convert a dictionary column of an SFrame into a sparse matrix format where\n",
        "    each (row_id, column_id, value) triple corresponds to the value of\n",
        "    x[row_id][column_id], where column_id is a key in the dictionary.\n",
        "       \n",
        "    Example\n",
        "    >>> sparse_matrix, map_key_to_index = sframe_to_scipy(sframe, column_name)\n",
        "    '''\n",
        "    assert type(x[column_name][0]) == dict, \\\n",
        "        'The chosen column must be dict type, representing sparse data.'\n",
        "    \n",
        "    # Stack will transform x to have a row for each unique (row, key) pair.\n",
        "    x = x.stack(column_name, ['feature', 'value'])\n",
        "    \n",
        "    # Map feature words to integers \n",
        "    unique_words = sorted(x['feature'].unique())\n",
        "    mapping = {word:i for i, word in enumerate(unique_words)}\n",
        "    x['feature_id'] = x['feature'].apply(lambda x: mapping[x])\n",
        "    \n",
        "    # Create numpy arrays that contain the data for the sparse matrix.\n",
        "    row_id = np.array(x['id'])\n",
        "    col_id = np.array(x['feature_id'])\n",
        "    data = np.array(x['value'])\n",
        "    \n",
        "    width = x['id'].max() + 1\n",
        "    height = x['feature_id'].max() + 1\n",
        "    \n",
        "    # Create a sparse matrix.\n",
        "    mat = csr_matrix((data, (row_id, col_id)), shape=(width, height))\n",
        "    return mat, mapping"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WgIlm_dag-JQ",
        "outputId": "8fdf6a08-385a-4029-93e2-7359835d5a00"
      },
      "source": [
        "%%time\n",
        "corpus, mapping = sframe_to_scipy(wiki, 'tf_idf')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CPU times: user 2min 19s, sys: 7.81 s, total: 2min 27s\n",
            "Wall time: 1min 46s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PEt5Oj9PzrAE",
        "outputId": "6418df17-3a56-4458-d697-5fba56b0a70d"
      },
      "source": [
        "start=time.time()\n",
        "corpus, mapping = sframe_to_scipy(wiki,'tf_idf')\n",
        "end=time.time()\n",
        "print (end-start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "101.95863151550293\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6OhU1eTYg-JS",
        "outputId": "98d5717f-59e4-443e-e1c3-4783499dc8f9"
      },
      "source": [
        "assert corpus.shape == (59071, 547979)\n",
        "print('Check passed correctly!')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Check passed correctly!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o-ftzJy8g-JU"
      },
      "source": [
        "## Train an LSH model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kXEZRho9g-JV"
      },
      "source": [
        "The idea behind LSH is to translate the sign of our tf-idf scores into a binary index (1 or 0) by using seeing if our score falls above or below a randomly defined line. This <a href=\"http://ethen8181.github.io/machine-learning/recsys/content_based/lsh_text.html\">link</a> is helpful for understanding LSH and our code in more detail.\n",
        "\n",
        "\n",
        "LSH performs an efficient neighbor search by randomly partitioning all reference data points into different bins. Today we will build a popular variant of LSH known as <strong>random binary projection</strong>, which approximates cosine distance. There are other variants we could use for other choices of distance metrics.\n",
        "\n",
        "The first step is to generate a collection of random vectors from the standard Gaussian distribution."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ca3OxLsFg-JY"
      },
      "source": [
        "def generate_random_vectors(dim, n_vectors):\n",
        "    return np.random.randn(dim, n_vectors)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SIxGMHntg-Ja"
      },
      "source": [
        "To visualize these Gaussian random vectors, let's look at an example in low-dimensions.  Below, we generate 3 random vectors each of dimension 5."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ART_eZwNg-Jb",
        "outputId": "944c85ee-2fa3-464c-fa7b-80a950438863"
      },
      "source": [
        "# Generate 3 random vectors of dimension 5, arranged into a single 5 x 3 matrix.\n",
        "generate_random_vectors(n_vectors=3, dim=5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.75322899, -1.10535438, -1.13383164],\n",
              "       [-1.11064154, -0.05901982, -0.89088113],\n",
              "       [-0.00732216,  1.18538306, -1.57587596],\n",
              "       [ 0.27720691,  1.20418541,  0.08869405],\n",
              "       [-1.45482111,  1.49143255,  1.95561393]])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DVNm2bvig-Je"
      },
      "source": [
        "We now generate random vectors of the same dimensionality as our vocubulary size (547979).  Each vector can be used to compute one bit in the bin encoding.  We generate 16 vectors, leading to a 16-bit encoding of the bin index for each document."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LpniGaUPg-Jl",
        "outputId": "08df9398-fbf9-4b66-ea75-79afb4e361ad"
      },
      "source": [
        "# Generate 16 random vectors of dimension 547979\n",
        "np.random.seed(0)\n",
        "n_vectors = 16\n",
        "random_vectors = generate_random_vectors(corpus.shape[1], n_vectors)\n",
        "random_vectors.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(547979, 16)"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cakH-MaPg-Jo"
      },
      "source": [
        "Next, we partition data points into bins. Instead of using explicit loops, we'd like to utilize matrix operations for greater efficiency. Let's walk through the construction step by step.\n",
        "\n",
        "We'd like to decide which bin document 0 should go. Since 16 random vectors were generated in the previous cell, we have 16 bits to represent the bin index. The first bit is given by the sign of the dot product between the first random vector and the document's TF-IDF vector."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UBE115q5g-Jq",
        "outputId": "3e427591-a847-4020-8a45-38994bd5d859"
      },
      "source": [
        "sample = corpus[0] # vector of tf-idf values for document 0\n",
        "bin_indices_bits = sample.dot(random_vectors[:,0]) >= 0\n",
        "bin_indices_bits"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True])"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8u8cbUlXg-Jr"
      },
      "source": [
        "Similarly, the second bit is computed as the sign of the dot product between the second random vector and the document vector."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZRG82YYLg-Js",
        "outputId": "e88946a7-8d3a-4a1e-99eb-4059b44d0f72"
      },
      "source": [
        "sample.dot(random_vectors[:, 1]) >= 0 # True if positive sign; False if negative sign"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mVJNJe9gg-Jt"
      },
      "source": [
        "We can compute all of the bin index bits at once as follows. Note the absence of the explicit `for` loop over the 16 vectors. Matrix operations let us batch dot-product computation in a highly efficent manner, unlike the `for` loop construction. Given the relative inefficiency of loops in Python, the advantage of matrix operations is even greater."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AlFlzxq-g-Jv",
        "outputId": "a54110c7-334c-4955-912d-b420d6276109"
      },
      "source": [
        "sample.dot(random_vectors) >= 0 # should return an array of 16 True/False bits"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ True, False, False, False,  True, False,  True, False,  True,\n",
              "         True,  True, False,  True,  True, False,  True]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GsBWHiN1g-Jw",
        "outputId": "b234a132-7b5b-468e-f923-5b37606ff46a"
      },
      "source": [
        "np.array(sample.dot(random_vectors) >= 0, dtype=int) # display index bits in 0/1's"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jy_mSEVSg-Jy"
      },
      "source": [
        "All documents that obtain exactly this vector will be assigned to the same bin. We'd like to repeat the identical operation on all documents in the Wikipedia dataset and compute the corresponding bin indices. Again, we use matrix operations  so that no explicit loop is needed."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1hNRx4Sfg-Jz",
        "outputId": "7ff2bdf4-61b8-4a5e-8c00-1f28fe74f720"
      },
      "source": [
        "corpus[0:2].dot(random_vectors) >= 0 # compute bit indices of first two documents"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ True, False, False, False,  True, False,  True, False,  True,\n",
              "         True,  True, False,  True,  True, False,  True],\n",
              "       [False, False, False, False,  True, False, False, False,  True,\n",
              "         True,  True, False, False,  True, False,  True]])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dOCSdnoLg-J1",
        "outputId": "fc761b7e-e1df-468b-8da5-145fcc55d047"
      },
      "source": [
        "corpus.dot(random_vectors) >= 0 # compute bit indices of ALL documents"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ True, False, False, ...,  True, False,  True],\n",
              "       [False, False, False, ...,  True, False,  True],\n",
              "       [ True,  True,  True, ...,  True,  True,  True],\n",
              "       ...,\n",
              "       [False, False, False, ..., False, False,  True],\n",
              "       [ True,  True, False, ...,  True,  True, False],\n",
              "       [ True,  True,  True, ...,  True, False,  True]])"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bnw4OMofg-J3"
      },
      "source": [
        "We're almost done! To make it convenient to refer to individual bins, we convert each binary bin index into a single integer: \n",
        "```\n",
        "Bin index                      integer\n",
        "[0,0,0,0,0,0,0,0,0,0,0,0]   => 0\n",
        "[0,0,0,0,0,0,0,0,0,0,0,1]   => 1\n",
        "[0,0,0,0,0,0,0,0,0,0,1,0]   => 2\n",
        "[0,0,0,0,0,0,0,0,0,0,1,1]   => 3\n",
        "...\n",
        "[1,1,1,1,1,1,1,1,1,1,0,0]   => 65532\n",
        "[1,1,1,1,1,1,1,1,1,1,0,1]   => 65533\n",
        "[1,1,1,1,1,1,1,1,1,1,1,0]   => 65534\n",
        "[1,1,1,1,1,1,1,1,1,1,1,1]   => 65535 (= 2^16-1)\n",
        "```\n",
        "By the [rules of binary number representation](https://en.wikipedia.org/wiki/Binary_number#Decimal), we just need to compute the dot product between the document vector and the vector consisting of powers of 2:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sxNxA5hSg-J4",
        "outputId": "3368842c-28f7-452b-d022-7b7937a971ef"
      },
      "source": [
        "index_bits = (sample.dot(random_vectors) >= 0)\n",
        "powers_of_two = (1 << np.arange(15, -1, -1))\n",
        "print(index_bits)\n",
        "print(powers_of_two)\n",
        "print(index_bits.dot(powers_of_two))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ True False False False  True False  True False  True  True  True False\n",
            "   True  True False  True]]\n",
            "[32768 16384  8192  4096  2048  1024   512   256   128    64    32    16\n",
            "     8     4     2     1]\n",
            "[35565]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ydFE7cd7g-J6"
      },
      "source": [
        "Since it's the dot product again, we batch it with a matrix operation:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XIS93tbPg-J7",
        "outputId": "061bedd3-0642-4e6c-f0df-1c70f83b61f2"
      },
      "source": [
        "index_bits = sample.dot(random_vectors) >= 0\n",
        "index_bits.dot(powers_of_two)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([35565])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U9roFrq7g-J8"
      },
      "source": [
        "This array gives us the integer index of the bins for all documents.\n",
        "\n",
        "Now we are ready to complete the following function. Given the integer bin indices for the documents, you should compile a list of document IDs that belong to each bin. Since a list is to be maintained for each unique bin index, a dictionary of lists is used.\n",
        "\n",
        "1. Compute the integer bin indices. This step is already completed.\n",
        "2. For each document in the dataset, do the following:\n",
        "   * Get the integer bin index for the document.\n",
        "   * Fetch the list of document ids associated with the bin; if no list yet exists for this bin, assign the bin an empty list.\n",
        "   * Add the document id to the end of the list.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1Cfj8l3Zg-J9"
      },
      "source": [
        "from collections import defaultdict \n",
        "\n",
        "def train_lsh(data, n_vectors, seed=None):    \n",
        "    if seed is not None:\n",
        "        np.random.seed(seed)\n",
        "\n",
        "    dim = data.shape[1]\n",
        "    random_vectors = generate_random_vectors(dim, n_vectors)  \n",
        "\n",
        "    # Partition data points into bins,\n",
        "    # and encode bin index bits into integers\n",
        "    bin_indices_bits = data.dot(random_vectors) >= 0\n",
        "    powers_of_two = 1 << np.arange(n_vectors - 1, -1, step=-1)\n",
        "    bin_indices = bin_indices_bits.dot(powers_of_two)\n",
        "\n",
        "    # Update `table` so that `table[i]` is the list of document ids with bin index equal to i\n",
        "    table = defaultdict(list)\n",
        "    for data_index, bin_index in enumerate(bin_indices):\n",
        "\n",
        "           \n",
        "        # Fetch the list of document ids associated with the bin and add the document id to the end.\n",
        "        # data_index: document ids\n",
        "        # append() will add a list of document ids to table dict() with key as bin_index\n",
        "            table[bin_index].append(data_index)   # YOUR CODE HERE\n",
        "    \n",
        "    # Note that we're storing the bin_indices here\n",
        "    # so we can do some ad-hoc checking with it,\n",
        "    # this isn't actually required\n",
        "    model = {'data': data,\n",
        "             'table': table,\n",
        "             'random_vectors': random_vectors,\n",
        "             'bin_indices': bin_indices,\n",
        "             'bin_indices_bits': bin_indices_bits}\n",
        "    return model"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3f30ve-3g-J_"
      },
      "source": [
        "**Checkpoint**. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7_7xHv63g-KB"
      },
      "source": [
        "def compare_bits(model, id_1, id_2):\n",
        "    bits1 = model['bin_indices_bits'][id_1]\n",
        "    bits2 = model['bin_indices_bits'][id_2]\n",
        "    print('Number of agreed bits: ', np.sum(bits1 == bits2))\n",
        "    return np.sum(bits1 == bits2)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J1wq3c1vg-KD",
        "outputId": "6f0528bd-fb9a-4e57-8d41-7a4215bcd34c"
      },
      "source": [
        "model = train_lsh(corpus, 16, seed=475)\n",
        "obama_id = wiki[wiki['name'] == 'Barack Obama']['id'][0]\n",
        "biden_id = wiki[wiki['name'] == 'Joe Biden']['id'][0]\n",
        "similariy = compare_bits(model, obama_id, biden_id)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of agreed bits:  15\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Iyt3dtaTg-KF"
      },
      "source": [
        "**Note.** We will be using the model trained here in the following sections, unless otherwise indicated."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OGQAVxxBg-KG"
      },
      "source": [
        "## Inspect bins"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "prlDvmmmg-KG"
      },
      "source": [
        "After generating our LSH model, let's examine the generated bins to get a deeper understanding of them. Here, we will look at these similar products' bins to see if the result matches intuition. Remember the idea behind LSH is that similar data points will tend to fall into nearby bins."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "08l-u0Irg-KH"
      },
      "source": [
        "# This function will help us get similar items, given the id\n",
        "def get_similarity_items(X_tfidf, item_id, topn=5):\n",
        "    \"\"\"\n",
        "    Get the top similar items for a given item id.\n",
        "    The similarity measure here is based on cosine distance.\n",
        "    \"\"\"\n",
        "    query = X_tfidf[item_id]\n",
        "    scores = X_tfidf.dot(query.T).toarray().ravel()\n",
        "    best = np.argpartition(scores, -topn)[-topn:]\n",
        "    similar_items = sorted(zip(best, scores[best]), key=lambda x: -x[1])\n",
        "    similar_item_ids = [similar_item for similar_item, _ in similar_items]\n",
        "    print(\"Similar items to id: {}\".format(item_id))\n",
        "    for _id in similar_item_ids:\n",
        "        print(wiki[_id]['name'])\n",
        "    print('\\n')\n",
        "    return similar_item_ids"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0jeIdbosg-KJ"
      },
      "source": [
        "Let us look at some documents and see which bins they fall into."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "id": "vCIqjZPTg-KK",
        "outputId": "5409f7c1-3a56-4118-ac3e-eb8ad9fbe673"
      },
      "source": [
        "wiki[wiki['name'] == 'Barack Obama']"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">35817</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Barack_Obama&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Barack Obama</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">barack hussein obama ii<br>brk husen bm born august ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;normalize&#x27;:<br>10.293348208665249, ...</td>\n",
              "    </tr>\n",
              "</table>\n",
              "[? rows x 5 columns]<br/>Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.<br/>You can use sf.materialize() to force materialization.\n",
              "</div>"
            ],
            "text/plain": [
              "Columns:\n",
              "\tid\tint\n",
              "\tURI\tstr\n",
              "\tname\tstr\n",
              "\ttext\tstr\n",
              "\ttf_idf\tdict\n",
              "\n",
              "Rows: Unknown\n",
              "\n",
              "Data:\n",
              "+-------+-------------------------------+--------------+\n",
              "|   id  |              URI              |     name     |\n",
              "+-------+-------------------------------+--------------+\n",
              "| 35817 | <http://dbpedia.org/resour... | Barack Obama |\n",
              "+-------+-------------------------------+--------------+\n",
              "+-------------------------------+-------------------------------+\n",
              "|              text             |             tf_idf            |\n",
              "+-------------------------------+-------------------------------+\n",
              "| barack hussein obama ii br... | {'normalize': 10.293348208... |\n",
              "+-------------------------------+-------------------------------+\n",
              "[? rows x 5 columns]\n",
              "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
              "You can use sf.materialize() to force materialization."
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pR51_ZLzg-Ka"
      },
      "source": [
        "**Quiz Question**. What is the document `id` of Barack Obama's article?\n",
        "\n",
        "**Quiz Question**. Which bin contains Barack Obama's article? Enter its integer index."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Xawh5PECg-Kh",
        "outputId": "58761892-2d9e-4b52-b22c-7ffc27fb4a14"
      },
      "source": [
        "model"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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              " 'bin_indices_bits': array([[False, False, False, ...,  True,  True, False],\n",
              "        [ True,  True, False, ..., False,  True, False],\n",
              "        [ True, False,  True, ...,  True,  True,  True],\n",
              "        ...,\n",
              "        [False, False,  True, ..., False,  True, False],\n",
              "        [False, False,  True, ..., False, False, False],\n",
              "        [ True,  True, False, ..., False,  True,  True]]),\n",
              " 'data': <59071x547979 sparse matrix of type '<class 'numpy.float64'>'\n",
              " \twith 10379283 stored elements in Compressed Sparse Row format>,\n",
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              "              3681: [919, 30171],\n",
              "              50023: [920, 13089],\n",
              "              6135: [921, 20943, 42372],\n",
              "              1638: [922, 19943, 36056],\n",
              "              36384: [923, 36536, 55471],\n",
              "              47179: [924],\n",
              "              58337: [925],\n",
              "              49766: [926, 6841],\n",
              "              32457: [927],\n",
              "              13544: [928, 1337, 4474, 49505],\n",
              "              49571: [929, 21544],\n",
              "              58055: [930, 1813, 6038],\n",
              "              213: [931],\n",
              "              44370: [932, 15070],\n",
              "              41050: [933],\n",
              "              26830: [934, 50448],\n",
              "              10032: [935, 25572, 47721],\n",
              "              9817: [936, 23101, 58259],\n",
              "              43580: [937],\n",
              "              1570: [938, 3628, 46153, 56459, 58256],\n",
              "              20797: [939, 27515],\n",
              "              930: [940, 38511],\n",
              "              12018: [941],\n",
              "              38344: [942, 40696],\n",
              "              36710: [943, 24719, 52770],\n",
              "              16528: [944, 51361],\n",
              "              48277: [945, 15073, 49828, 51910],\n",
              "              42158: [946, 27690],\n",
              "              21688: [947, 31799],\n",
              "              47850: [948],\n",
              "              26591: [949, 53326],\n",
              "              23708: [950, 26281, 31869],\n",
              "              14411: [951, 24873],\n",
              "              53969: [952, 5725, 26282, 40144],\n",
              "              41934: [953, 6152],\n",
              "              25628: [954, 1480, 39775, 58295],\n",
              "              46046: [955],\n",
              "              10782: [956],\n",
              "              42339: [957, 53286],\n",
              "              52302: [958, 10088],\n",
              "              2576: [959, 50653],\n",
              "              64108: [960, 23028],\n",
              "              57095: [962, 9475],\n",
              "              25023: [963],\n",
              "              53202: [964],\n",
              "              42880: [965, 48259],\n",
              "              63362: [966],\n",
              "              35463: [967, 13626],\n",
              "              13511: [968, 2952, 22825],\n",
              "              16289: [969, 7570, 15094],\n",
              "              62277: [970, 13190, 24200, 39515],\n",
              "              8701: [971, 37871],\n",
              "              1238: [972, 10128, 41549],\n",
              "              54100: [973, 14241],\n",
              "              10303: [974, 11615, 39395],\n",
              "              45570: [975, 16779],\n",
              "              12511: [976, 28897, 35723],\n",
              "              55821: [977],\n",
              "              2529: [978, 1881],\n",
              "              39941: [979],\n",
              "              56862: [980],\n",
              "              15175: [981, 34785],\n",
              "              64005: [982],\n",
              "              48219: [983],\n",
              "              5144: [984, 37625],\n",
              "              46923: [985],\n",
              "              2909: [986, 15253, 43421],\n",
              "              38649: [987, 26308, 32074],\n",
              "              9876: [988],\n",
              "              15869: [989, 27480, 56138, 57825],\n",
              "              15258: [990, 45672],\n",
              "              28965: [991],\n",
              "              8089: [992, 2960, 20688],\n",
              "              12158: [993],\n",
              "              56920: [994, 1077, 2417, 8975, 16428, 37820, 48318],\n",
              "              51329: [996],\n",
              "              15544: [997, 13959, 54088],\n",
              "              112: [998, 53040],\n",
              "              34794: [999, 29507],\n",
              "              15182: [1000],\n",
              "              46107: [1001, 9678, 28253],\n",
              "              44158: [1003, 44065, 45684],\n",
              "              11302: [1004, 30853],\n",
              "              8563: [1005],\n",
              "              50582: [1006],\n",
              "              ...})}"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vd8UmNXo6ee_",
        "outputId": "f527ca99-32d7-48a6-a4d4-e62b2cd8cb35"
      },
      "source": [
        "# document id of Barack Obama\n",
        "wiki[wiki['name'] == 'Barack Obama']['id'][0]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "35817"
            ]
          },
          "metadata": {},
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7zh9RXGP6hQ2",
        "outputId": "53539722-a964-4ca3-aabb-7fd1dab0c9a7"
      },
      "source": [
        "# bin_index contains Barack Obama's article\n",
        "print (model['bin_indices'][35817]) # integer format"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "38448\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qwaxfE7sg-Kj"
      },
      "source": [
        "Recall from the previous assignment that Joe Biden was a close neighbor of Barack Obama."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "id": "LhZaDjBpg-Kk",
        "outputId": "07c42654-0c8e-4c99-8502-f9018434d61b"
      },
      "source": [
        "wiki[wiki['name'] == 'Joe Biden']"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">24478</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Joe_Biden&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Joe Biden</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">joseph robinette joe<br>biden jr dosf rbnt badn ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;were&#x27;:<br>1.521978023354629, ...</td>\n",
              "    </tr>\n",
              "</table>\n",
              "[? rows x 5 columns]<br/>Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.<br/>You can use sf.materialize() to force materialization.\n",
              "</div>"
            ],
            "text/plain": [
              "Columns:\n",
              "\tid\tint\n",
              "\tURI\tstr\n",
              "\tname\tstr\n",
              "\ttext\tstr\n",
              "\ttf_idf\tdict\n",
              "\n",
              "Rows: Unknown\n",
              "\n",
              "Data:\n",
              "+-------+-------------------------------+-----------+\n",
              "|   id  |              URI              |    name   |\n",
              "+-------+-------------------------------+-----------+\n",
              "| 24478 | <http://dbpedia.org/resour... | Joe Biden |\n",
              "+-------+-------------------------------+-----------+\n",
              "+-------------------------------+-------------------------------+\n",
              "|              text             |             tf_idf            |\n",
              "+-------------------------------+-------------------------------+\n",
              "| joseph robinette joe biden... | {'were': 1.521978023354629... |\n",
              "+-------------------------------+-------------------------------+\n",
              "[? rows x 5 columns]\n",
              "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
              "You can use sf.materialize() to force materialization."
            ]
          },
          "metadata": {},
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dAlJeu9Gg-Km"
      },
      "source": [
        "**Quiz Question**. Examine the bit representations of the bins containing Barack Obama and Joe Biden. In how many places do they agree?\n",
        "\n",
        "1. 16 out of 16 places (Barack Obama and Joe Biden fall into the same bin)\n",
        "2. 15 out of 16 places\n",
        "3. 13 out of 16 places\n",
        "4. 11 out of 16 places\n",
        "5. 9 out of 16 places"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jg0phoAIg-Kn",
        "outputId": "7a3e8691-5602-4741-d05e-2c5420465e26"
      },
      "source": [
        "# document id of Joe Biden\n",
        "wiki[wiki['name'] == 'Joe Biden']['id'][0]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "24478"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n5YIQaBVg-Ko",
        "outputId": "838cc0be-dc4e-4ed1-94cf-4a46baa36ca5"
      },
      "source": [
        "# bin_index of Joe Biden\n",
        "print (np.array(model['bin_indices_bits'][24478], dtype=int)) # list of 0/1's\n",
        "\n",
        "# bit representations of the bins containing Joe Biden\n",
        "print (model['bin_indices'][24478]) # integer format"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0]\n",
            "37424\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XlHxsPE27QH6",
        "outputId": "c55ddd6e-683d-4c7b-a4e9-9f08f3e29743"
      },
      "source": [
        "model['bin_indices_bits'][35817] == model['bin_indices_bits'][24478]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True,  True,  True,  True,  True, False,  True,  True,  True,\n",
              "        True,  True,  True,  True,  True,  True,  True])"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gWnl-v7Q7Wws",
        "outputId": "609ff22c-9d8d-4705-8f30-504ac632e399"
      },
      "source": [
        "# sum of bits agree between Barack Obama and Joe Biden\n",
        "sum(model['bin_indices_bits'][35817] == model['bin_indices_bits'][24478])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "15"
            ]
          },
          "metadata": {},
          "execution_count": 79
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GfTSy-rzg-Ko"
      },
      "source": [
        "Compare the result with a former British diplomat"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ykx45_JEg-Kp",
        "outputId": "250c2f96-601b-4e03-996b-1d9248fb8b37"
      },
      "source": [
        "jones_id = wiki[wiki['name']=='Wynn Normington Hugh-Jones']['id'][0]\n",
        "compare_bits(model, obama_id, jones_id)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of agreed bits:  8\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {},
          "execution_count": 80
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OoChw0fQ7tNx",
        "outputId": "68ddf1fd-f9e3-4ce3-bac5-ed01ba5c2c6f"
      },
      "source": [
        "print (np.array(model['bin_indices_bits'][22745], dtype=int)) # list of 0/1's\n",
        "print (model['bin_indices'][22745]) # integer format\n",
        "model['bin_indices_bits'][35817] == model['bin_indices_bits'][22745]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0]\n",
            "53964\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True, False,  True,  True,  True, False,  True,  True, False,\n",
              "       False, False, False, False, False,  True,  True])"
            ]
          },
          "metadata": {},
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HtGm__eGg-Kp"
      },
      "source": [
        "How about the documents in the same bin as Barack Obama? Are they necessarily more similar to Obama than Biden?  Let's look at which documents are in the same bin as the Barack Obama article."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wVrMbxgcg-Kq",
        "outputId": "38aa55de-f533-403b-dd9f-2ac2ec2fce95"
      },
      "source": [
        "model['table'][model['bin_indices'][35817]]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[35817, 54743]"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CUJTpwB4g-Kq"
      },
      "source": [
        "There is one more document in the same bin. Which document is it?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 91
        },
        "id": "_mzTuvXkg-Kr",
        "outputId": "16548eea-9bbb-4b46-ebb9-c17ae8d141d7"
      },
      "source": [
        "doc_ids = list(model['table'][model['bin_indices'][35817]])\n",
        "doc_ids.remove(35817) # display documents other than Obama\n",
        "\n",
        "docs = wiki.filter_by(values=doc_ids, column_name='id') # filter by id column\n",
        "docs"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">54743</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Radovan_%C5%BDerjav&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Radovan %C5%BDerjav</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">radovan erjav born 2<br>december 1968 is a ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;hungarian&#x27;:<br>5.299520032885375, ...</td>\n",
              "    </tr>\n",
              "</table>\n",
              "[1 rows x 5 columns]<br/>\n",
              "</div>"
            ],
            "text/plain": [
              "Columns:\n",
              "\tid\tint\n",
              "\tURI\tstr\n",
              "\tname\tstr\n",
              "\ttext\tstr\n",
              "\ttf_idf\tdict\n",
              "\n",
              "Rows: 1\n",
              "\n",
              "Data:\n",
              "+-------+-------------------------------+---------------------+\n",
              "|   id  |              URI              |         name        |\n",
              "+-------+-------------------------------+---------------------+\n",
              "| 54743 | <http://dbpedia.org/resour... | Radovan %C5%BDerjav |\n",
              "+-------+-------------------------------+---------------------+\n",
              "+-------------------------------+-------------------------------+\n",
              "|              text             |             tf_idf            |\n",
              "+-------------------------------+-------------------------------+\n",
              "| radovan erjav born 2 decem... | {'hungarian': 5.2995200328... |\n",
              "+-------------------------------+-------------------------------+\n",
              "[1 rows x 5 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mAdgr8ZNg-Kr",
        "outputId": "c9849330-8fce-4207-ceda-44666331e59c"
      },
      "source": [
        "res = compare_bits(model, obama_id, docs[0]['id']), compare_bits(model, obama_id, biden_id)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of agreed bits:  16\n",
            "Number of agreed bits:  15\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jc-NNYxi8Hv7",
        "outputId": "16dadad8-741c-4fcf-98db-303053b2e4ed"
      },
      "source": [
        "def cosine_distance(x, y):\n",
        "    xy = x.dot(y.T)\n",
        "    dist = xy/(norm(x)*norm(y))\n",
        "    return 1-dist[0,0]\n",
        "\n",
        "obama_tf_idf = corpus[35817,:]\n",
        "biden_tf_idf = corpus[24478,:]\n",
        "\n",
        "print ('================= Cosine distance from Barack Obama')\n",
        "print ('Barack Obama - {0:24s}: {1:f}'.format('Joe Biden',\n",
        "                                             cosine_distance(obama_tf_idf, biden_tf_idf)))\n",
        "for doc_id in doc_ids:\n",
        "    doc_tf_idf = corpus[doc_id,:]\n",
        "    print ('Barack Obama - {0:24s}: {1:f}'.format(wiki[doc_id]['name'],\n",
        "                                                 cosine_distance(obama_tf_idf, doc_tf_idf)))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "================= Cosine distance from Barack Obama\n",
            "Barack Obama - Joe Biden               : 0.703139\n",
            "Barack Obama - Radovan %C5%BDerjav     : 0.973346\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rhRvsDYfg-Ks"
      },
      "source": [
        "**In summary**, similar data points will in general _tend to_ fall into _nearby_ bins, but that's all we can say about LSH. In a high-dimensional space such as text features, we often get unlucky with our selection of only a few random vectors such that dissimilar data points go into the same bin while similar data points fall into different bins. **Given a query document, we must consider all documents in the nearby bins and sort them according to their actual distances from the query.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XeZ6UB0cg-Ks"
      },
      "source": [
        "## Query the LSH model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a4p7_fHXg-Kt"
      },
      "source": [
        "Let us first implement the logic for searching nearby neighbors, which goes like this:\n",
        "```\n",
        "1. Let L be the bit representation of the bin that contains the query documents.\n",
        "2. Consider all documents in bin L.\n",
        "3. Consider documents in the bins whose bit representation differs from L by 1 bit.\n",
        "4. Consider documents in the bins whose bit representation differs from L by 2 bits.\n",
        "...\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nfs8q4Efg-Kt"
      },
      "source": [
        "To obtain candidate bins that differ from the query bin by some number of bits, we use `itertools.combinations`, which produces all possible subsets of a given list. See [this documentation](https://docs.python.org/3/library/itertools.html#itertools.combinations) for details.\n",
        "```\n",
        "1. Decide on the search radius r. This will determine the number of different bits between the two vectors.\n",
        "2. For each subset (n_1, n_2, ..., n_r) of the list [0, 1, 2, ..., num_vector-1], do the following:\n",
        "   * Flip the bits (n_1, n_2, ..., n_r) of the query bin to produce a new bit vector.\n",
        "   * Fetch the list of documents belonging to the bin indexed by the new bit vector.\n",
        "   * Add those documents to the candidate set.\n",
        "```\n",
        "\n",
        "Each line of output from the following cell is a 3-tuple indicating where the candidate bin would differ from the query bin. For instance,\n",
        "```\n",
        "(0, 1, 3)\n",
        "```\n",
        "indicates that the candiate bin differs from the query bin in first, second, and fourth bits."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JCv-CF3Lg-Ku"
      },
      "source": [
        "from itertools import combinations"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jMH6YQbNg-Ku",
        "outputId": "89790329-b6a1-46dd-ebe2-c8c5404f4e96"
      },
      "source": [
        "num_vector = 16\n",
        "search_radius = 3\n",
        "\n",
        "for diff in combinations(range(num_vector), search_radius):\n",
        "    print(diff)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(0, 1, 2)\n",
            "(0, 1, 3)\n",
            "(0, 1, 4)\n",
            "(0, 1, 5)\n",
            "(0, 1, 6)\n",
            "(0, 1, 7)\n",
            "(0, 1, 8)\n",
            "(0, 1, 9)\n",
            "(0, 1, 10)\n",
            "(0, 1, 11)\n",
            "(0, 1, 12)\n",
            "(0, 1, 13)\n",
            "(0, 1, 14)\n",
            "(0, 1, 15)\n",
            "(0, 2, 3)\n",
            "(0, 2, 4)\n",
            "(0, 2, 5)\n",
            "(0, 2, 6)\n",
            "(0, 2, 7)\n",
            "(0, 2, 8)\n",
            "(0, 2, 9)\n",
            "(0, 2, 10)\n",
            "(0, 2, 11)\n",
            "(0, 2, 12)\n",
            "(0, 2, 13)\n",
            "(0, 2, 14)\n",
            "(0, 2, 15)\n",
            "(0, 3, 4)\n",
            "(0, 3, 5)\n",
            "(0, 3, 6)\n",
            "(0, 3, 7)\n",
            "(0, 3, 8)\n",
            "(0, 3, 9)\n",
            "(0, 3, 10)\n",
            "(0, 3, 11)\n",
            "(0, 3, 12)\n",
            "(0, 3, 13)\n",
            "(0, 3, 14)\n",
            "(0, 3, 15)\n",
            "(0, 4, 5)\n",
            "(0, 4, 6)\n",
            "(0, 4, 7)\n",
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            "(0, 5, 6)\n",
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            "(0, 14, 15)\n",
            "(1, 2, 3)\n",
            "(1, 2, 4)\n",
            "(1, 2, 5)\n",
            "(1, 2, 6)\n",
            "(1, 2, 7)\n",
            "(1, 2, 8)\n",
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            "(1, 2, 11)\n",
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            "(1, 3, 4)\n",
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            "(2, 3, 4)\n",
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            "(3, 4, 5)\n",
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            "(4, 5, 6)\n",
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            "(5, 6, 7)\n",
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            "(5, 14, 15)\n",
            "(6, 7, 8)\n",
            "(6, 7, 9)\n",
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            "(6, 8, 9)\n",
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            "(6, 8, 12)\n",
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            "(6, 8, 14)\n",
            "(6, 8, 15)\n",
            "(6, 9, 10)\n",
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            "(6, 10, 11)\n",
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            "(6, 11, 12)\n",
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            "(6, 11, 14)\n",
            "(6, 11, 15)\n",
            "(6, 12, 13)\n",
            "(6, 12, 14)\n",
            "(6, 12, 15)\n",
            "(6, 13, 14)\n",
            "(6, 13, 15)\n",
            "(6, 14, 15)\n",
            "(7, 8, 9)\n",
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            "(7, 9, 10)\n",
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            "(7, 11, 12)\n",
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            "(7, 12, 13)\n",
            "(7, 12, 14)\n",
            "(7, 12, 15)\n",
            "(7, 13, 14)\n",
            "(7, 13, 15)\n",
            "(7, 14, 15)\n",
            "(8, 9, 10)\n",
            "(8, 9, 11)\n",
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            "(8, 9, 15)\n",
            "(8, 10, 11)\n",
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            "(8, 11, 12)\n",
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            "(8, 12, 13)\n",
            "(8, 12, 14)\n",
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            "(8, 13, 14)\n",
            "(8, 13, 15)\n",
            "(8, 14, 15)\n",
            "(9, 10, 11)\n",
            "(9, 10, 12)\n",
            "(9, 10, 13)\n",
            "(9, 10, 14)\n",
            "(9, 10, 15)\n",
            "(9, 11, 12)\n",
            "(9, 11, 13)\n",
            "(9, 11, 14)\n",
            "(9, 11, 15)\n",
            "(9, 12, 13)\n",
            "(9, 12, 14)\n",
            "(9, 12, 15)\n",
            "(9, 13, 14)\n",
            "(9, 13, 15)\n",
            "(9, 14, 15)\n",
            "(10, 11, 12)\n",
            "(10, 11, 13)\n",
            "(10, 11, 14)\n",
            "(10, 11, 15)\n",
            "(10, 12, 13)\n",
            "(10, 12, 14)\n",
            "(10, 12, 15)\n",
            "(10, 13, 14)\n",
            "(10, 13, 15)\n",
            "(10, 14, 15)\n",
            "(11, 12, 13)\n",
            "(11, 12, 14)\n",
            "(11, 12, 15)\n",
            "(11, 13, 14)\n",
            "(11, 13, 15)\n",
            "(11, 14, 15)\n",
            "(12, 13, 14)\n",
            "(12, 13, 15)\n",
            "(12, 14, 15)\n",
            "(13, 14, 15)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gkouSZzIg-Kv"
      },
      "source": [
        "With this output in mind, implement the logic for nearby bin search:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fxTLHpWQg-Kv"
      },
      "source": [
        "def search_nearby_bins(query_bin_bits, table, search_radius=2, initial_candidates=set()):\n",
        "    \"\"\"\n",
        "    For a given query vector and trained LSH model, return all candidate neighbors for\n",
        "    the query among all bins within the given search radius.\n",
        "    \n",
        "    Example usage\n",
        "    -------------\n",
        "    >>> model = train_lsh(corpus, num_vector=16, seed=143)\n",
        "    >>> q = model['bin_index_bits'][0]  # vector for the first document\n",
        "  \n",
        "    >>> candidates = search_nearby_bins(q, model['table'])\n",
        "    \"\"\"\n",
        "    num_vector = len(query_bin_bits)\n",
        "    powers_of_two = 1 << np.arange(num_vector-1, -1, -1)\n",
        "    \n",
        "    # Allow the user to provide an initial set of candidates.\n",
        "    candidate_set = copy(initial_candidates)\n",
        "    \n",
        "    for different_bits in combinations(range(num_vector), search_radius):       \n",
        "        # Flip the bits (n_1,n_2,...,n_r) of the query bin to produce a new bit vector.\n",
        "        ## Hint: you can iterate over a tuple like a list\n",
        "        alternate_bits = copy(query_bin_bits)\n",
        "        for i in different_bits:\n",
        "            alternate_bits[i] = ~alternate_bits[i] # YOUR CODE HERE \n",
        "        \n",
        "        # Convert the new bit vector to an integer index\n",
        "        nearby_bin = alternate_bits.dot(powers_of_two)\n",
        "        \n",
        "        # Fetch the list of documents belonging to the bin indexed by the new bit vector.\n",
        "        # Then add those documents to candidate_set\n",
        "        # Make sure that the bin exists in the table!\n",
        "        # Hint: update() method for sets lets you add an entire list to the set\n",
        "        if nearby_bin in table:\n",
        "            more_docs = table[nearby_bin] # Get all document_ids of the bin\n",
        "            candidate_set.update(more_docs) # YOUR CODE HERE: Update candidate_set with the documents in this bin.\n",
        "            \n",
        "    return candidate_set"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O7qJq3J0g-Kw"
      },
      "source": [
        "**Checkpoint**. Running the function with `search_radius=0` should yield the list of documents belonging to the same bin as the query."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eG2cnLH4g-Kx",
        "outputId": "b256f1fb-4928-4a08-e751-7321815248ac"
      },
      "source": [
        "obama_bin_index = model['bin_indices_bits'][35817] # bin index of Barack Obama\n",
        "candidate_set = search_nearby_bins(obama_bin_index, model['table'], search_radius=0)\n",
        "if candidate_set == set({35817, 54743}):\n",
        "    print('Passed test')\n",
        "else:\n",
        "    print('Check your code')\n",
        "print('List of documents in the same bin as Obama: {}'.format(candidate_set))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Passed test\n",
            "List of documents in the same bin as Obama: {35817, 54743}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N4Lj0NQ-g-Kx"
      },
      "source": [
        "**Checkpoint**. Running the function with `search_radius=1` adds more documents to the fore."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c0HemkfGg-Ky",
        "outputId": "05180650-c31b-4d04-c0d4-8e98ffefbe61"
      },
      "source": [
        "candidate_set = search_nearby_bins(obama_bin_index, model['table'], search_radius=1, initial_candidates=candidate_set)\n",
        "if candidate_set == set({42243, 28804, 1810, 48919, 24478, 31010, 7331, 23716, 51108, 48040, 36266, 33200, 25023, 23617, 54743, 34910, 35817, 34159, 14451, 23926, 39032, 12028, 43775}):\n",
        "    print('Passed test')\n",
        "else:\n",
        "    print('Check your code')\n",
        "print(candidate_set)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Passed test\n",
            "{42243, 28804, 1810, 48919, 24478, 31010, 7331, 23716, 51108, 48040, 36266, 33200, 25023, 23617, 54743, 34910, 35817, 34159, 14451, 23926, 39032, 12028, 43775}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UGPoJ3zBg-Ky"
      },
      "source": [
        "**Note**. Don't be surprised if few of the candidates look similar to Obama. This is why we add as many candidates as our computational budget allows and sort them by their distance to the query."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aJ0Mxb0Xg-Kz"
      },
      "source": [
        "Now we have a function that can return all the candidates from neighboring bins. Next we write a function to collect all candidates and compute their true distance to the query."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "3DQXz_Ejg-Kz"
      },
      "source": [
        "def query(vec, model, k, max_search_radius):\n",
        "  \n",
        "    data = model['data']\n",
        "    table = model['table']\n",
        "    random_vectors = model['random_vectors']\n",
        "    num_vector = random_vectors.shape[1]\n",
        "    \n",
        "    \n",
        "    # Compute bin index for the query vector, in bit representation.\n",
        "    bin_index_bits = (vec.dot(random_vectors) >= 0).flatten()\n",
        "    \n",
        "    # Search nearby bins and collect candidates\n",
        "    candidate_set = set()\n",
        "    for search_radius in range(max_search_radius+1):\n",
        "        candidate_set = search_nearby_bins(bin_index_bits, table, search_radius, initial_candidates=candidate_set)\n",
        "    \n",
        "    # Sort candidates by their true distances from the query\n",
        "    nearest_neighbors = turicreate.SFrame({'id':candidate_set})\n",
        "    candidates = data[np.array(list(candidate_set)),:]\n",
        "    nearest_neighbors['distance'] = pairwise_distances(candidates, vec, metric='cosine').flatten()\n",
        "    \n",
        "    return nearest_neighbors.topk('distance', k, reverse=True), len(candidate_set)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "whFf7Azlg-K0"
      },
      "source": [
        "Let's try it out with Obama:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7V3mOXSwg-K0",
        "outputId": "03c1fcc0-ae09-44e7-a15e-181c9fc3b981"
      },
      "source": [
        "query(corpus[35817,:], model, k=10, max_search_radius=3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(Columns:\n",
              " \tid\tint\n",
              " \tdistance\tfloat\n",
              " \n",
              " Rows: 10\n",
              " \n",
              " Data:\n",
              " +-------+------------------------+\n",
              " |   id  |        distance        |\n",
              " +-------+------------------------+\n",
              " | 35817 | 1.1102230246251565e-16 |\n",
              " | 24478 |   0.703138676733575    |\n",
              " | 38376 |   0.7429819023278823   |\n",
              " |  4032 |   0.8145547486714284   |\n",
              " | 43155 |   0.8408390074837325   |\n",
              " | 20159 |   0.844036884280093    |\n",
              " | 11517 |   0.8483420107162964   |\n",
              " | 46332 |   0.8897020225435585   |\n",
              " | 22063 |   0.8946710479694914   |\n",
              " | 10437 |   0.9001571479475322   |\n",
              " +-------+------------------------+\n",
              " [10 rows x 2 columns], 771)"
            ]
          },
          "metadata": {},
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YpGIV7VFg-K1"
      },
      "source": [
        "To identify the documents, it's helpful to join this table with the Wikipedia table:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 245
        },
        "id": "3eSkPciMg-K1",
        "outputId": "db3aa785-fdcd-4439-b0f8-dfef989988cd"
      },
      "source": [
        "query(corpus[35817,:], model, k=10, max_search_radius=3)[0].join(wiki[['id', 'name']], on='id').sort('distance')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">distance</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">35817</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.1102230246251565e-16</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Barack Obama</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">24478</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.703138676733575</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Joe Biden</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">38376</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.7429819023278823</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Samantha Power</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4032</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.8145547486714284</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Kenneth D. Thompson</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">43155</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.8408390074837325</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Goodwin Liu</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">20159</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.844036884280093</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Charlie Crist</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11517</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.8483420107162964</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Louis Susman</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">46332</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.8897020225435585</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Tom Tancredo</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">22063</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.8946710479694914</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Kathryn Troutman</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10437</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.9001571479475322</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">David J. Hayes</td>\n",
              "    </tr>\n",
              "</table>\n",
              "[10 rows x 3 columns]<br/>\n",
              "</div>"
            ],
            "text/plain": [
              "Columns:\n",
              "\tid\tint\n",
              "\tdistance\tfloat\n",
              "\tname\tstr\n",
              "\n",
              "Rows: 10\n",
              "\n",
              "Data:\n",
              "+-------+------------------------+---------------------+\n",
              "|   id  |        distance        |         name        |\n",
              "+-------+------------------------+---------------------+\n",
              "| 35817 | 1.1102230246251565e-16 |     Barack Obama    |\n",
              "| 24478 |   0.703138676733575    |      Joe Biden      |\n",
              "| 38376 |   0.7429819023278823   |    Samantha Power   |\n",
              "|  4032 |   0.8145547486714284   | Kenneth D. Thompson |\n",
              "| 43155 |   0.8408390074837325   |     Goodwin Liu     |\n",
              "| 20159 |   0.844036884280093    |    Charlie Crist    |\n",
              "| 11517 |   0.8483420107162964   |     Louis Susman    |\n",
              "| 46332 |   0.8897020225435585   |     Tom Tancredo    |\n",
              "| 22063 |   0.8946710479694914   |   Kathryn Troutman  |\n",
              "| 10437 |   0.9001571479475322   |    David J. Hayes   |\n",
              "+-------+------------------------+---------------------+\n",
              "[10 rows x 3 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 98
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6UPorLOUg-K2"
      },
      "source": [
        "We have shown that we have a working LSH implementation!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ERUinbyHg-K3"
      },
      "source": [
        "# Experimenting with your LSH implementation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vv_FNaj7g-K3"
      },
      "source": [
        "In the following sections we have implemented a few experiments so that you can gain intuition for how your LSH implementation behaves in different situations. This will help you understand the effect of searching nearby bins and the performance of LSH versus computing nearest neighbors using a brute force search."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TLt1CK7eg-K4"
      },
      "source": [
        "## Effect of nearby bin search"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d3D9A_zsg-K4"
      },
      "source": [
        "How does nearby bin search affect the outcome of LSH? There are three variables that are affected by the search radius:\n",
        "* Number of candidate documents considered\n",
        "* Query time\n",
        "* Distance of approximate neighbors from the query"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "59S7b6b8g-K5"
      },
      "source": [
        "Let us run LSH multiple times, each with different radii for nearby bin search. We will measure the three variables as discussed above."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "id": "juZuOF7mg-K5",
        "outputId": "a25c2812-45c2-4789-d985-04b86fab02d8"
      },
      "source": [
        "wiki[wiki['name']=='Barack Obama']"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">35817</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Barack_Obama&gt; ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Barack Obama</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">barack hussein obama ii<br>brk husen bm born august ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{&#x27;normalize&#x27;:<br>10.293348208665249, ...</td>\n",
              "    </tr>\n",
              "</table>\n",
              "[? rows x 5 columns]<br/>Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.<br/>You can use sf.materialize() to force materialization.\n",
              "</div>"
            ],
            "text/plain": [
              "Columns:\n",
              "\tid\tint\n",
              "\tURI\tstr\n",
              "\tname\tstr\n",
              "\ttext\tstr\n",
              "\ttf_idf\tdict\n",
              "\n",
              "Rows: Unknown\n",
              "\n",
              "Data:\n",
              "+-------+-------------------------------+--------------+\n",
              "|   id  |              URI              |     name     |\n",
              "+-------+-------------------------------+--------------+\n",
              "| 35817 | <http://dbpedia.org/resour... | Barack Obama |\n",
              "+-------+-------------------------------+--------------+\n",
              "+-------------------------------+-------------------------------+\n",
              "|              text             |             tf_idf            |\n",
              "+-------------------------------+-------------------------------+\n",
              "| barack hussein obama ii br... | {'normalize': 10.293348208... |\n",
              "+-------------------------------+-------------------------------+\n",
              "[? rows x 5 columns]\n",
              "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
              "You can use sf.materialize() to force materialization."
            ]
          },
          "metadata": {},
          "execution_count": 99
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4jGAfQDtg-K5",
        "outputId": "03d1969e-90b2-449b-9ba6-ad0fb563bf9e"
      },
      "source": [
        "%%time\n",
        "num_candidates_history = []\n",
        "query_time_history = []\n",
        "max_distance_from_query_history = []\n",
        "min_distance_from_query_history = []\n",
        "average_distance_from_query_history = []\n",
        "\n",
        "for max_search_radius in range(17):\n",
        "    start=time.time()\n",
        "    result, num_candidates = query(corpus[35817,:], model, k=10,\n",
        "                                   max_search_radius=max_search_radius)\n",
        "    end=time.time()\n",
        "    query_time = end-start\n",
        "    \n",
        "    print('Radius:', max_search_radius)\n",
        "    print(result.join(wiki[['id', 'name']], on='id').sort('distance'))\n",
        "    \n",
        "    average_distance_from_query = result['distance'][1:].mean()\n",
        "    max_distance_from_query = result['distance'][1:].max()\n",
        "    min_distance_from_query = result['distance'][1:].min()\n",
        "    \n",
        "    num_candidates_history.append(num_candidates)\n",
        "    query_time_history.append(query_time)\n",
        "    average_distance_from_query_history.append(average_distance_from_query)\n",
        "    max_distance_from_query_history.append(max_distance_from_query)\n",
        "    min_distance_from_query_history.append(min_distance_from_query)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Radius: 0\n",
            "+-------+------------------------+---------------------+\n",
            "|   id  |        distance        |         name        |\n",
            "+-------+------------------------+---------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |     Barack Obama    |\n",
            "| 54743 |    0.97334561058472    | Radovan %C5%BDerjav |\n",
            "+-------+------------------------+---------------------+\n",
            "[2 rows x 3 columns]\n",
            "\n",
            "Radius: 1\n",
            "+-------+------------------------+------------------------------+\n",
            "|   id  |        distance        |             name             |\n",
            "+-------+------------------------+------------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |         Barack Obama         |\n",
            "| 24478 |   0.703138676733575    |          Joe Biden           |\n",
            "| 34159 |   0.9430865736846581   |       Jennifer Hudson        |\n",
            "| 23926 |   0.9608039657958866   | Se%C3%A1n Power (politician) |\n",
            "| 36266 |   0.9615994281067699   |         Ralph Weber          |\n",
            "| 33200 |    0.97101213334657    |         Emrah Yucel          |\n",
            "| 28804 |   0.9729856623983864   |     Matthew McConaughey      |\n",
            "| 54743 |    0.97334561058472    |     Radovan %C5%BDerjav      |\n",
            "|  7331 |   0.9735542076945761   |       Joselo D%C3%ADaz       |\n",
            "| 43775 |   0.9790856334914729   |       Carly Rae Jepsen       |\n",
            "+-------+------------------------+------------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 2\n",
            "+-------+------------------------+--------------------------------+\n",
            "|   id  |        distance        |              name              |\n",
            "+-------+------------------------+--------------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |          Barack Obama          |\n",
            "| 24478 |   0.703138676733575    |           Joe Biden            |\n",
            "|  9051 |   0.9008406076426497   |         Newt Gingrich          |\n",
            "| 46253 |   0.9158128432084635   |        Francisco Rezek         |\n",
            "|  110  |   0.9346379007684388   |      Abdel Fattah el-Sisi      |\n",
            "| 40837 |   0.9370458058764901   |    Dovey Johnson Roundtree     |\n",
            "| 34159 |   0.9430865736846581   |        Jennifer Hudson         |\n",
            "| 28320 |   0.9460512776474829   |          Robert Reich          |\n",
            "| 33070 |   0.9466276757770745   |          Claude Allen          |\n",
            "|  3818 |   0.9484009651426074   | Tom Sawyer (Kansas politician) |\n",
            "+-------+------------------------+--------------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 3\n",
            "+-------+------------------------+---------------------+\n",
            "|   id  |        distance        |         name        |\n",
            "+-------+------------------------+---------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |     Barack Obama    |\n",
            "| 24478 |   0.703138676733575    |      Joe Biden      |\n",
            "| 38376 |   0.7429819023278823   |    Samantha Power   |\n",
            "|  4032 |   0.8145547486714284   | Kenneth D. Thompson |\n",
            "| 43155 |   0.8408390074837325   |     Goodwin Liu     |\n",
            "| 20159 |   0.844036884280093    |    Charlie Crist    |\n",
            "| 11517 |   0.8483420107162964   |     Louis Susman    |\n",
            "| 46332 |   0.8897020225435585   |     Tom Tancredo    |\n",
            "| 22063 |   0.8946710479694914   |   Kathryn Troutman  |\n",
            "| 10437 |   0.9001571479475322   |    David J. Hayes   |\n",
            "+-------+------------------------+---------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 4\n",
            "+-------+------------------------+---------------------+\n",
            "|   id  |        distance        |         name        |\n",
            "+-------+------------------------+---------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |     Barack Obama    |\n",
            "| 24478 |   0.703138676733575    |      Joe Biden      |\n",
            "| 38376 |   0.7429819023278823   |    Samantha Power   |\n",
            "| 23737 |   0.8101646334648858   |  John D. McCormick  |\n",
            "|  4032 |   0.8145547486714284   | Kenneth D. Thompson |\n",
            "| 14754 |   0.826854025896727    |     Mitt Romney     |\n",
            "| 43155 |   0.8408390074837325   |     Goodwin Liu     |\n",
            "| 20159 |   0.844036884280093    |    Charlie Crist    |\n",
            "| 11517 |   0.8483420107162964   |     Louis Susman    |\n",
            "| 40184 |   0.8601570123329991   |     Chuck Hagel     |\n",
            "+-------+------------------------+---------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 5\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "| 23737 |   0.8101646334648858   |    John D. McCormick    |\n",
            "|  4032 |   0.8145547486714284   |   Kenneth D. Thompson   |\n",
            "| 14754 |   0.826854025896727    |       Mitt Romney       |\n",
            "| 24848 |   0.8394067356676752   |     John C. Eastman     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 6\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "| 23737 |   0.8101646334648858   |    John D. McCormick    |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 7\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 8\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 9\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 10\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 11\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 12\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 13\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 14\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 15\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "Radius: 16\n",
            "+-------+------------------------+-------------------------+\n",
            "|   id  |        distance        |           name          |\n",
            "+-------+------------------------+-------------------------+\n",
            "| 35817 | 1.1102230246251565e-16 |       Barack Obama      |\n",
            "| 24478 |   0.703138676733575    |        Joe Biden        |\n",
            "| 38376 |   0.7429819023278823   |      Samantha Power     |\n",
            "| 57108 |   0.7583583978869675   |  Hillary Rodham Clinton |\n",
            "| 38714 |   0.7705612276009974   | Eric Stern (politician) |\n",
            "| 46140 |    0.78467750475065    |       Robert Gibbs      |\n",
            "|  6796 |   0.7880390729434776   |       Eric Holder       |\n",
            "| 44681 |   0.790926415366316    |  Jesse Lee (politician) |\n",
            "| 18827 |   0.7983226028934733   |       Henry Waxman      |\n",
            "|  2412 |   0.799466360041952    |     Joe the Plumber     |\n",
            "+-------+------------------------+-------------------------+\n",
            "[10 rows x 3 columns]\n",
            "\n",
            "CPU times: user 10.4 s, sys: 256 ms, total: 10.7 s\n",
            "Wall time: 10.5 s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nOT2wcYbg-K6"
      },
      "source": [
        "Notice that the top 10 query results become more relevant as the search radius grows. Let's plot the three variables:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 926
        },
        "id": "1Zc0Ja1yg-K6",
        "outputId": "70fdcc03-c41f-44e3-ae17-61038c8428c6"
      },
      "source": [
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(num_candidates_history, linewidth=4)\n",
        "plt.xlabel('Search radius')\n",
        "plt.ylabel('# of documents searched')\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()\n",
        "\n",
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(query_time_history, linewidth=4)\n",
        "plt.xlabel('Search radius')\n",
        "plt.ylabel('Query time (seconds)')\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()\n",
        "\n",
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(average_distance_from_query_history, linewidth=4, label='Average of 10 neighbors')\n",
        "plt.plot(max_distance_from_query_history, linewidth=4, label='Farthest of 10 neighbors')\n",
        "plt.plot(min_distance_from_query_history, linewidth=4, label='Closest of 10 neighbors')\n",
        "plt.xlabel('Search radius')\n",
        "plt.ylabel('Cosine distance of neighbors')\n",
        "plt.legend(loc='best', prop={'size':15})\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jR45w8+ZNdu/eTfXq1XX5Dx9mbB05OTlhbGysmCUB2a4dHBwwMTHh0KFDeo2onJ317+SVLVuW+Ph4NBqNQiFHRkZiZWWFubm53nqFoXr16qSkpHD58mWqVaumyz9//rxiHAqKg4MDvr6+imX8dHJ6P+l7uHmNc36Ij4/PZjV/79493X57+t979+7h6OioKxMZGal7H+noc2VpZ2fHwoULWbhwIadOnWLWrFn07NkTHx8fvL29Cyy3PgyaGUspvfJIqlPkLJSxVD7tBfmW4rUqygPqK49cZ8Nf2ZddioQqgRC0FDLN0ElOgJ+6wt0zxdOnikoajx8/Ztu2bXTv3p3Q0FBFmjdvHpGRkfz++++AdjnSzs6OdevWsXbtWt566y3FXmfLli0JDw+nZs2a+Pr6KlJmRaOPhIQEQKkgDh8+rLDcNTExoV69emzZskVRd+vWrYrrgIAAUlJSePjwYTY5fH19c5xtNmzYECEEGzZs0OVJKdmwYQN+fn65yl9QmjRpgq2trWL5X6PRsG3bNtq1a1fo9lu2bMnly5epUKFCtnGoXbu23jrly5fH1dU1z3HOLz///LPudXx8PLt37+aVV14BoFatWlhZWSnGAbQGalWrVs1xVq4PHx8fZs+eTWpqKufPny+UzPpQQygWEy5WLpyLPqe7jkq8x8LgFnRYdJCbMQm6/E9/Pk01l1LUdi+tr5nCUfstSIiB7SMz8hLTA0vsAgf1ML5K8bBlyxY0Gg0ffvghjRopV2KaNm3KZ599xurVq2nVqhWmpqZ07tyZefPmcefOHZ2RUDojRoxg1apVBAQEMGzYMNzc3IiMjGT//v34+fkpjHCy0rhxY2xsbBg4cCCjR4/WGe64ubkpyo0dO5YuXbowdOhQOnbsyKFDh/j1V60Fe/osuFq1arz33nsEBwczevRofH19SUxMJDw8nIsXL/LNN9/olaFGjRp0796doUOH8ujRIypVqsSyZcs4f/683pllXmg0GrZv3w7ArVu3iIuL0yn6119/HSsrKywsLPjkk0+YOnUq9vb2OqcfqampDBs2LN99ZqV3794sWbIEf39/Ro4cScWKFXnw4AFhYWG4uroyfPjwbHWMjY0ZNWoUo0aNokyZMjRt2pStW7dy+vRpwLAjW1mxtLRk3LhxxMfHU65cOebMmcPTp0/58MMPAe3M96OPPmLatGmYmJjg6+vLpk2b2L59u27lJjf8/PwICgqiVq1aCCFYtmwZ1tbWOmVfpEgpDUqAFTAUrYOPvWl/3wcsDW3jRUkNGjSQhWXK4Smy1opaurQyfKWUUsrTN2Nl1XHbpceYX3Spyed7ZdSjxEL3mSP7ZkoZYqtMC3ykjLtbfH2qFIqzZ8+WtAiF4o033pBVqlTJ8f7gwYNl6dKlZWKi9nO/e/duCchy5crJlJSUbOVv3bol+/btK52dnaWZmZn08PCQPXv2lGfOnJFSSnn16lUJyG3btmWru2PHDlmzZk1pYWEha9euLX/99VfZvHlz2aVLF0W5hQsXSjc3N2lpaSnbtWsn161bJwF54sQJXZnU1FQ5f/586e3tLc3MzKSTk5Ns1qyZ/P7773Mdj8ePH8uhQ4fq5G/QoIHcuXOnokxISIh0dHTMtZ3M71Vfunr1qkLWadOmSTc3N2lhYSH9/Pzk33//nWf7Hh4e8uOPP1bkLV++XALy0aNHurzY2Fj5wQcfSHd3d2lqaird3NxkUFCQPHjwoK4MIL/44guFTOPGjZNOTk7SxsZG9ujRQy5evFgCMiYmRvH+sv4v+/TpIzP/NqeP14EDB2SdOnWkmZmZ9PHxkfv371fUS05OlhMnTtTJWaNGDblq1apc205n5MiRslatWtLGxkaWLl1a+vv7ywMHDuQ6fnl9d4HjUo/eEdIApxBCCFdgH1AVuA7cBVwBD+AC4C+ljCyKh4PnAV9fX5mTRaChLP1nKYtOZhx271uzLx/7fgzAzyduMnztP4ryTSo5srLfK5gYF4PHLClh5ydwdIky36UW9P1Ve05Z5bni3Llz1KhRo6TF+E8zbdo0PvvsM6Kjo18oT14vGgMGDGD37t1cv369pEUpEvL67goh/pJS+mbNN3SZehbagBCvSSkPZWq0CbARbXjFvvkR+GUn61njSE3Gs0pQPXf+iXjIisPXdHmH/33ArF0X+PT1YvgBFgLafA6aaDi9LpNQZ2B1MPTaBGZWOddXUXnJuX//Pp9//jktWrTAysqKP/74g5kzZ9K/f39VERchZ86cYe3atTRp0gQjIyN27NjB8uXLmTlzZkmLVuIYqozbAWMyK2IAKeVhIcR4tP6qVTKR9azxPc09xfW49jU4ezuOsGsZpvVfH7iCj3tp3vApV/QCGRlBp8XaPeNLuzLybxyB9X0h+Ec1sITKfxYzMzPOnz/PypUrefjwIWXLluXDDz9k6lQ1THtRYm1tzcGDB1m0aBGPHz/Gw8ODmTNn8vHHH5e0aCWOoWuiNsDtHO7dTLtvEEKI8kKIDUKIh0KIOCHEJiGEQfGQhRBeaXVjhRCPhRChQohs030hxDUhhNSTOhkqZ2EpY6W00ruvUZrvmxobsahnPVxslccARm84xYW7jygW0gNLlM/i4efSLtj8Pujx+6qi8l+gdOnSbN++naioKJKSkrhx4wYzZszQOR5RKRq8vLwIDQ0lJiaGp0+fcunSJUaOHKn3WNF/DUOV8QXgnRzu9QIMsvMWQlgBvwPVgT5pbVYBQoUQ1nnUdQQOArWAQUC6V4BQIYS+td1dwKtZ0n5D5CwKsi5T39PcI+v+vHMpC77q1QBT44wPouZpCoN+OM7DhJxDoxUKMyvosVa7X5yZ0+u0+8pqYAkVFRWVZ46hyngO0D3N+1Y/IUQ7IcT/hBC7gB5Adkek+hkIVAQ6SSk3Sym3AB3RGoINyqPuYMAFaC+lXCul3IY2mpQGmKynfJSU8s8sKcZAOQuNrZktFsYWuuvElETinsZlK1e/gj2TOyoV47UHGj5ac4LU1GJSjJZ22n1i+yxHm8KWwgFD/5UqKioqKkWFoU4/VgHvoZ2VfgP8CnwL+ADvSSl/yqV6ZjoCf0opL2dq+ypwCHgzj7qNgUtSyn8z1X0M/AG8IYR4rs5MCyH0zo710aNRBYIbllfkhV64z4K9l4pNPkq5aP1Y22RxARf6GYQtK75+VVRUVFSyYfA5Ginl10A5oCbwWtpfNyllfn65awL63D+FA3n5FksBnurJfwJYkt1FZwchhEYI8UQI8eez3C9Ox1BlDDD5zZrUKa88YrRw7yV2ny3GE2MOXtoZctbAEttHwekN+uuoqKioqBQ5+TrUKqVMlVKek1IeSvubX4sfB0DfUnE02qNTuXEBqJK2dwyAEMIISHeFkjkm4TZgGNAG6AkkAj8LIXKMfSWEeFcIcVwIcbwwvlIzk9WIKzdlbG5izJJe9XGyUbrUG7H2JP/ejy8SefTiWgt6rAOTzMc3JPw8CK49nxFlVFRUVF42DFbGQogqQojvhRAX0yyZLwohVgghKhengJlYglbelUKISkKIssBCIH3jU/dgIKUcJqVcKaX8Q0q5AWgJHAc+z6lxKeXXUkpfKaVvfvyV5kZex5uyUra0JYt61MfYKMOg69GTZAb98BfxT5JzqVlIKjSGbj+AUaaV/tRk2PYhJOtbjFBRUVFRKUoMUsZCCH/gH7QGU38Ci9P+dgBOCyGaG9hfDPpnwDnNmHVIKa+gneU2AC6jPWr1KjA/rYj++GXauilo3Xe6pynxZ0J+lqnTaVzRkXFZHH9cvhfPqPX/ZLPGLlKqtMoeWOLB5exeu1RUDGTSpEkIIbKlwMDAQrc9a9Ys9u3bly1fCMGiRYuyVyhiLl68yKRJk4iNjS2yNrds2UKNGjUwMzPD09Mzx3JTp04lMDAQW1tbhBCKoBeZOXToEI0aNcLCwgIvLy8WLlxYZLIaQt++ffH1zXbyNE/8/f156623ci1z7do1hBD88ssvBRXvucPQmfFc4ATgIaXsLaUcJaXsDXgCJ9PuG0I42n3jrHgDZ/OqLKXcCLilla8spWyA9oxzhJTyhoEyPLOzOwVRxgD/a+pJp7pKxx87ztxlyf4rRSabXmq/BQ36KPP2z4RHd4u3X5WXltKlS3PkyBFF+uKLLwrdbk7K+Flx8eJFJk+eXGTKOCUlhd69e1OnTh1+//13RSSirCxdupTk5GRatGiRY5nLly/Tpk0bvLy82L59O4MGDWLEiBE5BrMoDiZMmMCKFSueWX8vOoZaIHsD3aSUis1LKeUjIcRMIO/wF1q2AnOEEBXTZroIITyBpsAnhjSQNss9l1a3HNCNPI5WpVladwNuSCmfmWbJukyd2SVmbggh+LyzDxci4zl3J+M41Oxd56nlZstrVYpmGV0vARMg/Getpy6Ap/GwZzIE5T+6jIqKiYkJjRs3zruggWSNXfuycOfOHeLi4ujRo0eeYRVv3LiBkZERv/zyS47hB2fPnk25cuVYtWoVJiYmBAQEcOPGDSZPnkz//v2fiZONSpWy2tS+OJTE58zQmfFNQH+wTm3+LQPbWQZcA7YIId4UQnQEtgARwNL0QkIIDyFEshBiYqY8UyHEfCFEJyFEgBBiGNp94HAyzcyFEN2FEGuEEL2FEC2EEMFAKFAfGGOgnEVCQWfGAJZmxizt1YDSlhkegFIlDFt9gohoTZHJmA1rJ2gxTpn3z08QEVZ8far857hz5w79+vWjYsWKWFpaUrVqVcaPH8/Tpxk2CulLkT/++CO9e/fGzs6ODh064OnpyYMHD5g8ebJu6TvzLDklJYVPP/2UMmXK4OzszJAhQ3jy5Imi/xs3bhAcHIyDgwNWVla0adOGCxcuKMp8/vnnVK5cGQsLC1xcXGjbti13795l3759dOjQAdB6lBJC5LqsDNr4ubVr18bc3Jzy5cszbtw4kpO1diArVqygfHnt0cY333wTIQSTJk3KsS1DQg3u2LGDzp07Y2KSMd8KDg7m5s2bnDmTczzzSZMm4eTkxIkTJ2jcuDFWVlbUq1ePP/74I1vZb775hpo1a2Jubo6HhwezZs1S3Ne3TL1v3z58fHywsLCgYcOGhIWF4eTkpPf9/vTTT1SuXBlbW1vatWvHzZvZY7/HxcXxzjvvUKpUKZydnZk8ObvLid9//123XO/i4sL7779PfHzGvHLfvn0IIdi1axcdO3bExsaGoUOHAvDtt9/i7e2NpaUlTk5ONG/enPDw8BzHrzAYOjOeCUwWQhyWUurcYgoh3IAQYLohjUgpHwshAtDu8/6AdoNyL/BRllm3AIxRPixItN66egB2aB8QvgOmSykzWxldBZzRzpYdgMdolXZbKWUmp8zFTxlL5Qw2OjGapNQkTI0Mc7FXwdGKhd3r0Xd5mM4xVqwmiUE//MXGwU2wNDPOvYGC4tsf/loB9zLtHGwfBQNDtT6uVZ49k4oh3nVBmPQw31XSlU46xsbGREVF4eDgwLx587C3t9ftwd6/f5+lS5cqyo8cOZLOnTuzfv16jI2Nsbe3p0WLFrz11lsMGDAAAG/vjJORc+fOJSAggFWrVnHq1CnGjh2Lh4cHo0ePBiA6Oho/Pz8cHR1ZsmQJVlZWzJgxg8DAQC5evIilpSUrV65k+vTpzJw5k5o1a/LgwQN+//13Hj9+TP369ZkzZw4jR45k06ZNlC1bFnNzpVvbzPz2229069aN3r17M3v2bE6dOsWECRN48OABS5YsoX379mzatInOnTszZ84cmjZtiru7e77HOZ3Hjx8TERFB9erVFfnpkYTOnz9P7dq1c6yv0Wjo06cPw4cPx9XVlcmTJ9O5c2euX7+OlZU2oMzs2bP59NNPGT16NP7+/vz1119MmDABKysrnSLLyq1bt3j99ddp0qQJ06dP5+7du/Ts2ZOEhIRsZY8ePcrt27eZO3cuCQkJfPjhh7z77ru6OM7pjBo1ijfeeIMNGzZw4MABJk+ejJOTE0OGDAEgPDyctm3b0qpVKzZu3EhERASffPIJV65cYefOnYq2+vfvz//+9z8++ugjLCwsOHDgAO+99x5Tpkzh1VdfJS4ujiNHjvDwYf6/A4aQozIWQqzMkmULXBFC/AlEovWG1TjtdXO0ijFP0vZ2u+RR5jfMF5oAACAASURBVBoKSyKQUiajNSDLq/0/gQBDZCluTI1NcbBwIDpRGwxCInmQ8ABXa1eD22hetQwjW1dj9q6Mp/azd+L49OfTzHu7TvEsNxmbQLuZ8H2HjLw7J+HkKqjfu+j7U3lpefDgQTb/zrt37yYwMJA5c+bo8po2bYq1tTX9+vXjiy++wMwsYyGucePGfPnll4o2TExMcHd317sE7unpqdurbNOmDYcOHWLTpk06ZTx//nweP37MyZMncXBw0PXv6enJd999x5AhQwgLC6N169a8//77unY7d+6se12tWjUA6tWrl+eseOLEifj7+/P9998D0LZtWwDGjh3L+PHjcXd3p169erp2C7usn76PbWen9Ftgb6+1nY2Jyd0RYUJCAgsWLCAgQPszWrZsWerVq8eBAwdo27YtcXFxTJ48mfHjxxMSEgJAq1at0Gg0TJs2jcGDB2NsnH2isGDBAqysrNi2bZtuCdjW1pZu3bplKxsXF8evv/6qk/nu3bsMHz482/JxzZo1dQ9vbdq04d69e0yfPp3BgwdjZGTE1KlT8fDwYOvWrTqZHBwc6NatG0eOHOHVV1/VtdW1a1dFYJA5c+bg4+PD2LFjdXkdO3bMdewKQ27TnGZonXukp2S0FsseaM/2eqRdp6bdV9FDbqEUDeV9/0q0ralU4D+fuKUIwVjkeDUD7yx+UvZMhoSisx5VefkpXbo0x44dU6RGjRohpWTBggW6JUBTU1N69uzJkydPuHFDaYvZvn37fPXZunVrxbW3t7diiXPPnj20atUKW1tbkpOTSU5OplSpUjRo0ID0OOZ169Zl+/bthISEEBYWRkpKSoHef0pKCn///Tddu3ZV5Hfr1o3U1FSOHDlSoHaLEzMzM/z9/XXX6asO6WN45MgRHj9+TNeuXXXjl5ycTEBAAJGRkXqXkwGOHTtGq1atFMo0J+XWsGFDnSLOLMOtW8od0aCgIMV1586duX37tk6GsLAwgoKCFA8HXbp0wcTEhIMHlX4Usn7O6taty4kTJxg+fDgHDhxQbKEUBzkqYymlp5TSy8BUsVilfIEpzL5xOkII5rxdh8rOyuBY0349R+j5/LdnMK2nKp2BaKK01tUqKgZiYmKCr6+vIpUqVYoFCxYwcuRIgoKC2LJlC2FhYbrZb2JioqINFxcXfU3nSNYZoZmZmaLNqKgo1q5di6mpqSKFhoYSEREBQL9+/Zg+fTrr1q2jUaNGuLi4MH78+Hwr5fQoUFnfQ/p1dHS0vmqFIv39Z11OTZ8RZ1Zy+ihVqpRiXzp9lSJ9DKOiogDtrDTz+KVbd6ePYVbu3r1LVh8OFhYW2NhkD/qn73+YWYZ0nJ2d9V7fuXNH9zfr2BsbG+Po6Jht7LOWCwwMZPny5Rw4cAB/f3/d8vfjx4/1vr/C8lz5c34ZKQplDGBjbsLSdxrQadEhHqU5AElJlQxa9Rff9WmIXxWnQsuaDbsK4Dcc9mUyCTi6VLtU7awvUJZKsVGAvdrnmfXr1/PWW2/x2Wef6fLOntV/urGot2IcHBzo2LEjEyZMyHavVKlSgNZIavjw4QwfPpyIiAh+/PFHxo0bh7u7O++9957BfTk5OWFqasq9e8rvfWRkpE6Wosba2pry5ctz/rwymF76dda95PySLvMvv/yi90EpfQk/K66urmT1bpiYmKgwpsovWcc1/bps2bK6v1nLpKSk8ODBg2xjr+9z1qdPH/r06cP9+/fZtGkTw4cPp1SpUsyYMaPAMudEvqxxhBCuQohXhBDNsqYil+wlwdmy8MvU6VQqY8O8bnUVeU+TUxmw8hhHrzwocLu50vQDrVJOR6bAjjFqqEWVQpGQkJDN6OnHH380uH7W2W5+aNmyJeHh4dSsWTPbrF2fIilfvjyffPIJlStX1j0w5DRTy4qxsTENGjRg/fr1ivx169ZhZGSk2LMsStq1a8fPP/+smMmvXbuW8uXLU6tWrVxq5s2rr76KpaUlt2/fzjZ+6Ssf+mjYsCG7d+9WGGzldDTLULKex043qEs3gGvUqFG2cdi0aRPJycl5HiHLTJkyZRg0aBCvvfZajg+NhcWgmXGa1fQPaA21st1Ga+lcTKa9LzZZZ8b3NYXze93K24VpnWoxfnPG8YTEpFT6rTjGyv6NaOCRl4vvfGJqCW2mw9pMbr2v7odz28C7+IwZVF5uWrVqxcKFC2nUqBGVKlXixx9/5PLly3lXTKN69er8+uuvtG3bFhsbG6pVq5ajEsjKiBEjWLVqFQEBAQwbNgw3NzciIyPZv38/fn5+dO/enUGDBuHg4EDjxo0pXbo0oaGhXLp0iZkztds06Up76dKlBAcHY2VllaOF8uTJk2nTpg3/+9//CA4O5vTp00yYMIGBAwcWyGp6//793L9/n7/++gvQHmMqU6YM3t7eur3VUaNG8eOPP/LOO+8wcOBAjh07xtKlS/nqq68KvdJgZ2fHpEmT+PDDD7l+/TrNmjUjNTWVixcvEhoamqPDko8++ogvv/ySDh06MHz4cO7evcuMGTOwsrIy6LiWPsLDwxk0aBBdunThwIEDfPvtt/zf//2frr3x48dTr149OnXqxODBg7l58yZjxoyhTZs2eT4IhYSEEB0drVuiPnHiBPv37y+WWTEAUso8E1pnHfeBj4HWaJWyIhnSzouSGjRoIIuKAxEHZK0VtXSp385+RdLuN39ckR5jflGkWhN3yn8iYoqkfQWpqVJ+31HKENuMNK+WlE81Rd+XipRSyrNnz5a0CIUmJCREOjo66r336NEj2bdvX2lvby/t7e1l//795bZt2yQgT58+LaWU8urVqxKQ27Zty1b/+PHjslGjRtLKykoCMjQ0VEopJSC/+OKLPOW4deuW7Nu3r3R2dpZmZmbSw8ND9uzZU545c0ZKKeXy5ctlkyZNpL29vbS0tJS1a9eW33zzjaKNOXPmyAoVKkhjY2Pp4eGR61isWbNG1qpVS5qamko3Nzf56aefyqSkJN393N5rVpo3by7RToAUKSQkRFHujz/+kA0bNpTm5ubSw8ND/t///V+ebef0P9M3rj/88IOsX7++tLCwkHZ2dvKVV16Rc+fO1d3v06ePzPpb+vvvv8vatWtLMzMzWadOHXngwAFpbm4u58+fr3h/Xbp0UdQLDQ3V+9lYtWqVDA4OljY2NtLJyUlOnDhRpqamKuru2bNHvvLKK9Lc3FyWKVNGDh48WD569CjHttPZtm2bDAgIkE5OTtLc3FxWrVpVfv7559naz0pe313guNSjd4Q0YLlRCBEDfCCl/KHIngKeY3x9fWW6VWVhuRB9gbe2ZfhZ9bT1ZFvQtiJp+6t9/zJzp3JfqLSlKasHNsa7nG2R9KHj3nn4qol2mTod/7Hgb5DjNJV8cu7cOd25UBWVl5WDBw/y2muv8fvvv+fq3vNFIq/vrhDiLyllNqfdhq4NJADFaLb78qLPJaYhD0CGMNi/Eh8FVlHkPUxI4p1vj3Ip8lGR9KHDuTo0GqTMOzgfYg11Ca6iovJfZ8yYMaxZs4Z9+/bplvh9fHxo3tzQWEMvL4Yq42XAO8UpyMtKafPSmBllODBISE4gPqno4hN/2LIKg/2VPmAfPH5Kj2+OcjWqiE3w/T8B60xHE5IT4bfxRduHiorKS8uTJ08YNWoUrVu35tNPP+W1115j586dBd4zfpnIzQNXv0yXN4F3hBB7gR1AtsNxUkqDPHD91xBCUMaqDLfiMw6r39fcp5SZYcYmhrQ/uk01nian8u3Bqxl9PHpCj2V/sm7Qq5R3sCqSvrAoDS1DYGsmd3dnt8CV/VBRfbJVUVHJnQULFrBgwYKSFuO5JDdran2xtjwBfQv7EgPdYf4XcbFyUSjjSE0kFe2Kzk+KEILx7WvwJDmFVX9mLBvfeZhI9zSFXM6uiCKQ1O0Jx7+F2ycy8naMgff+AGPDfG6rqKioqCjJbW3AKx9J9cCVC0Xl+CM3hBBM6ViLt32VRyVuxiTQY9mf3Isr2JnMbBgZwetzlHn3z8Gxb4umfRUVFZX/ILm5w7yen/QshX7ReBbKGMDISBsHuVPdcor8aw809PjmKFHxT3KomU/cfbUz5MyETofHUUXTvoqKisp/DHXX/BlQFMEiDMXYSDCnax1er60MLHH5Xjy9vjlKzOMicnbeMgQy73s/eQh7pxRN2yoqKir/MQxSxkKIq0KIKzmky0KIv4QQXwshCudn7SUl6/Gm4poZp2NibMT/BdcjsIay3/N3H/HOd0d5mJBU+E5KuYD/GGXe3yuVe8kqKioqKgZh6Mx4P1p3l2WBq8CfaX/LoTUCuw50AI4JIZoUg5wvNGWslJFKCusS0xBMjY34smc9mldV9n3mVhx9vgsj/klyDjXzwSuDwDHzOWcJ20dDamrh21ZRUVH5D2GoMv4DeAh4SSlbSil7SClbojXeikN73Kky8A8wuVgkfYF5VnvGWTE3MWbpOw14taKjIv9kRCz9lh9D87SQCtnEDNpl8dN6MwxOrytcuyoqKir/MQxVxmOAKVLKu5kzpZR3gGnAGCnlY+D/gFeKVsQXn6zKOCoxiuTUIpiZGoCFqTHf9vWloacygETYtWgGfH+cxKSCBU3XUTkQqmUJ/r57IjwpYg9gKi8sGzduJCAgADs7O8zNzalatSojRozg9u3bAFy7dg0hBL/88ksJS5qddevWsWLFiiJrLzU1lSFDhuDi4oIQgkmTJuktd/nyZQYNGoSPjw/Gxsb4+/vrLSelZPr06ZQvXx5LS0uaNWvGyZMni0xeQxBCsGjRonzVMfR/PmnSJJyciiE87HOIocq4PJCTKW4i4Jb2+hZglkO5/yzmxubYmWcEy06VqTxIKKaQh3qwMjPhu74NqVNeGbD78L8PeG/VXzxJLqRCbvMZGGcKhxcfCQdmF65NlZeCjz/+mLfffpuKFSvyww8/8NtvvzF8+HD27t3LkCFDSlq8PClqZbxp0yYWL17M559/zpEjRxgwYIDecuHh4Wzfvp1q1apRtWrVHNubMWMGU6dOZcyYMWzbtg0bGxsCAwO5e/dujnWKmiNHjtC1a9dn1t/LiqHK+BzwsRBCEYBUCGEBjEy7D9o95OIzFX6BKaml6nRKWZiy8n+vUDNLAIl9F+4z9KcTJKUUYp/XwQuaDFPmHVkMUZcK3qbKC8+2bduYN28ey5Yt45tvvqFDhw40b96cwYMH8/fff/Puu++WtIjPnPPnz2Nvb0+/fv1o3LhxjiEUO3ToQEREBOvXr6dmzZp6yyQmJjJjxgzGjh3L0KFDCQwMZP369QWaqRaGxo0b4+LiknfB54yUlBSePi2i0yVFgKHKeDTQGLghhFguhJgphFiO1nCrETAqrVwT4LeiF/PFJ6sR172EZx93o7SVKT/0b0Q1F6Urzt1nI/lozUmSC6OQXxsBtm4Z16lJsPMTKKKgGCovHvPnz6d+/fr069cv2z1jY2PatWuXY92UlBQmTZpEhQoVMDc3p2bNmvz000+KMuHh4bRt2xYHBwesra2pUaMGX375paLMli1b8PX1xcLCAldXV0aPHk1SUsZpgps3b/L222/j7OyMpaUllSpVYsKECQD07duXjRs3sn//foQQuS4rA2g0Gj744ANcXV2xsLCgYcOG/PZbxs+hv78/EyZMICYmRtfetWvX9LZliK/mw4cPExcXx9tvv63Ls7a2pkOHDuzYsSPXup6enowcOZL58+fj7u6Ovb09wcHBxMbGKspFR0fz7rvv4uLigoWFBU2aNOHo0aOKMlmVv5SSCRMm4OzsjK2tLf369WPNmjV6369Go2HQoEGULl0ad3d3QkJCSNVjAHro0CHq16+PhYUFdevW5eDBg4r7hnxe+vbti6+vL5s3b6ZmzZpYWFhw9OhRYmNjGTBgAOXKlcPCwoIKFSowcODAXMevOMjNHaYOKeUeIUR9YDzQDK1V9R1gDzBNSnkurdwHxSXoi86zPt6UEw7WZqwa0IhuXx/hyv2MQBK/nr6DmYkRc7rWwdioAMHHzayh9VTYkOmH9/IeuLgLqrUtAsn/29T+Xn/g+mfN6T6nDSqXlJTE4cOH+fjjjwvUz8SJE5k1axYhISE0bNiQjRs30rNnT4QQdO/eHdDOHmvUqMGqVaswNzfnwoULxMXF6dpYt24d3bt3Z9CgQUyfPp1///2XsWPHkpqaypw5Wi9yvXv3JiEhga+//ho7OzuuXLnC+fPasKQTJkzgxo0bxMbGsnjxYoAcZ7IAAwcOZOvWrUyfPp3KlSuzbNky2rdvT2hoKH5+fixevJh58+axYcMGdu7cCUDZsmULND6gnWUbGxtTpYoycluNGjVYu3ZtnvXXrVuHj48PX3/9NTdv3mTEiBF8+umnuvf65MkTAgMDiY2NZfbs2Tg7O/PVV18RGBjIpUuXcHV11dvuggULmD59OuPGjcPPz48tW7YwevRovWVHjx5Nly5d2LBhA3v37mXKlCnUrFlT8YCh0Wjo1asXY8eOpWzZssydO5d27dopZDDk8wLaverRo0czceJEXF1d8fLyYsSIERw+fJj58+fj6upKREQEBw4cyHP8ihqDlDGAlPIs0KMYZXmpKell6syUKWXOTwMa0+3rI1x/oNHl/3ziFuYmRkwPqo1RQRRyzc5at5jXD2Xk7fwEKrUAE/Oc66m8dDx48IAnT55QoUKFfNeNjo5mwYIFjB8/nvHjtVHB2rRpw82bN5k0aRLdu3cnKiqKq1evsmXLFmrX1j6otGzZUteGlJJRo0bRu3dvnXIBMDc3Z8iQIYwdOxZHR0fCwsJYvXo1HTp0AFAYSlWqVAkHBwdSU1Np3LhxrjKfO3eO1atXs3z5cvr06aOT2cfHh6lTp7Jr1y68vb1xd3fHxMQkz/YMISYmBhsbG4yNjRX59vb2aDQanj59iplZziY8pqambN68GRMTrRo4e/Ysa9as0Y3XqlWrOHPmDOHh4TqFHxgYSLVq1Zg7dy6zZ2e3C0lJSWHWrFm89957TJmidQLUunVrrl69SkRERLbyzZo1Y+7cuQC0atWKnTt3smnTJoUyTkhI4LPPPqNHD636adGiBRUqVGDBggXMmDHDoM9LOg8ePGDPnj3UrVtXlxcWFsaQIUPo1q2bLq9Xr145jltxoXrgekY8T8oYwLW0BT8NbIxblgASa45FMGlbeMFiLgsB7WaCyPSxirkKR77MuY7KS40Q+X+oO3PmDBqNJptRULdu3bh48SL379/HwcGB8uXL895777F27Vru3VN+ny5evMiNGzd4++23SU5O1qWAgAASExM5c+YMAHXr1mXs2LGsWLGCGzcKHpv72LFjSCkVMhsZGdG1a9dsS6rPCy1atNApYgBvb2/u3bunW8bfs2cPDRo0wMvLSzd+AM2bN+f48eN624yIiODu3bt07NhRkZ/1Op3WrVsrrr29vbl582a2ckFBQbrXNjY2tGrVirCwMMCwz0s6bm5uCkUM2s/A7NmzWbx4MRcvXtQr57MgR2UshPhOCOGV6XVuSY0SkAdZl6mL0yWmobjZWfLTwEa42loo8lceuc5nv54rmEJ2rQ2+WfYID8yBuNuFkFTlRcPR0RFzc/MCKbg7d+4AZDMKSr+Ojo7GyMiI3377DVdXV/r164erqyuvvfYaJ05oPcBFRWn9pL/++uuYmprqkpeXF4BulrZ27Vp8fX0ZPnw4Hh4e1K1bl7179xZIZhsbG6yslOFKXVxc0Gg0PHlSRH7hM2Fvb098fDwpKcrTEDExMVhZWeU6Kwaws1OerjAzM0NKqZM1KiqKP//8UzF+pqamLF++XO8sF9BZcZcpo7SRyXqdmwyJicqgNjY2NlhaKicNzs7Ous+JIZ+XrHmZWbRoEZ06dWLKlClUq1aNKlWqsGbNGr3yFie5LVO3QHtuGCAAbZjEnFCtdPLgeZsZp+PhaM2PAxvRbemfikAS3xy8SlXXUrztWz7/jbYYB2c2QkKM9jrpsfbscRd9UTlVDMHQvdrnBVNTU5o2bcquXbuYNm1avuqm76Peu3cPR8cMhzWRkdoHWAcHBwCqV6/Oxo0bSUpK4o8//mDMmDG0b9+emzdv6sp8/fXX1KtXL1sf6UrZzc2NFStWkJqaSlhYGJMmTaJjx47cuHFD0bchMsfHx6PRaBQKOTIyEisrK8zNi36bpnr16qSkpHD58mWqVaumyz9//jzVq1cvdPsODg74+vry1VdfZbuX0/tJ38PNPBvVd50f4uPjSUhIUCjke/fu6T4nhn5eQP9KjZ2dHQsXLmThwoWcOnWKWbNm0bNnT3x8fPD29i6w3Pklt6hNXlLKf9Jee6Zd55TUEIp5UMby2bvENJRKZWz4aWAjHKyVT9LLDlwp2OzYygECJijzTq+H60cKIaXKi8ZHH33E8ePH+f7777PdS01N1RkxZaVWrVpYWVmxfv16Rf66deuoWrVqtlmWqakpAQEBjBgxgjt37hAbG0u1atVwc3Pj2rVr+Pr6ZktZFa2RkRGNGzcmJCQEjUbD9evaQHT6Zmr6aNiwIUIINmzYoMuTUrJhwwb8/PzyrF8QmjRpgq2trWKcNBoN27Zty9VS3VBatmzJ5cuXqVChQrbxS9+nz0r58uVxdXVly5YtivytW7cWSpaff/5Z9zo+Pp7du3fzyita/1L5/bzkho+PD7NnzyY1NVVnyPesMNiAS6Vw2FvYY2JkovO8FZ8UjyZJg5WpVR41nw1VXUrxQ/9XeHPRIZJTtQr40r14wm/HUcutdP4bbNAXji+HyEwzuh2j4N39YGScYzWVl4cOHTowYsQI+vfvz6FDh3jzzTexsbHh/PnzLFmyBE9PT9q2zW5p7+DgwEcffcS0adMwMTHB19eXTZs2sX37dlavXg3AqVOnGDlyJN26daNixYrExMQwc+ZM6tSpo5sJzZ07l3feeYe4uDjatWuHmZkZV65cYfPmzWzYsIGkpCTatGlD7969qVq1Kk+ePGHu3Lm4urpSo0YNQDv73LJlC5s3b8bd3Z1y5cpRrly5bDLXqFGD7t27M3ToUB49ekSlSpVYtmwZ58+f1zuzzAuNRsP27dsBuHXrFnFxcTpF//rrr2NlZYWFhQWffPIJU6dOxd7enurVqzNv3jxSU1MZNmxYbs0bRO/evVmyZAn+/v6MHDmSihUr8uDBA8LCwnB1dWX48OHZ6hgbGzNq1ChGjRpFmTJlaNq0KVu3buX0ae3vgCFHtrJiaWnJuHHjiI+Pp1y5csyZM4enT5/y4YcfAoZ9XnLDz8+PoKAgatWqhRCCZcuWYW1trVP2zwwppUEJsAY+ADYAoUCVtPxgoHo+2imf1sZDtH6tNwEVDKzrlVY3FnicJoevnnJGwFjgGloPYf8AXQyVsUGDBrI4aL2+tay1opYuXYm9Uiz9FIZ+y8Okx5hfdGnS1jMFb+zaISlDbJUp7JuiE/Yl5uzZsyUtQpGxYcMG6e/vL21tbaWpqamsUqWK/Pjjj+WdO3eklFJevXpVAnLbtm26OsnJyXLixInS3d1dmpqayho1ashVq1bp7kdGRspevXpJLy8vaW5uLl1cXGRwcLC8fv26ou/t27dLPz8/aWVlJUuVKiXr1Kkjx40bJ5OSkmRiYqIcMGCArFq1qrS0tJSOjo6yffv28tSpU7r69+/fl506dZL29vYSkCEhITm+z8ePH8uhQ4dKZ2dnaWZmJhs0aCB37typKBMSEiIdHR3zHLP0MdGXrl69qiuXmpoqp02bJt3c3KSFhYX08/OTf//9d57te3h4yI8//liRt3z5cgnIR48e6fJiY2PlBx98oPs/uLm5yaCgIHnw4EFdGUB+8cUXCpnGjRsnnZycpI2NjezRo4dcvHixBGRMTIzi/WX+n0spZZ8+fWTm39/08Tpw4ICsU6eONDMzkz4+PnL//v2Kenl9XvS1nc7IkSNlrVq1pI2NjSxdurT09/eXBw4cyHMMcyKv7y5wXOrRO0IasAwphCgP7APcgfNALaChlPJvIcRSwFhKqd+vm7IdqzTF+ATtmWWJ1re1FeAjtf6tc6rrCJwCHgEhgAYYAfgCr8i0s85pZT9D6xlsHPAX2geGgcAbUsrtecnp6+src7IWLAzvbH+Hk/cz/MZ+0/obGpVtVOT9FIZfT91hyE9/666dbMw4MrYlpsYFNLzf0B/OZCzdYWkPw/7WLmWr5Mi5c+d0szMVlRedAQMGsHv3bt3y/8tMXt9dIcRfUkrfrPmGLlPPRatAq6L1P53Zh9h+tMrREAYCFYFqUsrLaYKdAi4Bg4B5udQdDLgAzaSU/6bV/R24gjZS1Ntpec5oFfEMKeWctLqhQojKwAwgT2VcXDyvRlyZaVnDmVIWJjxK1C6nR8U/5Y9L9wmoXkB3d62nwoUdWiMu0Bp1hU6H9nNyr6eiovJCcubMGdauXUuTJk0wMjJix44dLF++nJkzZ5a0aM81hk53WgEhUsrrZLecvkVGoIi86Aj8ma6IAaSUV4FDwJt51G0MXEpXxGl1H6MN7/iGECL9waIN2mAVq7LUXwXUTj+uVRJkVcbPw/GmrFiYGvOGj9Ir0Ka/bxW8Qdty0CyLF6bj38LdMwVvU0VF5bnF2tqagwcP0qNHDzp06MCvv/7KzJkzC+yN7b+CocrYDO3ysD5KA4bGA6wJ6PsVDgfysiFPQTkjT+cJYAlUytTHE+BylnLhaX+fna16FrIq4+fJojoznesrXf79djaShwlJOZQ2gMZDwD7TM5BMhW0fQsqzCSOpoqLy7PDy8iI0NJSYmBiePn3KpUuXGDlyZIEcwPyXMFQZnwK65HCvHdp9WUNwAGL05EcD9nryM3MBqJK2dwyAEMKIjPjJDpn+xsrsm+HRWcopEEK8K4Q4LoQ4XpgzcbnxIixTA/h62FPeIeNM39PkVHacvlPwBk0toO3nyrxbx9UwiyoqKippGKqMZwP9hRDL0AaKAPAWQkwG+qfdL26WoJV3pRCihcKVRgAAIABJREFUkhCiLLAQrYU1QCFCDoGU8msppa+U0jc/59Lyw4uijIUQBNVTzo43nSjEUjVA1bZQrb0y78AsuHFUf3mVgp3xVlFRKTEK8501SBlLKTcB7wNd0UZqAlgJfAQMlVLqP72fnRj0z4BzmjFnluEK0BNogHYJ+jbwKjA/rUj61C0GsBPZ10TSZ8TRlBDPo0vMnAiqpzQDCLsaTUS0JofSBiAEdFwI1pkeSGQqbBoIiXE51/uPYmpqSkJCQkmLoaKikg8SEhIwNTUtUF2Dz6tIKZegNdRqA/RCuzztLqX8Oh/9haPd082KN3DWABk2psngDVSWUjYAbIAIKWW6E9xwwJyMPeTMfWBIP8VF1pjGUQlRpKSm5FC6ZPFysqZ+BaXf2M2FnR1bO0Gnxcq82OuwY0zh2n0JcXZ25tatW2g0GnWGrKLynCOlRKPRcOvWLZydnfOuoId8eeBKs17ek2fBnNkKzBFCVEyb6SKE8ASaAp8YKEMKcC6tbjmgG8pl8p1AEtpZ9ORM+b2AM2nW2yWCpYklpcxK8eip1hYuRaYQ8yQGJ0unkhIpV4Lqu/P3jYxg45tO3GJoQOXCGWJUaQWvDIKwpRl5//wEVVtDzaCc6/3HsLW1BeD27du6KDoqKirPL6ampri4uOi+u/nFYGWcyViqAmCR9b6UcqUBzSwDhgJbhBDpTj+mAhGA7tdZCOEB/AtMkVJOScszBWahPdcch3aGPRbtTHhuJjnuCSHmAWOFEI+Av9Eq7AC0R6tKFBcrF50yBu1S9fOqjDv4lGXKtnCSUrQzs6tRjzkZEUu9CnnZ2uVBq8lw9QDcP5eRt+0jcH8FSht6Su7lx9bWtsBfbBUVlRcLg5aphRDeaD1vHQLWACuypOWGtJM2sw4ALgI/AD8CV4EAKWV85i4B4yzySaAKWqW9A+1+9XdAGyll1iNP49B69voQ2IV25v22lPIXQ+QsTrIZcT1+Po24AOyszAiorpS3UGeO0zG1hC7LwDhTYIrEWPh5EKQWyg5PRUVF5YXE0D3jxWhn0W8D1dFaMGdOBkdtklLekFJ2kVLaSilLSSk7SSmvZSlzTUoppJSTMuUlSynfkFK6SCnNpZSVpJTjpZTZrIqklClSymlS/n979x0eZZU9cPx70khCb1FAqgVFsbDIosIK2BvNXll17fW3us2CjV3rWlZ37btiryhiwYoiKCrSBFREuqCEXtJIcn5/3DcwM5lJ3iTTcz7PM0+Y+7Y7vIEz9773nqtdvX33VdVXQ/dLhFQZUV0ldM7xhDkrKSuPQsDcuTccNjq4bMln8MWDDT+3McakGL/BuA9wraq+pqoLVHVp6CuWlUwnqZCFK9DgngW0yt8xOnBD0TYm/RClLxD9L4PuhwaXfXQbrJodnfMbY0yK8BuM1xA++5Wpo9DpTcneMs7JyuCEfYOXjBs3Y0V0Tp6RAcMfhtyAUduV2+C1C6CsAdOojDEmxfgNxvcBl4mILUTbQO3zgqc3FRYnZ0rMQCP7BA+q+vj71WwoitJ3s5ad3PzjQGt+gA9Gh9/fGGPSkN/R1O2BnsB8EfmA6okzVFX9rtzUqBU0Ta1nxgD7d25F93ZNWbzGrby0rUKZMGcVZ/fvGp0L9BoG+58FswLW9vj6cdj9SDflyRhj0pzflvENQDfcaOZLvfehL+NDKmXhqiIijAzJyPV6tLqqqxxzR/BiEgDjL4Utyd9zYIwxDeU3HWZGLS/rvvapTW4bsmRHh8Tmss0Ulyd/2sPhIcF4xrIN21vKUdGkOYx8HAKfhGwthPGXgWWgMsakOd/pME10ZEgG7fKDk3ykQld15zb59OsevODV6w1Nj1ntIgfCoX8OLvvxPbf+sTHGpDELxglQkJd6z42B6l3VM1dEP2/ywGtdJq5A790AhQuiex1jjEkiFowTINUSf1Q5dt8O5GTt+JVZvq6Y6UtrXGyr7jKzYORjkNN8R1l5MYz7A5Tb7DpjTHqyYJwAqRqMW+Rmc2Sv4AFoUZtzHKhNdzj2ruCyVbNh0t+jfy1jjEkCFowTIFWDMVSfc/zWnFWUbIvBMpD7nQ69hgeXTX0AFn8W/WsZY0yCRQzGIjJORHbz/nyOiLSNX7XSW6qlxAw0cPf2tGu2Y4GHzSXlfPRdDL5MiMDx90HzwOxf6haTKI5y17gxxiRYTS3jYUDV8Nn/AbvGvjqNQ6qlxAyUnZnBCfvFKD1mqPw2MOIR3CJenk0/w1t/tOlOxpi0UlMw/hU4yPuz4JYwNFHQPj8kJWZRaiW2ODFkJadPFxSyZktpbC7W41A4+IrgsnnjYM5LsbmeMcYkQE3B+GXgPhGpwAXiaSJSEeFVHp/qpodqLePi1VRq6qzju3fHFuxe0Gz7+/JKZcLslbG74JAb3JKLgd6+FtYvid01jTEmjmoKxv8HnArcimsZjwX+EeF1e2yrmV7ys/Nplh0YzMpZX5I6z0FFpNo6x1FPABIoqwmc+CRk5e4oK9sM4y6ECvseaIxJfREXilCXzeEVABH5PfCAqtpCs1FSkF/Alo1btr9fXbSatnmpM0Zu+AEdueu977c/up2zYiMLV29mt4LmNR9YX+17wpFj4J1rd5Qt/xKm3Fs9a5cxxqQYv7mpu1sgjq5Unt4E0KFlHgfvGvzlYdyMGLaOAQ78g1vJKdAnd8CK6bG9rjHGxJjvecYi0kFE7hGRr0XkJ+/nXSKycywrmK6qBePi1ArGACMOqN5VXVkZw3F+IjDs3xCY21srYNwFULol8nHGGJPkfAVjEdkDmA1cCWwBvvJ+XgXMEpHdY1bDNJXqLWOAo/fZmbzsHassrdpYwrRFa2N70WYFLiAHWrcIJv41ttc1xpgY8tsyvhPYCOyhqoNV9XRVHQzs4ZXfGasKpqt0CMbNmmRx9D7BHSPjYjmQq0rPo6Hv+cFlM5+B+W/G/trGGBMDfoPxYOBGVV0SWKiqS4Gbve2mDlI5C1egESErOb377SqKy2KQHjPUkWOg3R7BZROuhE0xnGJljDEx4jcY5wCbI2zb7G03dZDKWbgCHbJbOwqaN9n+fmtZBe/P/yX2F87Jh5GPQ0b2jrLi9fDGJVCZOnO2jTEG/AfjWcAVIhK0v4gIcKm33dRBOnRTA2RmCMNDWsevxXpUdZWO+8OQ64PLFn0Cn95h6TKNMSnFbzC+FTgc+E5EbhWRS0TkFmAecARwS6wqmK7a5LYhI+C7zcbSjZRWxCilZIyFruQ05cdCVm8qic/FD74Sug4ILvv0TnjxDChaF586GGNMA/mdZzwROB7XJX098G/gBtyI6uNV9f2Y1TBNZWVk0S63XVBZqraO99y5BXt1aLH9faXC+FlxenabkQkjH4XclsHlP7wDjwyAJVPjUw9jjGkA3/OMVXWiqvYFmgOdgeaq2k9V34tZ7dJcunRVA5wY0jqOy6jqKi13gZOfgiYtgss3/Qxjj4dP7oTKOAwqM8aYevIdjKuoapGq/qyqRbGoUGOSTsF46H4dyQhY6fC7VZuYv3JT/Cqw6xC4aDJ0+k1wuVbCJ/+AsUNhYxy/IBhjTB3UORg3lIh0FpFXRWSjiGwSkXEi0sXnsV1EZKyILBORYhFZICJjRKRpyH6fiIiGeV0dm09VP+kUjAta5DJw9+ClIV+fGaN1jiNp0x3OneieI4daOsV1W/8wMb51MsYYH+IajEUkH/gY2BMYBZwN7A5MCg2oYY5tCnwI/A64ETgWeAK4BvhvmEPm4NZjDny9GJUPEiU7NQ2e3pSqc42rhA7kemPWSsor4jzNKCsHjrwNznotOG0mQPE6eOFUePevUJ6ag+WMMekp4qpNMXIB0APoqaoLAURkDvAjcBFwbw3HHoIL3EcFDBibJCJtgGtFJD+k63yzqk6L+ieIovZ5wS3JwqLCBNUkOo7stTPNmmSxpdQta1i4uZSpP63l0D3a13JkDOx2OFwy1S2zuPjT4G1fPgxLp7rnzG13jX/djDEmRLy7qYcC06oCMYCqLgamAsNqObYqsUjog8gNuM8hpJh06qYGyMvJ5JiQ9Jivz4hzV3Wg5jvD2W/AYaNBMoO3/TIHHv0dzE6qzhJjTCMV72C8NzA3TPk8oFctx36Ia0HfKSK9RKSZiAzBLVbxiKpuDdn/AO+59DYRmSMi51c7Y4KFZuFK9W5qgBEhXdUT5/2yvaWcEBkZMPAaOG8itAwZmlC2BV6/CF6/2FZ9MsYkVF2WUDzAG2y1RkTKRaSPV/4PETna52naAOvDlK8DWtd0oKqWAAO8Os/DzXn+CHgLuDxk98nA1biW+Em4IP6EiNwQ6fwicqGITBeR6YWF8ekuDm0ZFxYVoimeOap/97Z0bJm7/X3Jtkomzo1DeszadO4HF38Gew2tvm32C66VvMqW7DbGJIbfJRQHAF/gBl49H3JcJXBx9KtWrQ65wEtAAW7g16HAn4BTcUlItlPV0ar6uKp+qqrjVfVE4A3gehFpFu78qvqYqvZV1b7t28fnGWeznGbkZ+Vvf19WWcaG0g1xuXasZIRJjzkukV3VgfJawSlPw/H3QVZu8LZ1P8ETh8O0RyyVpjEm7vy2jO8A3sN1M/8xZNsMoI/P86wnfAs4Uos50PnAIOBYVX1WVSer6j240dQXi8h+tRz/ApAL9PZZ17hIt+fGUH1U9ReL1rJyQ3GCahNCBPqeBxdMgvZ7Bm+rKIOJf4EXToetMV6X2RhjAvgNxn2Ah9X1oYY2G9YAfpuS83ABPVQvYH4tx/YG1qvqTyHlX3k/9/JZh6Rq9qRjMN6toDn77rIjPaUqvDEryRJu7NTLBeQ+o6pvW/Cul0pzSvzrZYxplPwG4xIgP8K2DsBGn+d5E+gvIj2qCkSkG27aUm0rw/8CtBaR3ULKf+v9rO1/+zOBYuBbn3WNi3QMxgAjq3VV/5x8z8Nz8mHov+Ck/1VPpbl5JYw9ASbdbqk0jTEx5zcYTwGuFgmaH1L1P+v5uEQefjwOLAHGi8gwERkKjAeWA49W7SQiXb1BYqMDjn0KN2jrHREZJSKDReRPwD3AN7jpUYjIQBF5W0TOF5HDRGSkiIzHDea6Jcyo64RK12B8wn4dyQrIj7lw9Rbm/hzH9Jh1sc9IN7irU9/gcq10yzGOPcFSaRpjYspvML4R11U92/uzAqNEZBLQH59LKHqBcAiwAHgGeA5YDAxR1cC5JQJkBtZPVZd415oFjAHewSUReQw4QlWrUj2t8o671dvnaVw3+hmqeqfPzxs3ocE4HaY3AbRt1oRBPYOfXryWLAO5wmndzU1/OiRMxtSlU+GRQ+D7d+JeLWNM4+B3CcXZuDSUv+KWUBR2TCc6VFV/8HtBVV2mqieqagtVba6qw71AG7jPElUVVb05pHy+qp6iqp1VNU9V91DVa1V1fcA+C1X1GFXtpKpNVLWZqh6sqi/4rWM8hc41TpeWMcDIPrsEvZ8weyXb4p0esy4ys+GIW+CscdA0ZBhE8Xp48XT44CYbbW2Mibq6LKE4Q1UPwy2huAvQQlUHq+rMmNWuEWifH5ISszi1U2IGGrJnAc1zd2RcXbu1jMkLUuDz7XYYXDwVegyuvm3q/fDBjRaQjTFR5XeecXbVQg6qWqKqK6vyQItIUxHJjmUl01k6t4xzszM5ft+OQWVxXee4IZrv5FrIh98CGSEp3D9/ECb9IzH1MsakJb8t4ydwg6/CeZSAwVembtrmtUUC0mqvK1lHWUVZAmsUXaFzjj+Y/ysbi7clqDZ1lJEBA652yzLmtQneNvkumHx3YupljEk7foPxYNyo53DeBA6LTnUan+yMbNrmtQ0qS6eu6r5dW9O5Td7292Xllbz77aoE1qgeOh8IZ78OuS2Dyz8e41rJxhjTQH6DcQEQqf+0ENgpwjbjQ7pObwIQEUYcEDyQa9yMFOmqDtRxf9dtndM8uPz9G+CrSJ1Gxhjjj99gvJrIaSR7A5Y7sAEK8tI3GEP1BCBfLVnH8nVFEfZOYrv0hTNfgeyQ/DfvXAsznk5MnYwxacFvMH4LuFFE9g0sFJHeuKlOE6JdscYknVvGAN3aNaVPl1ZBZWM/X5J8Gbn86HoQnP5i9YUm3rwSZr+UmDoZY1Ke32A8GtgAfCMin4vIyyIyFbdIxEYg4tKEpnbpHoyh+pzjJ6Ys5uqXZiV2reP66nEonPocZOYEFCq8cTHMez1h1TLGpC6/ST/WAAcCt+MSfuzv/fw7cKC33dRTumbhCnT8vh1o3iR4itD4WSs5/l+f8e0Kv6nNk8juh8PJY4OnPWklvPYH+P7txNXLGJOS6pL0Y4O3TvBBXuarg1X1ZlVNwf9Jk0s6zzWu0io/h/tP25+87Myg8iVrixj58FSenLI49bqt9zwWTnwCJOCfUWU5vDwKfvwgcfUyxqQc38HYxE5j6KYGOGyvnZhwxSHsuXPwiORtFcptb83nD2Ons25ris2x3nsEDH8EAuaKU7kNXjoLFn2SqFoZY1KM72DsrZQ0UUTmi8iikFfoGsOmDqqlxCwqTL1Wok+7FTTnjcsO4az+Xapt++j71RzzwGSmLUqxwfn7neqWYgxUXgIvnA5LP09MnYwxKcVvOswbgf8BHXGrJn0a8pocqwo2Bi1yWpCbuWN0bklFCZvKknS5wSjIzc5kzPDePHxmn6Dc1QC/birljMencf+HC6ioTKEvJH3OgWPvCS7bVgTPnQwrpiemTsaYlJFV+y6AW7P4AVX9v1hWprESEQryC1i2edn2stVFq2nZpGUNR6W+Y3p3YJ9OLbnyxZnMXLZhe3mlwv0f/sgXP63lgdMOYOeWuTWcJYn0uwAqyuC963aUlW2BZ0bCqDdd4hBjjAnDbzd1W2wucUw1lufGoTq3yefliw7ikkG7Vtv25eJ1HPPAZD76LoVGlx90GRw2OrisdCM8MwJ+nZeYOhljkp7fYPwpsF8sK9LYNdZgDJCdmcFfjt6Tp8/rR7tmOUHb1hdt4/yx07l1wnxKyysSVMM6GngN/O7PwWXF6+DpYVC4IDF1MsYkNb/B+GrgXBE5R0TaiUhG6CuWlWwMGsNc49r8bo/2vHPVQAbu3q7atv9OXcxJD3/BkjVbE1Czehh8HRx8ZXDZ1kIYewKstfGOxphgfoPoAmAf3CCuX4FtIa8Um4+SfEKDcWFR+qzcVBcFzXMZe24//nx0TzIzJGjbtz9v5Lh/fcb4WSmw0IQIHHEr9LsouHzLL66FvGFZ+OOMMY2S3wFctwIpNLQ19TTmbupQGRnCpYN247fd23LlCzP5eUPx9m1byyq46sVZTF24hpuH7k1+jt9f4QQQgWPuhIpS+OapHeUbl7sW8u/fgZadIh5ujGk8fP1Ppqo3x7gejV5oFq7G2E0d6jddW/POlQP5y2tzmDjvl6BtL09fwTdL1/PQGX3Yq0OLBNXQBxE47j4oL4PZz+8oX78Enh7qAnJzW4HUmMbOnvUmCWsZh9cyP5uHz+rDbcP3IScr+Nf1p8KtDPv3VJ6dtjS5k6RkZMCwh2CfE4PL1y50XdZbUyzJiTEm6nz38YlIDnAM0BMInfipqnpbNCvW2LTPC87Cta5kHdsqt5GdkZ2gGiUPEeHs/l3p27U1lz8/g58KdwziKiuv5IY35jJ14RruGLkvLfOT9O8rIxNGPArlpfD9WzvKC7+DZ4bBqAmQ1zpx9TPGJJT4aVGISEdgCtAN9+y4amTN9oNVNbP6kampb9++On16/LMmHfrSoawrWbf9/QcnfcDOTXeOez2SWVFZOTeNn8cr36yotq1Tqzz+dfoB/KZrEge18jJ46Uz48f3g8o594JzxkJvEXe7GmAYTkW9UtW9oud9u6ruBQqALLhD/FuiBW0Jxofdn00A2val2+TlZ3H3yftx/6v40zQn+/vfzhmJOefQLHvn0JyqTNZVmVg6c8gz0GBRcvnIGPD4EvvgPbLUVSY1pbPwG44HAP4GV3vtKVV2iqqOBV4F/RTzS+GbPjf0bfkAn3r5yIPt0Cm5JVlQqd7z7PRc8PZ0NRUk64y47F057HroeEly+9kd472/wzz3hxTPhh3ehYlti6miMiau6pMNcqaqVwFYgsB/wY2BQlOvVKFkwrptu7Zry2iUHc/6A7tW2ffT9ao771xRmLlufgJr5kNMUzngJdjmw+rbKbe658gunwb294L3rYfV38a+jMSZu/AbjFUBVWqSfgCMDtvUDSqJZqcbKuqnrrklWJjce34snR/WlVcjgrapu6/9NXZyco62bNIczX4V9ToJISey2roYvHoL/9IfHBsPXT0Bxkn7BMMbUm99gPAk41Pvzo8C1IvK+iLwN3IbrqjYNFDrX2FrG/h221068dcUA9u/cKqh8W4Vyy4T5XPrcDDaVJGGXb14rOOlJ+L95cNhN0Ha3yPuunAFvXwP39IRXzoWFH0JliuTrNsbUyG8wvgF4GEBVHwauAvKBDsBdwDV+LyginUXkVRHZKCKbRGSciFRfaT78sV1EZKyILBORYhFZICJjRKRpmH0vEJHvRaRURH4QkYv91jFRQqc3NdaUmPW1S2u3AtR5h1Tvtn537i+c8OAU5v68MQE186FFRxj4R7h8Opz/AfQZBTnNw+9bUQrzxsGzJ8J9+8CHt8CahfGtrzEmqnxNbYraxUTygdlAKS7AKzAGF9j3VdWIqwB4AXcmkA3cDCwDDgRuAd5U1VMD9r0A14K/HfgQOAy4DrjM+zJRo0RNbfph3Q+cNOGk7e+7tejGhBG2cmV9TJy7ij+9MofNpeVB5TlZGdx0Qi/O6NcFEYlwdJIoK3LPjmc+C4snU2tG2s79Yf8zYO8RNkXKmCQVaWqT33nGHwOXqur3YbbtATyiqkN8nOcq4F6gp6ou9Mq6Az8Cf1bVe2s49kjgPeAoVX0/oPwO4FqghaoWiUgWbtT3u6o6KmC//wJDgQ6qWmN/ZaKC8YaSDQx8aeD293lZeXx5xpfJHzSS1NK1W7n0uRnMW7mp2rZh+3fkHyN607RJEue2DrRhGcx+EWY951Jp1iQ7H/YaCgecCV0HuAxgxpikECkY+/2faBAQ6at2c3Y8T67NUGBaVSAGUNXFIjIVGIYL1JFULXQb+j/rBlx3e1XEOghoDzwbst8zwLnAANwz8KTTsklLcjJyKKt0U3KKy4vZsm0LzSN1V5oadW3rRluPeXs+z04LXiVp/KyVzP15I/858zf03DkF/n5bdYFD/wwDr4Vln8PM52D+G7CtqPq+24pgzovu1aoL7HcGtO8Z/zobk256HgPZeTE5dV2aBZGa0LsCW3yeY29gfJjyecDJtRz7Ia4FfaeIXILrpu6He379SEAX997ez7lhrgHQiyQNxiJCQX4BK7bsyC61umi1BeMGyM3OZMzw3hzYrQ1/G/ctRWU7Bjy53NZTGDO8Nyf9ZpcE1rIOMjKg2wD3OvYumD/eBeZln4fff8My+PSO+NbRmHT1x+/jH4xF5FxcSxJcIH5MRDaH7JaHW+f4I5/XawOEm5exjuC5y9WoaomIDABeY0dgBXgCuDzkGoS5zrqQ7UFE5ELgQoAuXXyNJ4uJcMF411a7Jqw+6WLY/p3Yu2NLLntuBj/8uuPXuGRbJde+MpuvFq/llqH7kJeTQlldmzSHA85yr7U/wewXYNYLsKl6qlBjTHKr6WFSJVDhvSTkfdVrLW6U9fmxrSaISC7wElAAnI3rGv8TcCrw74aeX1UfU9W+qtq3ffv2tR8QI5b4I3Z2K2jGG5cdwslhWsEvT1/BiP9M5adCv508SabtrjDkBrh6Dpz9OvQ+GbJC13MxxiSriC1jVR0LjAUQkUnAJeEGcNXResK3gCO1mAOdj3t2vZuq/uSVTRaRjbhW+yOqOjvgPK2BVSHXgB0t5KRkwTi28nIyufvk/TiwextGj59LybbK7du+/2UzQx+cwu0n7svQ/TomsJYNkJEJuw5xr+INMO91WPaFWy3KGNMwWU1id2o/O6nq4HDlItJWVeuyGOs8djzTDdQLmF/Lsb2B9QGBuMpX3s+9cNOmqrqw9yY4GPfyftZ2nYSyLFzxcUrfzuy7S0sufW4GiwKWZNxaVsGVL8zkq8VrueG4XuRmp1C3dai8VtD3XPcyxiQ1X3MevAQafwp431tEVgCrRWS6iPhd5+9NoL+IbF/lSUS6AYd422ryC9BaREJTFP3W+/mz9/MLYA1wZsh+Z+FaxVN91jUhLAtX/Oy5cwvevHxA2Fbws9OWcdIjn7NsbZjRysYYE2V+JyBeARQHvL8XN6XoaqAlcKvP8zwOLAHGi8gwERmKG129HJekAwAR6Soi5SIyOuDYp4DNwDsiMkpEBntfEO4BvsELst4c4huBUV52rkEicitwHjBaVZN0KR/Huqnjq1mTLB44bX/+PmIfcjKD/znM/XkTxz34GRPn/pKg2hljGgu/wbgr8D2AiLTEDZ76s6o+CNwEHOXnJN70oyHAAty83+eAxcAQVQ0cOSNAZmD9VHUJ0B+Yhcva9Q5wAfAYcIS3olTVvo8AlwCn4BKFnA5crqoNHugVa+3zLSVmvIkIZ/62K+MuPZgubfKDtm0uKefiZ7/htrfmU1ZeGeEMxhjTMH7nGWfgRlODS5qhwCfe++W4Ec6+qOoy4MRa9lnCjiQegeXzcQHWz3UeJaC1nSpCW8ZrStZQXllOVkaKZIpKYft0aslbVw7gz6/MYeK84Nbwk1MW883S9Tx4+gF0DgnYxhjTUH5bxj8Cx3l/Pg34XFWrHqZ1JMlHKKeSJplNaNVkx8pDlVrJ2uK6jJEzDdEiN5uHz+rD6ON7kZUR/H1w1vINHHbvp4x5az7rtib10w5jTIrxG4zvAa4WkTXAGcCDAdsGA3OiXbHGzJ4bJ5aIcN6A7rx88UF0ahWcbaesvJInpizm0Lsm8eBHP7I1ZCEKY4ypD1/BWFWfxz0nvh0YrKrjAjb/SnBwNg1kwTg59OnSmreuGMCQPas/hdlcWs4/P1jAoXd/wtNgBvA+AAAcaklEQVRfLLHnycaYBvG9nIuqTlHVf6rq5JDym1T1nehXrfGyucbJo3XTHJ44py93nbgvHVpWz2i1Zkspo8fP4/B7P2X8rJ+prIzfkqTGmPQRMRiLSBcRyQ74c42v+FU5/YUG48JiG1GdSBkZwikHdmbStYO47tg9aZmXXW2fZeuKuOrFWZzw0BQ+XVBIPNcJN8akvppaxouBA7w/L/He1/QyUWLd1MkpNzuTC3+3K5P/PJhLB+1Kbnb1fz7zVm5i1H+/4vTHpzFzWW0ZXo0xxqlpvsx5wE8Bf7av+nESmoXLuqmTS8u8bP589J78/uBuPPDRj7z49XIqQrqnpy1ax4j/fM5Re+/En47ak90KmiWotsaYVFDbQhFVf34qLrUxgLWMU0VBi1z+PqI3fxjYg3++/wNvzVlVbZ/35v3KB/N/5eTfdObqI3anQ8vYrIVqjEltvgdwmfixYJxaurdrykNn9GHC5QMYuHu7atsrFV6avpxBd3/C7e98x4Yim6NsjAkWsWUsIv+tw3lUVWO+pnFj0apJK7IysiivdHNYt27bytZtW2ma3TTBNTM16b1LS545/7dMXbiGuyZ+z+wVG4O2l5ZX8ujkRTz/1TIuPnRXzjukO3k5KbwqlDEmamp6ZjyE4OfErXCLQpQDa4G23vEbqX0tYlMHGZJBQV4BK7eu3F62umg13Vt2T2CtjF+H7NaONy47hHfn/sI97/3AojVbg7ZvLinn7vd+YOznS7jysN059cDOZGdaJ5UxjVnE/wFUtZuqdlfV7sDZwBZcKsw8Ve0A5OEWYNiMW57QRJF1Vac2EeHY3h14//9+x+0je7NTi+qLkq/eXMoNb8zlyPsm89aclZSWVySgpsaYZOB39YF7gdtV9eWqAlWtAF4SkXbA/UC/GNSv0bJgnB6yMjM4vV8Xhu/fiac+X8LDnyxkU0lwCs3Fa7Zy+fMzAWiVn81OzXMpaNGEgua57NSiCQXNm7BTi1wKWuRS0LwJBS2a0CTLureNSSd+g3FvYGGEbT8C+0SnOqaKZeFKL3k5mVwyaFfO6NeFhz/9if9NXUxpmBSaG4q2saFoGz/8urnG84UL2jttD9YWtI1JNX6D8S+4pQvfD7PtNFx+ahNFoXONrWWcHlrmZ/PXY6rmKC/g5ekrqs1R9sNv0G6dn0375k3smbQxUfD0ef1o26z6I6do8BuM7wfuE5EOwCu44LsTLkAfBVwdk9o1Yu3z2we9LyyylJjpZOeWudw+cl/+MLAH//54IVN/WkPh5lKindp6fdE21hdti+5JjWmkymOYe95XMFbVB0RkC3ATcEzApuXABapal2lQxgd7Ztw47Nq+Gfeeuj8AFZXK2i2lrN5cyq+bSvh1UymrN7ufhd7PXzeVsGZL9IO2MSax/LaMUdUnvbnHuwAdgFXACrWM+DFhKTEbn8wMcc97W+SyT6eWEfezoG1M+vEdjMFl9sC1hpfHpjqmSmjLeE3xGioqK8jMsAE5jV1dg/aaLWVU2ndmYxqsdX5OzM5dp2Bs4ic3K5cWOS3YVLYJgAqtYF3JumrPko2JJDBoG2OSmw2xTGLVnhsX23NjY4xJRxaMk1i1YLzVgrExxqQjC8ZJzEZUG2NM42DBOIlZFi5jjGkcfAdjEekkIveKyHQRWSQi+3jlV4vIb2NXxcbLsnAZY0zj4CsYi8jewLe41ZtWAl2BqjHeXYGrYlK7Rs66qY0xpnHw2zL+J/Ad0B0YCUjAts+B/lGulyFMSsxiS4lpjDHpyO884wHA6aq6RURCs078Cuwc3WoZsCxcxhjTWPhtGVdf622HdkCx3wuKSGcReVVENorIJhEZJyJdfBx3s4hohFdJyL5LIuw33G89k0Gb3DZkyY7vS5vLNlNc7vuv2hhjTIrw2zL+CjgXmBBm2ynAVD8nEZF84GOgFBgFKDAGmCQi+6rq1hoOfwKYGFLW1Ct7M8z+7wE3h5T94KeeySJDMmiX345ftv6yvWx10Wq6tuiawFoZY4yJNr/B+DbgQxF5H3geF0QPF5GrgBHA73ye5wKgB9BTVRcCiMgc4EfgIuDeSAeq6gpgRWCZiJztfYaxYQ5Zo6rTfNYraRXkF1gwNsaYNOerm1pVPwWG4wZw/Rc3gOsOYCAwXFW/9Hm9ocC0qkDsnXsxrmU9rA71rjIK98z6vXocmxIK8mxEtTHGpDvf84xV9W1V3R3YAzegay9V7aGq79bhensDc8OUzwN61eE8iEhnYDDwnKqWh9nlBBEpEpFSEZmWas+Lq9j0JmOMSX91XrXJa9UurHXH8NoA68OUrwNa1/FcZ+G+TITrop4AfA0sBnYCLgdeF5GzVfXZcCcTkQuBCwG6dKl1PFncWDA2xpj05zsYi0gL4FigCxC6Jpuq6m3RrJgP5wAzVXVO6AZVvSLwvYi8DkwDbgfCBmNVfQx4DKBv375Js/irpcQ0xpj05ysYi8ghuNZmqwi7KG6QV23WE74FHKnFHKk+/YA9gav97K+qFSLyCnCniHRQ1VV+r5VolhLTGGPSn99nxvcDS4ADgVxVzQh5hSYCiWQe7rlxqF7AfJ/nADdwaxtuZHddJU2r1w/rpjbGmPTnNxjvBdygqt+oalkDrvcm0F9EelQViEg34BDCzxWuRkRygNOAd1XVV35IEckCTgWWqeovte2fTEKDcWFxIZVaUw4WY4wxqcZvMF4GNInC9R7HtbDHi8gwERkKjAeWA49W7SQiXUWkXERGhznH8bhu7XADtxCR00XkRRE5R0QGi8hpwCSgD/CXKHyGuMrPzqdZdrPt78sry1lf4rtH3xhjTArwG4xvAf7qDeKqNy/D1hBgAfAM8BxuxPMQVd0SsKsAmRHqNwo3+vqtCJdZDBQAdwPvA4/gMn4draovNqT+iWJd1cYYk978jqY+HjdFaLGIfIELhoFUVUf5OZGqLgNOrGWfJQSvDBW4rcbkIF7WrSF+6pIqCvILWLRx0fb3q4tWs1fbvRJYI2OMMdFUl1WbFNhE+AFYKTUoKtXY9CZjjElvvoKxqnaPdUVMZDa9yRhj0pvvdJgmcdrntw96X1jsaxC5McaYFBGxZeytMbxKVbf5WW/YexZsYsC6qY0xJr3V1E29GDgIt5bxEmp/Luw38YepI+umNsaY9FZTMD4P+CngzzZIK0FsapMxxqS3iMFYVccG/PmpuNTGhNU2ty0ZkrE989bG0o2UlJeQmxW6XocxxphUVO8BXCLSS0ROFJGO0ayQqS4zI5N2ue2CymwQlzHGpA9fwVhEHhKRRwLejwRmA68A80XkwBjVz3isq9oYY9KX35bxMcDnAe9vwaWj3A83wOumKNfLhLBgbIwx6ctvMO6AG1GNiOyCy8J1u6p+C/wLt7SiiSELxsYYk778BuMioGrpoENxaTGne++3AM2jXC8TYqemwdObbK6xMcakD7+5qWcAl4nIMuAy4APV7YvqdgdWxaJyZgdrGRtjTPryG4yvBybiBm1tAC4O2DYc99zYxFD7vJCUmEU2mtoYY9KF34UivvZSYu4J/KiqmwI2Pwb8GIvKmR1Cs3BZN7UxxqQPvy1jVHUr8E2Y8rejWiMTVmg3dWFRIaqKSNhln40xxqQQ30k/RKS3iLwqIoUiUu79fFlE9ollBY3TLKcZ+Vn529+XVZaxoXRDAmtkjDEmWvwm/TgQ+BIYjJtffLf3cwjwpYj8JmY1NNvZIC5jjElPfrupbwfmAoep6uaqQhFpDnzobT8y+tUzgQryC1iyacn296uLVtOzTc/EVcgYY0xU+O2m7o9L8rE5sNB7fyduqUUTY9YyNsaY9OQ3GNe2fKItrxgHFoyNMSY9+Q3GXwLXed3S24lIU+AvwLRoV8xUFxqMbXqTMcakB7/PjK8DPgGWishbuIxbOwPHAvnAoFhUzgQLnWtsLWNjjEkPfpN+fCUi/YHRwFFAG2AdMAm4zVswwsSYdVMbY0x6qkvSjznASTGsi6lFtcQfxZYS0xhj0kHEZ8YikiEiJ9SU1MNLBHJCbKpmQrXNa4uwI+PWupJ1lFWUJbBGxhhjoqGmAVxnAS8AW2vYZzPwgoicHtVambCyM7Jpm9c2qMxax8YYk/pqC8b/U9XFkXZQ1SXAk8CoKNfLRGDPjY0xJv3U9My4D/Cgj3N8CJzp94Ii0hm4DzgCEO/4q1V1WS3H3QzcFGFzqarmBuybgZtydRFu1PcPwK2q+prfeiargvwC5q+dv/39C9+9wLRVNrPMGGNi7Zxe59A0u2lMzl1TMG4OrPdxjvXevrUSkXzgY6AU15pWYAwwSUT29VaGiuQJ3JrKgZp6ZW+GlN8GXItbh/kb4DTgFRE5XlXf8VPXZBU6vendJe8mqCbGGNO4nLj7iQkJxmuArsCUWs7RxdvXjwuAHkBPVV0IICJzcOshXwTcG+lAVV0BrAgsE5GzcZ9hbEBZAS4Q36Gq93jFk0RkN+AOIKWD8c5Nd050FYwxxkRZTc+Mp+DvWfDvqT1gVxkKTKsKxADeM+mpwDCf5wg0CvgVeC+g7CggB3g2ZN9ngd4i0r0e10kaQzoPoUlmk0RXwxhjTBTV1DK+H5giIvcBf1HVoDk0IpKNW0pxCDDA5/X2BsaHKZ8HnOzzHFXX74xb0vF+VS0PuUYpsDDkkHnez15AxEFpya5Hqx48f9zzTF4xmZLykkRXxxhjGo3ANeWjLWIwVtUvROQa4J/AmSLyPrDU29wVNwCrLXCNqvodQdSG8M+h1wGtfdfaOQvXsh8bUt4G2KCqoYtXrAvYXo2IXAhcCNClS5c6ViW+9mi9B3u03iPR1TDGGBMlNWbgUtX7RWQGbmTyCCDP21SMy1V9h6p+FtMaRnYOMNPLDNZgqvoY8BhA3759bRUqY4wxcVNrOkxVnQxM9qYLtfOK16pqRT2ut57wLeBILeawRKQfsCdwdYRrtBIRCWkdV7WI14U5xhhjjEkYv0sooqqVqrrae9UnEIN7brt3mPJewPww5ZGMArYBz0e4RhNg1zDXoI7XMcYYY2LOdzCOkjeB/iLSo6pARLoBh1B9rnBYIpKDmzf8rqqGywU5EReoQxORnAXMrSmjmDHGGJMI8Q7GjwNLgPEiMkxEhuJGVy8HHq3aSUS6iki5iIwOc47jcV3OoQO3AFDV1bj5yn8TkT+KyCAReRg36vtvUf00xhhjTBT4XkIxGlR1q4gMwaXDfAaXDvMjXDrMLQG7CpBJ+C8Lo3DPfd+q4VLXA1uAq9iRDvMUVa3pGGOMMSYhpPoMINO3b1+dPn16oqthjDEmzYjIN6raN7Q83t3UxhhjjAlhLeMwRKSQHQlOGqId/vN2pzL7nOnFPmd6sc+ZXLqqavvQQgvGMSQi08N1R6Qb+5zpxT5nerHPmRqsm9oYY4xJMAvGxhhjTIJZMI6txxJdgTixz5le7HOmF/ucKcCeGRtjjDEJZi1jY4wxJsEsGBtjjDEJZsG4HkSks4i8KiIbRWSTiIwTkS4+j80VkbtFZJWIFIvIFyLyu1jXua5E5CQReU1Elnr1/EFEbheR5j6O1Qiv/eNR97rwcpeHq+sGH8emxL0EEJFPargvE2s5Ninvp4jsIiIPen/vRV6duoXZr0H3SUQuEJHvRaTU+3dwcTQ/h4/r1/o5RaSviDzm1bNIRJaJyHMi0t3nNSL9foRbpjYm6nA/G/T7mOj7GUlcc1OnAxHJBz4GSnF5shUYA0wSkX1VdWstp3gSOA74E7AIuAx4T0QOUtVZsat5nV0LLAOuA1YABwA3A4NF5GBVrazl+KcIWPzDsyDKdYymK4GvA96X+zgmVe4lwKVAi5Cyg3CLqvhZMe0pku9+7gacAnwDfAYcGWG/et8nEbkA97lvBz4EDgP+IyKiqg9H5VPUzs/nPA23PO2/cMvIdgJuBKaLyP6qutzHdeYAF4WULalnnevD7/2Eev4+Jsn9DE9V7VWHF27xiQpgt4Cy7rj/vP9Yy7H74YL3uQFlWbiFLN5M9GcLqWv7MGXnePUfUsuxCoxJ9Gfw+TkHefU9vI7Hpcy9rOEzPIn7UtkmFe8nkBHw5z949ewWrfvk7bcaGBtS/l9cpqfsJPqc4f69dgUqgVt9XOMTYEqy309vW71+H5PlfkZ6WTd13Q0FpqnqwqoCdWskTwWG+Th2G/BSwLHlwIvAUSLSJPrVrR8Nv1Z0VcuxUzzrkqRS5l6G4/XwnAxMUNV1ia5PfWjtvTPQsPt0ENAeeDak/BmgLTCgThWuJz+fM9y/V1VdChSSIv9efd7PhkiK+xmJBeO62xuYG6Z8HtDLx7GLVbUozLE5uG6aZHao9/M7H/te4j2TKRKRj0VkYCwrFgXPiUiFiKwVkeel9jEAqX4vRwDNibAueBipdj+rNOQ+7e39DP33Ps/7Wdu/94QSkb2AAvz9ewU4QNw4mG0iMkdEzo9h9RqqPr+PSX0/7Zlx3bUB1ocpXwe0bsCxVduTkoh0Am4FPlTV2taXfBa33vRKXFfZn4CPReQIVf0kphWtu43AP4FPgU24Z+PXAV+IyAGqujrCcSl7Lz3n4Lrs3vWxbyrdz1ANuU9V20KPT/p7LCJZwCO4lvGTPg6ZDDyHe+7aCvf78YSIdFDVMTGraP3U9/cxqe+nBWNTKxFpBozHPRc/t7b9VfXsgLefich43LfRMSS4KyiUqs4EZgYUfSoik4GvcIO6bkhIxWJIRDoChwMPeF22NUql+2m2ewg4GDhOVcN9GQmiqqNDisaLyOvA9SJyv6puiUUl6yNdfx+tm7ru1hO+BRzpG7jfY2HHN7SkISJ5wASgB3CUqq6o6zlUdTPwNnBglKsXE6o6A9dCqKm+KXcvA5yF+7fvt4s6SIrdz4bcp6p/z6HHJ/U9FpE7gAuB81T1/Qac6gUgF+gdlYrFSB1+H5P6flowrrt57Hj2EKgXMN/Hsd29wTOhx5YBC6sfkjgikg28CvQFjlXVbxt4ylTLvVpTfVPqXoYYBcxW1dkNPE8q3M+G3KeqZ4mh/96rni3W9u897kTkeuAvwJWq+kyUTpsK9xlqr2dS308LxnX3JtBfRHpUFXgT0w+h9vmaE4Bs3CjWqmOzgFOB91W1NNqVrS8RycA9QxoCDFfVaQ04VwvgeFzXb9ITkb5AT2qub8rcy0DeZ+tFPVvF3jlS6X425D59gZvycmZI+Vm4VtTU6Fa1YUTkSlxX7fWq+lAUTnkmUAw09Et4TNXh9zGp76c9M667x4HLcc9UbsB9G7sNWE7AJHQR6Qr8hJvjdyu455Mi8hJwv9fqXAxcgpunHPoLkmj/xv0H9ndgq4j0D9i2QlVXhPuMInItLpBNYscAi2uBnUm+z4iIPIe7DzOADbgBXH8DfsYlUEiHexnoHNyz/+dCN6Ti/RSRk7w//sb7eYyIFAKFqvppXe6TiCwElqrqYQCquk1EbsQlhfgZlyRiCHAecIWqlsX68wXUrcbPKSKnAfcDE3GDmQL/vW5S1fkB5wr6nN5I5L8C43BJPlriek+GAn/V2hMZRY2Pz+n79zGZ72dYiZzknKovoAvwGm707WbgDapPwu+GC9Q3h5Tn4bIe/QKUAF8CgxL9mcJ8xiVe/cO9bo70GYETcN8w1+Dmd67F9Rj0S/RnivA5/4bLPLTRq+9y3FJsHdLlXgbUNxs3unZChO0pdz9r+B39pK73yfud/yRM+UW4MQSlwI/Apcn2OXEZqWr9uwj3OXHTu97FfQEtBbYAnwOnJ+Hn9P37mMz3M9zLllA0xhhjEsyeGRtjjDEJZsHYGGOMSTALxsYYY0yCWTA2xhhjEsyCsTHGGJNgFoyNMcaYBLNgbEwcichwEZksIqtFpFhElorIGyJydKLrFo6I3Cwi6mWtShoi8omIfBLwfpBXz0GJq5Ux9WfB2Jg48dIVvo5LNHA+cBwufSG4TECm/mbgFo+fkeiKGFMfSfVt15g0dy3whqoGLtr+MfC4lws8bkSkiSYgf7aXkrJco5xtSFU3AfXOn25MolnL2Jj4aYNLyViNqlYGvheR7iLynIgUikipiMwSkREh++wmIs+IyGKvy3uRiDwsIq1D9ntKRFaIyEEi8rmIFAN3edvai8h/RGS5d53l3jmbhFSxu4i8LSJbvK710bV9gRCRbl7X8aUicpeIrMSlIGzlXfdREVkgIkXedZ8XkU5hznOaiHzv1W9e6N+Dt0+1bmoRWSIiT4XZV0Xk5oD3e4jI696jgxIRWSYiryRb17xJb/bLZkz8fAWMEpFFwHhVXRBuJxHpjMufvBr4P1w+6VOB10RkuKpWrQ7WEZdL+2rcWq09gOuAd3BdtoFaAi8C93j7FHtB+3Pcl4QxuBzdBcAwIAcXOKu8DvwPuA+XH/gW79r/8/G5rwe+xq2xm4nLD93F+/k37/N1BK4BporInqpa4v1dHA48j1uv9hqgPfAALs/2Dz6u7cfbuL+/S3A5jzsBx2KNFRNPiU6ObS97NZYXsAcu4FUlv1+DW8D9yJD9nsQFqLYh5R8As2o4fxYwwDv3AQHlT3llw0L2vxWoCNw3zDlv9o49N6T8W9wShDV93m7esTPA5cGvYd9MoLO3/4iA8qm4dWYzAsr6U30xiEFe2aCAsiXAU2GuFbjYSTvv/dBE/37Yq3G/7JufMXGiriV8AHAobmnKWcAI4D1vOc4qR+NatxtFJKvqBbwH7Cdu/VZEJEdErvO6cItxq9h85p2jZ8jltwFvhZQdCXytqjN9VP/tkPdzca1bP95Q1WrPiEXkEhGZLSJbcMs6LvM29fS2ZwIHAq9qQDe+urW1l/i8dm3WAouAO0TkAhHZPUrnNaZOLBgbE0eqWqGqk1X1BlU9HNe1/C1wU8Cz3gLcusPbQl53e9vbej9vx7Vcn8WNzO4HjPS25YZculBVK0LK2gIrfFZ9Xcj70jDXiGRVaIGIXAH8B7em7Ehc3avW4K06bztcd/SvYc4ZrqzOvC8JRwDTcX+fC7xn75dE4/zG+GXPjI1JIFVdKSJP4J6D7o57rrwW18K9M8JhK72fpwFPq2rV9ChEpFmkS4Upq3o+Gmvhrn0a8JGqXlNVICLdQ/apWrN2pzDH7wQsreW6Jbhn39uJSNvQnVR1EXCOiAiwH3A5bgH6Jar6bi3XMCYqrGVsTJyISIcIm/b0flaNtJ4I7AvMU9XpYV5VA6vyccEq0Ll1qNL7QD8R2a8Ox0RLrXX3WvJfAycFjtwWkd/inkfXZimwT0jZcZF2VmcW8EevKPRYY2LGWsbGxM9cEfkQ9zx4MdACN2r3YuBlVa16Zjoa10KeLCIP4Z6PtsYFhx6qep6330Tc6OxvgYW47t6D61Cf+4AzgA9FZAyuu7wdbjT1xaq6ub4f1IeJwF9E5DrcZx0CnBRmv5twXxreEJFHcaOpbyHCFLEQLwL/FZH7cM/L9wN+H7iDiOyL65V4Cfd3mOntU46bA25MXFgwNiZ+rscF31tx3awVwALgr8D9VTup6jIR6Yt7HvwPXABaixs0NTbgfFcAghsMBi7In44LbrVS1Q0icghuWtNfcc+Qf8UFobL6fMA6uBVohZu6lQt8ChyFG0wVWMcPReRM3N/FOFzAvBq4ysc1xuJGaJ8PXITr+h/hnaPKL7iBY38EdsF1bX8LHK+q39TvoxlTdxJmkKMxxhhj4sieGRtjjDEJZsHYGGOMSTALxsYYY0yCWTA2xhhjEsyCsTHGGJNgFoyNMcaYBLNgbIwxxiSYBWNjjDEmwf4fNm7ujYDZgrEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-yTdYmVng-K7"
      },
      "source": [
        "Some observations:\n",
        "* As we increase the search radius, we find more neighbors that are a smaller distance away.\n",
        "* With increased search radius comes a greater number documents that have to be searched. Query time is higher as a consequence.\n",
        "* With sufficiently high search radius, the results of LSH begin to resemble the results of brute-force search."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sDHuqOVDg-K7"
      },
      "source": [
        "**Quiz Question**. What was the smallest search radius that yielded the correct nearest neighbor, namely Joe Biden?\n",
        "\n",
        "**Quiz Question**. Suppose our goal was to produce 10 approximate nearest neighbors whose average distance from the query document is within 0.01 of the average for the true 10 nearest neighbors. For Barack Obama, the true 10 nearest neighbors are on average about 0.77. What was the smallest search radius for Barack Obama that produced an average distance of 0.78 or better?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FC-ndnArg-K8",
        "outputId": "76fccb56-17d9-4183-98c2-1dbed22e7415"
      },
      "source": [
        "for i, v in enumerate(average_distance_from_query_history):\n",
        "    if v <= 0.78:\n",
        "        print (i, v)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6 0.7735510321399475\n",
            "7 0.7707191289494768\n",
            "8 0.7707191289494768\n",
            "9 0.7707191289494768\n",
            "10 0.7707191289494768\n",
            "11 0.7707191289494768\n",
            "12 0.7707191289494768\n",
            "13 0.7707191289494768\n",
            "14 0.7707191289494768\n",
            "15 0.7707191289494768\n",
            "16 0.7707191289494768\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rUGyh1sTg-K8"
      },
      "source": [
        "## Quality metrics for neighbors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "04YcaVVsg-K9"
      },
      "source": [
        "The above analysis is limited by the fact that it was run with a single query, namely Barack Obama. We should repeat the analysis for the entirety of data. Iterating over all documents would take a long time, so let us randomly choose 10 documents for our analysis.\n",
        "\n",
        "For each document, we first compute the true 25 nearest neighbors, and then run LSH multiple times. We look at two metrics:\n",
        "\n",
        "* Precision@10: How many of the 10 neighbors given by LSH are among the true 25 nearest neighbors?\n",
        "* Average cosine distance of the neighbors from the query\n",
        "\n",
        "Then we run LSH multiple times with different search radii."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PYjiOB-Mg-K9"
      },
      "source": [
        "def brute_force_query(vec, data, k):\n",
        "    num_data_points = data.shape[0]\n",
        "    \n",
        "    # Compute distances for ALL data points in training set\n",
        "    nearest_neighbors = turicreate.SFrame({'id':range(num_data_points)})\n",
        "    nearest_neighbors['distance'] = pairwise_distances(data, vec, metric='cosine').flatten()\n",
        "    \n",
        "    return nearest_neighbors.topk('distance', k, reverse=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2Q8fsqUNg-K-"
      },
      "source": [
        "The following cell will run LSH with multiple search radii and compute the quality metrics for each run. Allow a few minutes to complete."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2LpQ0JGTg-K-",
        "outputId": "a93f0bee-327e-4fca-80fd-b39775154d24"
      },
      "source": [
        "%%time\n",
        "max_radius = 17\n",
        "precision = {i:[] for i in range(max_radius)}\n",
        "average_distance  = {i:[] for i in range(max_radius)}\n",
        "query_time  = {i:[] for i in range(max_radius)}\n",
        "\n",
        "num_queries = 10\n",
        "for i, ix in enumerate(np.random.choice(corpus.shape[0], num_queries, replace=False)):\n",
        "    print('%s / %s' % (i, num_queries))\n",
        "    ground_truth = set(brute_force_query(corpus[ix,:], corpus, k=25)['id'])\n",
        "    # Get the set of 25 true nearest neighbors\n",
        "    \n",
        "    for r in range(1,max_radius):\n",
        "        start = time.time()\n",
        "        result, num_candidates = query(corpus[ix,:], model, k=10, max_search_radius=r)\n",
        "        end = time.time()\n",
        "\n",
        "        query_time[r].append(end-start)\n",
        "        # precision = (# of neighbors both in result and ground_truth)/10.0\n",
        "        precision[r].append(len(set(result['id']) & ground_truth)/10.0)\n",
        "        average_distance[r].append(result['distance'][1:].mean())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 / 10\n",
            "1 / 10\n",
            "2 / 10\n",
            "3 / 10\n",
            "4 / 10\n",
            "5 / 10\n",
            "6 / 10\n",
            "7 / 10\n",
            "8 / 10\n",
            "9 / 10\n",
            "CPU times: user 1min 31s, sys: 1.01 s, total: 1min 32s\n",
            "Wall time: 1min 31s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 926
        },
        "id": "_VMpA4itg-K_",
        "outputId": "45fda8e6-ae4b-49df-8bba-7b519da127d0"
      },
      "source": [
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(range(1,17), [np.mean(average_distance[i]) for i in range(1,17)], linewidth=4, label='Average over 10 neighbors')\n",
        "plt.xlabel('Search radius')\n",
        "plt.ylabel('Cosine distance')\n",
        "plt.legend(loc='best', prop={'size':15})\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()\n",
        "\n",
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(range(1,17), [np.mean(precision[i]) for i in range(1,17)], linewidth=4, label='Precison@10')\n",
        "plt.xlabel('Search radius')\n",
        "plt.ylabel('Precision')\n",
        "plt.legend(loc='best', prop={'size':15})\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()\n",
        "\n",
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(range(1,17), [np.mean(query_time[i]) for i in range(1,17)], linewidth=4, label='Query time')\n",
        "plt.xlabel('Search radius')\n",
        "plt.ylabel('Query time (seconds)')\n",
        "plt.legend(loc='best', prop={'size':15})\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SqKjbOlfg-K_"
      },
      "source": [
        "The observations for Barack Obama generalize to the entire dataset."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "snaqOPJig-LA"
      },
      "source": [
        "## Effect of number of random vectors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TlUY_c5eg-LA"
      },
      "source": [
        "Let us now turn our focus to the remaining parameter: the number of random vectors. We run LSH with different number of random vectors, ranging from 5 to 20. We fix the search radius to 3.\n",
        "\n",
        "Allow a few minutes for the following cell to complete."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nRz5ABvdg-LB",
        "outputId": "8211e410-b65d-4161-8f26-59e3e77c1cd0"
      },
      "source": [
        "precision = {i:[] for i in range(5,20)}\n",
        "average_distance  = {i:[] for i in range(5,20)}\n",
        "query_time = {i:[] for i in range(5,20)}\n",
        "num_candidates_history = {i:[] for i in range(5,20)}\n",
        "ground_truth = {}\n",
        "\n",
        "num_queries = 10\n",
        "docs = np.random.choice(corpus.shape[0], num_queries, replace=False)\n",
        "\n",
        "for i, ix in enumerate(docs):\n",
        "    ground_truth[ix] = set(brute_force_query(corpus[ix,:], corpus, k=25)['id'])\n",
        "    # Get the set of 25 true nearest neighbors\n",
        "\n",
        "for num_vector in range(5,20):\n",
        "    print('num_vector = %s' % (num_vector))\n",
        "    model = train_lsh(corpus, num_vector, seed=143)\n",
        "    \n",
        "    for i, ix in enumerate(docs):\n",
        "        start = time.time()\n",
        "        result, num_candidates = query(corpus[ix,:], model, k=10, max_search_radius=3)\n",
        "        end = time.time()\n",
        "        \n",
        "        query_time[num_vector].append(end-start)\n",
        "        precision[num_vector].append(len(set(result['id']) & ground_truth[ix])/10.0)\n",
        "        average_distance[num_vector].append(result['distance'][1:].mean())\n",
        "        num_candidates_history[num_vector].append(num_candidates)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "num_vector = 5\n",
            "num_vector = 6\n",
            "num_vector = 7\n",
            "num_vector = 8\n",
            "num_vector = 9\n",
            "num_vector = 10\n",
            "num_vector = 11\n",
            "num_vector = 12\n",
            "num_vector = 13\n",
            "num_vector = 14\n",
            "num_vector = 15\n",
            "num_vector = 16\n",
            "num_vector = 17\n",
            "num_vector = 18\n",
            "num_vector = 19\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "HY7mVKRcg-LC",
        "outputId": "f51e825c-b4e7-4aac-a8bc-001d4f81b10c"
      },
      "source": [
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(range(5,20), [np.mean(average_distance[i]) for i in range(5,20)], linewidth=4, label='Average over 10 neighbors')\n",
        "plt.xlabel('# of random vectors')\n",
        "plt.ylabel('Cosine distance')\n",
        "plt.legend(loc='best', prop={'size':15})\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()\n",
        "\n",
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(range(5,20), [np.mean(precision[i]) for i in range(5,20)], linewidth=4, label='Precison@10')\n",
        "plt.xlabel('# of random vectors')\n",
        "plt.ylabel('Precision')\n",
        "plt.legend(loc='best', prop={'size':15})\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()\n",
        "\n",
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(range(5,20), [np.mean(query_time[i]) for i in range(5,20)], linewidth=4, label='Query time (seconds)')\n",
        "plt.xlabel('# of random vectors')\n",
        "plt.ylabel('Query time (seconds)')\n",
        "plt.legend(loc='best', prop={'size':15})\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()\n",
        "\n",
        "plt.figure(figsize=(7,4.5))\n",
        "plt.plot(range(5,20), [np.mean(num_candidates_history[i]) for i in range(5,20)], linewidth=4,\n",
        "         label='# of documents searched')\n",
        "plt.xlabel('# of random vectors')\n",
        "plt.ylabel('# of documents searched')\n",
        "plt.legend(loc='best', prop={'size':15})\n",
        "plt.rcParams.update({'font.size':16})\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9+vQhPDw8byBXREQEV1xxRd7lzg0bNrBy5UqGDBmSd56kpCSmTJlCaGiox9e8efPYtWuXx3N6D/A5duwYF110Ebt27WLChAn8/PPP/Pbbb3Ts2JG0tLS882dnZ+O9Ipr349x6VapU8YjjpptuIisri717fa8bs3fvXmJiYoiKisoXa2pqKunp6YDzRz0pKYkffvgBcD6UnH322TRo0CDv+QHatm3r8fy5l7Xd34viHOhUrVo1jh8/nu/DxuHDh4mKisr7oFWQqlWrejwOCwtDVfNed1JSEosWLcr3+33vvffy/X5z5Y7iLup3VlgMub//XDExMfmWoK1Zs2be7zX3u/d7m/v40KFD+crcvfbaa1x55ZU8+eSTtGzZkubNm/Ppp5/mq2fKro8W7eDBz35H3RJxcJDw8pCzGHhWvcAFht0zLjUne6+2LMhNuL6mo0ybNo2XX36Z4OBgBg8ezOWXX87OnTuZMmUKNWrUoF+/fnl1Y2NjGTBgAI8++mi+81SqVMnjsfdcvoULF7J7927mzJlDq1at8sqPHDmS93NcXBzBwcF4rxXu/Tg2NpaQkBAWLFjgc+BTzZq+d2SpU6cOx48fJzU11SMhJyYmEhUVRXh4OABNmzYlISGBKVOm0KtXL7744gvGjRvn8fwAX375pc8/9i1btizwfTgdrVq1Ijs7m82bN3s8x/r16z3e01MVGxtLQkIC//lP/un+ue+Nt9x7uEX9zk7G8ePHOXHihEdC3r9/P3XqOIvu5X7fv38/1avnLXFPYmJi3uvI5ev9r1q1Kq+88gqvvPIKq1at4oUXXmDo0KF06NCBNm1Oa18ZUwreW7CNJ77wXMspJEh49bqz6N++TgGtSo/1jI1PKSkpfPHFF1x33XXMmzfP42vChAkkJibm9QAvuugiqlatytSpU5kyZQpXX3113uArgPPPP581a9bQtm1bEhISPL7ck4MvudOb3P+o//LLLx6jbUNCQjjrrLOYOXOmR9tZszzXkenXrx/Z2dkcOXIkXxwJCQkF9hC7du2KiDB9+vS8MlVl+vTp9OrVy6PukCFD+Pzzz/n88885ceKExweZs88+m8jISP744w+fz+/9waS4nHPOOVSuXNnjVkJqaipffPEF/fv3P+3zn3/++WzevJkGDRrke03t27f32aZ+/frUrl27yN/Zyfr888/zfj5+/Dhz5syhWzdnL5l27doRFRXl8T6AM0CtRYsWBfbKfenQoQPjx48nJyeH9evXn1bMpuS99dPWfIk4NFj4z7AuZSIRg/WMTQFmzpxJamoqo0ePpnv37h7HevbsyTPPPMPkyZO58MILCQ0N5aqrrmLChAns3bs3b5RtrnvvvZePPvqIfv36cddddxEfH09iYiI//vgjvXr18hjF6q1Hjx7ExMQwcuRIxowZw+7duxk7dizx8fEe9R566CEGDRrEqFGjGDBgAAsWLOCrr5wR7Lm94JYtW3L77bczZMgQxowZQ0JCAmlpaaxZs4aNGzfy9ttv+4yhdevWXHfddYwaNYpjx47RtGlT3nrrLdavX5+vN3jttdfywAMP8MADD9C7d++83hg4PauxY8cyevRoduzYQe/evcnJyWHjxo3MmzfPI5H4KzU1la+//hqAPXv2cPTo0bwPDZdccglRUVFERETwj3/8g6eeeopq1arRqlUrJkyYQE5ODnfddddJP6e3G2+8kYkTJ9KnTx/uv/9+mjRpwsGDB1m8eDG1a9fm73//e742wcHBee9TjRo16NmzJ7NmzeL3338H/Juy5S0yMpKHH36Y48ePU7duXf71r3+RkZHB6NGjAafne8899/D0008TEhJCQkICM2bM4Ouvv/Zr/nyvXr0YOHAg7dq1Q0R46623iI6Ozkv2pmz6v3mbGf/tBo+ysJAg3hjWhb6tSm5/4pPma1SXfRX/aOry5rLLLtPmzZsXePyOO+7QKlWqaFpamqqqzpkzRwGtW7euZmdn56u/Z88evemmm7RmzZoaFhamDRs21KFDh+rq1atV9c9Rs1988UW+trNnz9a2bdtqRESEtm/fXr/66is977zzdNCgQR71XnnlFY2Pj9fIyEjt37+/Tp06Nd+o2JycHH3ppZe0TZs2GhYWpnFxcdq7d2+dNGlSoe9HSkqKjho1Ki/+Ll266DfffOOzbs+ePRXQiRMn+jz+4YcfaufOnTUiIkKrVq2q3bp10xdffDHv+PDhw7Wwf1vuct83X1+5I5JzX/fTTz+t8fHxGhERob169dJly5YVef6GDRvqfffd51H23nvvKaDHjh3LK0tOTta7775b69Wrp6GhoRofH68DBw7U+fPn59XBbTR1bkwPP/ywxsXFaUxMjF5//fX6+uuvK6CHDx/2eH3e/y6836PHH39cq1evrj/99JN27NhRw8LCtEOHDvrjjz96tMvKytLHHnssL87WrVvrRx99VOi5c91///3arl07jYmJ0SpVqmifPn30p59+KvI9LO9/C8qzl+dszDejpMXDX+tPG/cHLCYKGE0tquojRRt/JCQkaEGjRdetW0fr1q1LOSLj7umnn+aZZ57h0KFDtrd0OXHLLbcwZ84cduzYEehQio39LSh9qsqEORt59QfPtfQjQ4N556YEzmkauHXMRWSpqiZ4l9tlanNGOHDgAM8++yx9+/YlKiqKn3/+meeff56bb77ZEnEZtXr1aqZMmcI555xDUFAQs2fP5r333uP5558PdGimHFNVnvtmPW/8uNWjPDosmPf+2o1ujWMLaBlYlozNGSEsLIz169fzwQcfcOTIEerUqcPo0aN56qmnAh2aKUB0dDTz58/ntddeIyUlhYYNG/L8889z3333BTo0U06pKk99uY53F2zzKK8UHsL7I7rRpaH39vVlhyVjc0aoUqVK3kAmUz40btyYefPmBToMc4bIyVEen7WGDxd53uKoHBHChzd3p2P9qgW0LBssGRtjjCnXcnKUh//7O5MXey4yUzUqlI9u7k67+CoBisx/loxLkKqW+IbUxpiyywbIlrzsHOXBz1Yxfann8qix0WF8fEt3WtepHKDITo4t+lFCQkNDbT9eYyq4EydO5K3RbopfVnYO905dkS8Rx8WE8+mtPcpNIgZLxiWmZs2a7Nmzh9TUVPt0bEwFo6qkpqayZ8+eApdZNacnMzuH0VNWMHPFHx7ltSqHM+W2HrSoVTIr2pUUu0xdQipXdj6R/fHHH3m72xhjKo7Q0FBq1aqV97fAFJ+s7Bzunryc2av3eZTXrRLBJyN70CguOkCRnTpLxiWocuXK9h/RGGOKUU6O8uBnv+dLxPFVI/n01h7Uj40qoGXZZsnYGGNMuaCqPPXVWj5b5nmPuEFsFJNv7UF81fK7wI8lY2OMMeXCv7/fxHsLtnuU1asWyZTbelCnSvlNxGADuIwxxpQD7y3YxstzN3mUxcWE89HN3ct9IgZLxsYYY8q4z5buzrcfsbOyVrdyOVjLF0vGxhhjyqzv1uxjzGerPMoiQ51NH8rTPOKiWDI2xhhTJv2yJYlRk5eTnfPnWg2hwcIbN3Qp05s+nIpST8YiUl9EpovIERE5KiIzRKSBn20bu9omi0iKiMwTkQSvOi1E5N8iskpEjovIXhGZJSIdfZzvfyKiPr7uKa7Xa4wx5uSt2JXMyElLyMjKySsLEvj3kLPo3aJGACMrGaU6mlpEooAfgHRgOKDA08A8EemgqimFtK0OzAeOAbcBqcC9rrbdVHWdq+pFQF9gErAMqAqMARaJSC9VXep16lWu87nbfsov0hhjzGnZlHiMm95bTEpGtkf5s1e155L2dQIUVckq7alNI4EmQEtV3QwgIquATTgJcUIhbe8AagG9VXWLq+0PwFbgCeBaV71Pgf9TtzUoXfW2A6OBG73Oe0xVF53eyzLGGFMcdh1KZdg7v5Kc6rly4cOXtGZwV78uopZLpX2ZegCwKDcRA6jqNmABcEURbXsAm3ITsattCvAzcJmIhLjKktRrMWhVPQJsBOKL5VUYY4wpdvuPpjHsnV9JPJruUX5n36aM7N0kQFGVjtJOxm2B1T7K1wBtimibDWT4KE8HIoGmBTUUkVigHbDOx+GzXPevM133mW8uIg5jjDHF7EhqJje+u5gdB1M9yof1aMD9F7UMUFSlp7STcSxw2Ef5IaCooXEbgOaue8cAiEgQ0M3t3AV5FRDgZa/yn4B7cHrsV+NcLn9bRB4p6EQicquILBGRJQcOHCgiZGOMMUVJzcjir+8vZv2+Yx7lAzrW5ckB7SrEvvDlaWrTRJx4PxCRpiJSB3gFaOw6nuOrkYg8BFwPjHK/PA6gqo+p6luq+qOqzlTVQcB/gYdFJMbX+VT1TVVNUNWEGjXOvBF9xhhTmtKzsrntw6Us25nsUd6vVU1evLYjQUFnfiKG0k/Gh/HdAy6ox5xHVbcCQ4EuwGbgD+Bs4CVXlb3ebUTkdmAc8IiqvutnjJOBCKC9n/WNMcacguwc5e9TVvDzpiSP8m6NY3l9aGdCg8tTf/H0lPYrXYNz39hbG2Ctj3IPqvoZziCsNkAzVe0CxAC7VHWne10RuQF4HXhRVZ85hVi16CrGGGNOharyzxm/8/XvnlshtouvzNvDE4gIDQ5QZIFR2sl4FtBDRPKGxYlII6Cn61iRVDVbVdep6hYRqQsMBv7jXkdEBgLvAW+r6v0nGeNQ4ATw+0m2M8YY4wdVZdzX65iyZJdHeZMa0Uz6azcqR4QGKLLAKe15xm8Bo4CZrkFSCjwF7ALeyK0kIg2BLcCTqvqkqywUeAH4ETiK08N+CKe3/aJb2944l5pXAu+LSA+3509X1eWueucC/wBm4MxBroKzEMkA4B+FLUBijDHm1L3+vy289fM2j7K6VSL48ObuVI8JD1BUgVWqyVhVU0SkH8593g9xRjh/D9yjqsfdqgoQjGfPXYHmOIOxqgK7gXeBcarqPuWpHxAOdMaZv+xuB9DI9fNe1/mfBOKATJzVuK5X1cmn9UKNMcb49OGiHYz/doNHWfXoMD68pTvxVcv/VoinSrzWxzAnISEhQZcsWRLoMIwxplyYuWIP90xZgXvaqRQewuRbe9AuvkrgAitFIrJUVRO8yyvOUDVjjDEB88P6RO6butIjEYeHBPHOTV0rTCIujCVjY4wxJerXrQe546NlZLlthRgSJEwc1oVujQtbr6nisGRsjDGmxKzec4RbJi0h3W0rRBGYMLgTfVvVDGBkZYslY2OMMSVi8/7j3PjuYo6lZ3mUP3VFOwZ0rBugqMomS8bGGGOK3Z7kE9zwzq8cSvHc3+eBi1syrEfDAEVVdlkyNsYYU6ySjqdzw9u/svdImkf5bb2b8Lc+BW6wV6FZMjbGGFNsklMzuPGdxWxN8lw3aUjX+vyjf6sKsQPTqSjtFbiMMcacYXJylIVbDzJ96W6+Wb2PE5nZHscvbV+HZwa2t0RcCL+TsYicBTwK9MZZAaubqi4TkXHAT6r6TQnFaIwxpgzanpTCZ8t2M2PZHvYkn/BZ59zmcbw0uBPBFWQrxFPlVzIWkV7AXGAr8AnO+tK5coDbAUvGxhhzhjuWlslXq/YyfeluluwodOdbOjeoyhs3dCEsxO6IFsXfnvFzwLfAlThrRrsn42XAjcUclzHGmDIiO0dZuOUg05fu4ps1+0jLzCm0ft0qEVzbtT63n9e0wm2FeKr8TcadgatUVUXEezHrJKBG8YZljDEm0LYeOJ53Gdp7ZLS3iNAg+rerw9Vd6nF2k+oE2WXpk+JvMk4Dogo4Vgc4UjzhGGOMCaSjbpehlxZxGRqgW6NYru5Sj/7ta1OpAu5DXFz8TcbzgXtEZKZbWW4P+Wbgh2KNyhhjTKnJzlEWbE5i+tLdfLtmn8fSlb7EV41kUOd4rupcj0Zx0aUU5ZnN32T8KM7ewCuB6TiJeLiITAC6AF1LJjxjjDElZcuB43y21LkMve9o4ZehI0OD6d++Nld3qUePxnYZurj5lYxVdaWI9AbGAw8DgjOI62fgPFXdUFh7Y4wxZcORE5l8ueoPpi/dzfKdyUXW79bYuQx9Sfs6xITb0hQlxe93VlWXAeeLSAQQCySramqJRWaMMabYHEnN5Mkv1/LFqj/IKOIydL1qkQzqXI9BnevRoPoN/V4AACAASURBVHpBw4VMcfJ3nnEoEKaqKaqaBvzhdiwayFDVzBKK0RhjzGlIz8pm6DuLWL3naIF1osKCuaR9HQZ1rkf3xrF2GbqU+dszfhsIBa73cewNIAMYUVxBGWOMKT7Pz95QYCLu0SSWq7vUp3+72kTbZeiA8fed7ws8UMCxWTj3ko0xxpQxP6xP5N0F2zzK6lWL5OouzmXo+rF2Gbos8DcZ1wT2F3DsAFCreMIxxhhTXBKPpnH/tFUeZfFVI/nq7nOpEmlzgssSfxcM3Q+0L+BYe+Bg8YRjjDGmOGTnKPd8uoJDKRl5ZcFBwivXnWWJuAzyNxl/CTwqIh3cC0WkPc5Upy+KOzBjjDGnbuKPW1i41bOfdO+FLejSsFqAIjKF8TcZPwYkA0tF5BcRmSoiC3A2iTgCPOLvE4pIfRGZLiJHROSoiMwQkQZ+tm3sapssIikiMk9EEnzUCxKRh0Rku4ikichKERlUwDlHish6EUkXkQ0icru/r8UYY8qipTsOMWHORo+yns2qc8d5TQMUkSmKX8lYVZNwVtl6FmfBj06u788AXV3HiyQiUThLZ7YChgM3AM2Bea4pUoW1rY6zLGc74DZgiOvQPBFp7VX9KWAs8BrQH1gETBORS7zOORJnNPhnwF+AacDrInKHP6/HGGPKmiMnMrl78gqyc/7c0yc2OowJ13ay6UplmKh6b8JUgk8mMhqYALRU1c2ussbAJmCMqk4opO0jOAm2papucZVF4+yx/KOqXusqqwnsAp5T1cfd2n8P1FDVDq7HITjzpWer6nC3eu8CA4A6Rc2dTkhI0CVLlpzcm2CMMSVEVbnzk2V8/fs+j/L3bupK31Y1AxSVcSciS1U13xXd0t7xeQCwKDcRA6jqNpx1r68oom0PYFNuIna1TcFZkvMyV3IFuBgIAz7yav8R0N6V/AHOxtn60bveh0B1oJe/L8oYY8qCyYt35UvEN/dqbIm4HPA7GYvIcBH5RkTWishWr68tRZ8BgLbAah/la4A2RbTNxllcxFs6EAnk3gxp6yrb7FVvjet7G7d6+IjHu54xxpR5GxOP8cQXazzK2sVXZsxfWgYoInMy/F0O81HgCZzEtQIn2Z2KWMDXBpmHgKKG+G0ALhSR6qp60BVXENDN7dy535M1//X3Qz7q4SMe73rGGFOmpWVmc9cnyz22PowKC+aVIWcRHhIcwMiMv/xd9ONm4N+q+veSDKYIE4G7gQ9E5G4gFWdaVe5l58JXPi8mInIrcCtAgwZ+DQI3xpgS9fRXa9mQeMyj7Kkr2tGkRkyAIjIny9/L1NUpnrnEh/HdAy6ox5xHVbcCQ3H2T96MM/jqbOAlV5W9bs9RVUS8hw3m9nQPudXDRzze9bzjeFNVE1Q1oUaNGoWFbIwxJe6b1Xv5aNFOj7KBZ8UzqEu9AEVkToW/yfhHoGMxPN8a/rxX664NsLaoxqr6GRDvqt9MVbsAMcAuVc3917gGCOfPe8juz4Hb8+TeXPGOx7ueMcaUSXuSTzBmuudyl42qR/HUle0CFJE5Vf4m43uAv4rIjSIS51pUw+PLz/PMAnqISJPcAhFpBPR0HSuSqmar6jpV3SIidYHBwH/cqnwDZOL0ot0NA1a7Rm8DLASSCqh3CGeEtzHGlElZ2TmMnryco2lZeWWhwcKr13UmxnZfKnf8/Y3lLuXyXgHH1c9zvQWMAma65g0rzgIdu3AW3wBARBoCW4AnVfVJV1ko8AJOL/0oTo/2IZwe7ot5gajuF5EJwEMicgxnlbDBQD+cqVW59TJdA9NeF5E9wFxXnRHAXarqa+S2McaUCa/8sJklOzzv7o25uBXt61UJUETmdPibjJ/ESZynRVVTRKQfzn3eD3FW8foeuEdVj7tVFSAYz5674qzWdT1QFdgNvAuM85E4HwaOA6OB2jgjsa9V1S+94pkoIgrch7NF5E5glKq+frqv1RhjSsqirQd57YdNHmXntajBzb0aF9DClHWlugLXmcZW4DLGlLbDKRn0//fP7DualldWo1I4s0efS1xMeAAjM/4oKytwGWOMOUWqygPTV3okYhF46dpOlojLOb/v8otIGM6mCy2BCK/DqqpPFWdgxhhjPE36ZTtz1+33KLutd1N6NY8LUESmuPi7AlddnB2TGuHcu82dw+t+jduSsTHGlJA1fxxh3NfrPco61a/KfRe1CFBEpjj5e5l6PHAAaICTiLsDTXC2UNzs+tkYY0wJSM3I4q7Jy8nI/nOhwUrhIbx63VmEBtvdxjOBv5epzwXux1n1CiBHVbcDj4lIMPAKRe+6ZIwx5hSMnbWGrQdSPMrGXdWe+rFRAYrIFLeTWQ7zD1XNAVLwXELyB6BPMcdljDEGmLXyD6Yu2e1Rdm1CPS7vWDdAEZmS4G8y3g3kjhDYAlzkdqwbkJavhTHGmNOy82Aq/5zxu0dZ0xrRjB3ga1VhU575e5l6HnAe8F+clbL+T0Q64Sw7eTFuq2cZY4w5fZnZOdz16XKOp/+53GVYSBCvXteZqDBb7vJM4+9v9BFcuxmp6n9EJARnickonCUqnyyZ8IwxpmJ68buNrNyV7FH28CWtaVO3coAiMiXJr2Ssqkk4myrkPn4VeLWkgjLGmIrs500HmPjjFo+yC1rX4sazGwYoIlPS/LpnLCI/iEirAo61EJEfijcsY4ypmA4cS+fvU1Z6lNWuHMH4qzuQf5t2c6bwdwBXH6CgayOVcO4nG2OMOQ05Ocp901aSdDw9ryxI4OUhnagWHRbAyExJO5nZ4gXtKNEUZ4ckY4wxp+Ht+Vv5aeMBj7JR/ZrTo0n1AEVkSkuB94xF5K/AX10PFXjTtT+wu0igHc42iMYYY07Ryl3JvPDNBo+yro2qcXe/ZgGKyJSmwnrGOUC260u8Hud+HQT+A9xcsmEaY8yZ61haJnd/upysnD8vQFaJDOXlIWcRYstdVggF9oxVdRIwCUBE5gF3qOr6guobY4w5eTk5yqP/Xc2Og6ke5c8P6kB81cgARWVKm79Tm/r6KheR6qp6sHhDMsaYM1taZjYLtxxkzrpEvl+XSOLRdI/jw3o04C/tagcoOhMI/m6hOBKoqqrjXY/bA7OBOiKyHLhMVfeVXJjGGFO+HUrJYN76/cxZm8hPmw6QmpHts17LWpV45NI2pRydCTR/V+C6C3jT7fEEIBl4HrgbZwWuW4s3NGOMKd+2JaUwd20ic9YmsmTHIXIKmpPiEhUWzKvXn0VEaHDpBGjKDH+TcUNgPYCIVMGZV3ylqn4tIgeBZ0soPmOMyUdV2X8sHRGoERNeZhbDyM5RVuw6zJy1+5mzdh9bvLY9LEhUWDDntajBAxe3pEmNmBKO0pRF/ibjIJzR1AC9cKY6/c/1eBdQs3jDMsYY39Kzsrn5/SXM3+ys0BsTHkKjuCgaVY+mcVy0871GNI2rR5fKQhknMrL5edMB5q5L5If1+0k6nuFXu1qVw7mgdS0uaFOLs5tUt95wBedvMt4EXIqzd/EQ4BdVzR36Vxc4VAKxGWNMPh8v2pmXiAGOp2exes9RVu85mq9ulchQGsVF08SVpBvFRTkJOy6ayhGhpxzD/mNp/LBuP3PXJfLzpiTSs3KKbgS0ql2Ji9o4Cbhd3SoEBZWNHr0JPH+T8b+AD0VkOFANuMbtWF9gVXEHZowx3rJzlPd/2e53/SMnMlm5Kznf7kcAcTFhrgTt9KgbuyVs7y0KVZXN+4/z3dpE5q5LZMWuZLSI+78AIUFC9yaxXNi6Fue3rkX92Ci/YzcVi79Tmz4RkZ1Ad+A3Vf3J7XAiMKskgjPGGHffr0tk56HUoiv6Iel4BknHM1iy43C+Y7Uqh+cl6PCQYOZt2J9vHnBBKoWH0KdVTS5oXZM+LWtSJfLUe+Cm4vB7h2pVnQ/M91H++Mk8oYjUB14CLsRZ2WsucI+q7vSjbQPgKZzeeA2c+9VTgWdVNcVVpw8wr5DTnK2qi1x13weG+6jzb1W9x8+XZIwpJe8t2O7xeFDnejz4l5ZsTUphe1IK2w66vielsP1gKhl+Xj72lng0ncSj6Sza6t8duPiqkVzYphYXtK5Ft8axhIXYqlnm5BS2NnUDYK+qZrp+LpSfyTQK575zOk4SVOBpYJ6IdMhNqAW0jcZJ3KHAo8BOoCvwBNAcGOyqugw428cp3gFigd+8yg8AA7zK9hb1WowxpWvtH0dZuNVzjaERvRpRs3IENStH5NtMISdH2Xs0LS85b3NL2LsOpZKZ7cd15kK0j6+Sl4Bb16lUZkZ0m/KpsJ7xNpykthjYTsG7NuXyZyjgSKAJ0FJVNwOIyCqcAWK34cxfLkhPnKR7sap+5yqbJyKxwP0iEqWqqap6FFjk3lBEGgKtgRdV1XumfUZuT9kYU3a9t2Cbx+PujWNpW7dKgfWDgoT4qpHEV42kZ7M4j2NZ2TnsST6Rl6C3H0zNS9i7D6f6nA8cFhzE2U2rc2GbWpzfuiZ1qthSlab4FJaMRwBb3H4+vY+RjgHAotxEDKCq20RkAXAFhSfj3DkK3kMmk3GmXhX2sfQG1/FJJx2xMSbgko6nM3PlHx5lI3o1PuXzhQQH0bB6NA2rR0NLz2MZWTnsOpya16M+ciKT1nUq07tFDWLC/b6zZ8xJKWqjiNyf3y+m52sLzPRRvgbPEdq+zMXpQT8vInfgXKbuBowGJhZ2iRu4EVimqqt9HKspIklAVWArzuXsf/noQRtjAuSTX3d63P+tHxvJBa1rlchzhYUE0bRGDE1t8Q1Tikr7Y14skH/oojNPuVphDVU1TUR6AZ/hJO9cbwOjCmonImfjXN4e7ePwCmCp63wRwECc1cSaA7cUcL5bcS392aBBkbfSjTGnKT0rmw8X7fAoG352I4Jtjq45gxQ2gOvdkziPqmqJ7mksIhHAFJzVvm7gz57xY0AWcEcBTYcDmcAn3gdU9WWvoq9F5Dhwj4g8r6qbfLR5E9c63QkJCcVx6d4YU4ivVu3lwLE/dzWKDgvm2q71AxiRMcWvsJ5xPzzvE1cFquAkvoNAdVf7I/ju7fpyGN894IJ6zO5uBvoAzVQ19172TyJyBHhTRCaq6kr3BiISDlwLfKWqSfhnMnAPkIBzWdwYEyCqyrteA7euSah/WqtnGVMWFTgZTlUbqWpjVW2M0xM9jrMUZqSq1gEigeuAY8AwP59vDc59Y29tgLVFtG0PHHZLxLkWu7639tFmAE7yP5WBW9brNSbAluw47LHMpQjcdE6jwAVkTAnxd2b6BJyFNabmDmxS1WxVnYKzjaL35d6CzAJ6iEiT3AIRaYQzbamoVbz2AdVEpJlXeXfX9z0+2gwHkoCv/IwPYChOIvaej2yMKWXvzvfsFZ/fqiaN4qIDFI0xJcffZNwe2FzAsU1AOz/P8xbOnOWZInKFiAzAGV29C3gjt5KINBSRLBF5zK3t+zi98K9FZLiI9BWRB3DWzV4KLHB/IhGpCVwMTFbVTO9AXM/xk4j8TUQuEpHLXffJ7wLe8NEDN8aUol2HUvl2zT6PshE9T306kzFlmb/JeB/OvVdfhuCsT10k1/SjfsBG4EPgY5zFRfqp6nG3qoKziEiQW9vtQA+cEdBPA1/jLCLyJnChqnqvezcU5552QZeoj+GM4n4Qp1c+BegE3A3c6c/rMcaUnA8X7fBYfKNV7Uqc3bR6wQ2MKcf8ndr0MvCSiNQBpuEk31o4CfpinAFPfnEtmzmoiDrb8bGIh6qupeAPBd51X8JZA7ug44eAK/05lzGmdKWkZzF5secKuyN6NrYlJ80Zy99dm/7tmvLzONDf7dAuYKSqnsw0KGOMKdRny3ZzLC0r73FsdBgDOtUNYETGlKyT2bXpHdc91XpAHZzNFHar+rOrpzHG+CcnR/PtzjS0ewMiQv1Z/t6Y8umkVuByJd5dri9jjCl2P248wLakP1e3DQ0WhvVoGMCIjCl5tummMaZM8V7k49L2dahVOSJA0RhTOiwZG2PKjI2Jx/h5k+dieaezO5Mx5YUlY2NMmeF9rzihYTU61KsamGCMKUWWjI0xZcLhlAxmLNvtUWa9YlNRWDI2xpQJnyzeSbrbnsXxVSO5qE3J7FlsTFnjdzIWkXgRmSAiS0Rkq4i0c5XfIyLdi2pvjDEFyczO4cOFnnsW33h2Q0KCrb9gKga//qWLSFvgd5zdm/4AGgJhrsMNgdElEp0xpkKYvXof+46m5T2ODA1mSNcGAYzImNLl78fOF4F1QGPgKjyXqvwFZ81oY4w5Jd67M13dpR5VomzPYlNx+LvoRy/gOlU9LiLey+AkArWLNyxjTEWxbOdhVuxK9ii7qWejwARjTID42zP23hHJXRxwohhiMcZUQN694j4ta9C0RkyAojEmMPxNxouBvxZw7Fq89hI2xhh/7D1ygtmrbc9iY/y9TP0UMFdEvgM+ARS4QERGAwOB3iUUnzHmDPbBwh1ku21a3KxmDOc2jwtgRMYEhl89Y1X9EWfv38bAuzgDuJ4DzgWuVNVfSyxCY8wZ6URGNp/86rln8V97NrI9i02FdDJbKH4FfCUizYCawEFV3VBikRljzmgzlu/myInMvMdVIkO56qx6AYzImMA5qS0UAVR1M7C5BGIxxlQQqvn3LL6+ewMiw2zPYlMx+Z2MRaQycAnQAPDez0xV9aniDMwYc+b6eVMSm/cfz3scHCTcYHsWmwrMr2QsIj2BL4CCtk9RnEFexhhTJO89i/u3q03dqpEBisaYwPN3atPLwHagKxChqkFeX3ZtyRjjly0HjvO/DQc8ymx3JlPR+XuZujVwraouLclgjDFnvve97hV3ql+Vzg2qBSYYY8oIf3vGO4HwkgzEGHPmO5KayfSlnnsW/9WWvjTG72T8BPAP1yAuY4w5JZ/+tpMTmdl5j2tVDueS9nUCGJExZYO/yfgyoBawTUS+FJEPvL4m+fuEIlJfRKaLyBEROSoiM0TEr73SRKSBiEwSkZ0ickJENorI0yIS7VXvfyKiPr7u8XHOK0VkuYikicgOEXnEx2YYxpjTlJWdwwf59ixuRKjtWWzMSe3apMBRoK2P4+qjLB8RiQJ+ANKB4a52TwPzRKSDqqYU0jYamAuEAo/iXDrvitNrbw4M9mqyCrjNq2y71zkvBj4D3gHuBc4CxgGVgAf9eU3GGP98tzaRPcl/7ikTHhLE9d1sz2JjwM9krKrFNdRxJNAEaOlaPAQRWQVswkmcEwpp2xMn6V6sqt+5yuaJSCxwv4hEqWqqW/1jqrqoiHieA+ar6q1u54sBHhGRl1R1XyFtjTEnwXt3pqs6x1MtOixA0RhTtpT29aEBwKLcRAygqttwdn26ooi2uf9rj3qVJ+O8jpNa0FZE6gOdgI+8Dn2I0/vufzLnM8YUbNXuZJbsOOxR9lfbncmYPAUmY9f92VC3nwv98vP52gKrfZSvAdoU0XYuTg/6eRFpIyIxItIPGA1M9HGJ+yzXfelMEVklIjf7iAXveFwfDlL9iMcY4yfvpS/PbR5Hi1qVAhOMMWVQYZeptwFn4+xlvJ2i7wv7M+gpFjjso/wQUOhEQ1VNE5FeOPd417gdehsY5VX9J+BjYCPOqmE3Am+LSB1VfdotFgqI57DbcQ8icitwK0CDBna/y5iiJB5N48tVf3iU2XQmYzwVloxHAFvcfvZrkFZJEZEIYArOjlE34Azg6gY8BmQBd+TWVdXHvJrPFJHPgYdF5GVVPc4pUtU3gTcBEhISAvqeGFMefLRoB5nZf/5XaRwXTZ8WNQMYkTFlT4HJWFUnuf38fjE932F894AL6jG7uxnoAzRT1dwPCT+JyBHgTRGZqKorC2k/GWdP5vbAQrfn8xVPNZzeujHmNKRlZvOxjz2Lg4Jsz2Jj3J3yAC7XfdtBIlL3JJqtwffUqDbA2iLatgcOuyXiXItd31v7GUPuR/TcS90e8YhIIyDKj3iMMUWYteIPDqVk5D2uFBHCoM62Z7Ex3vxKxiLymohMdHt8FbASmAasFZGufj7fLKCHiDRxO1cjnGlLs4pouw+oJiLNvMq7u77vKaL9UOAE8DuAqu7EeQ1DveoNAzKB2UWczxhTCFXNtzvTkK71iQ4/6W3UjTnj+dsz7g/84vb4CeBLoCNOz/RxP8/zFs5gsJkicoWIDABmAruAN3IriUhDEckSEfd7v+8Dx4CvRWS4iPQVkQeAfwFLcaZHISLnishXInKziJwvIleJyEycaVVPeI26/idwnoi8ISJ9ROTvwCPAv22OsTGnZ+GWg6zfdyzvcZA4K24ZY/Lz9yNqHVyrV4lIPZxLuzer6u8i8grOClZFUtUU13Skl3Dm8wrwPXCP16AqwRmdHeTWdruI9ADG4qzaFYeTxN8EnlHVHFfVva52T7rqZOKsxnW9qk72iudrEbka58PETUAizgpcz/jzeowpLzbvP8bEH7eSlZ1DQqNYzmlancZx0YiU3L3bd72mM13ctjb1Y6NK7PmMKc/8TcapQIzr5/NwFt5Y4np8HGf5SL+4Lg8PKqLOdnws4qGqa4Fri2i7mZNYsENVZwAz/K1vTHkzc8Ue/vHZ73kbNPx3hTPNqE6VCM5uWp2eTeM4p1l16lSJLLbn3J6UwvfrEz3KbJEPYwrmbzJeBtwpIjuBO4E5bj3Rxji9UWNMGZKRlcO4r9fx/i/bfR7feySNGcv2MGOZM9yicVw05zStTs9mcfRoUp3Y01iq8v1ftqNuE//axVemayPbs9iYgvibjB8GvsEZ8JQM3O527Er+HNFsjCkDEo+mcefHy/ItQVmYbUkpbEtKyZuK1KZO5bzk3LVxLDF+Drw6mpbJtCW7PMpG9GxcopfEjSnv/N0o4jfXkpetgE2q6r4+9Js4y1QaY8qAX7ce5M5PlpN0PN2jPCwkiGHdG7Jp/zF+236ItMycAs7gWLv3KGv3HuXt+dsIDhI61qtCz2ZxnN20Op0bVCMi1Peie9OW7CYl4889i2tUCufSDrZnsTGF8XuOgWsU8lIf5V8Va0TGmFOiqrwzfxvPzl5Pdo7n4nDxVSOZOKwL7etVASA9K5vlO5P5ZctBFm5JYvnOZLJyCl5QLjtHWbYzmWU7k3n1h82EhwSR0Kga5zSN45ym1WkfX4WQ4CCyc5T3f/GczjSse0PCQ2yLcGMK43cyFpH2OKOOz8NZoeowMA94UlV9bf5gjCklx9OzeHD6Kr76Pf/wjd4tavDvwZ08tisMDwmmR5Pq9GhSHS5sQUp6Fou3H2LhloMs2JzE2r1HPe75ekvPymHB5oMs2HwQgErhIXRvEkvtKhHsOvTnnsVhwUEM7WFruBtTFL+SsWtRjx9xFs2YhbMAR23gcuBSEemtqvl6zcaYkrd5/3Fu/2gpm/fnX3L97vObM/r85gQXsfxkdHgIfVvWpG9LZ83owykZLNp6kF+2HOSXLUlsOeC9KZqnY+lZzF23P1/5FZ3qEhcTfhKvxpiKyd+e8bM4Ww2er6p5s/hFpBLO1obPAhcVf3jGmMLM/n0v909b6XGPFqByRAgvDe7E+a1rndJ5q0WH0b99Hfq3d+717juSxi9bkpzkvDmJP46k+XUem85kjH/8TcY9gBvcEzGAqh4TkeeBSb6bGWNKQlZ2Di98u4E3f9qa71jrOpWZOKwzDatHF9vz1a4SwVWd63FV53qoKjsOprLAlZwXbjnosf50rnOaVqdN3crFFoMxZzJ/k3FRWwXaVoLGlJIDx9K5a/IyFm3Nv7HYVZ3jeebK9kSGldyAKRGhUVw0jeKiGdq9ITk5yobEYyzYnMTCLQdZtecI9apF8uxV7UssBmPONKKFjdLIrSQyF6gC9PO6TB0N/AAcUdUKd5k6ISFBlyxZUnRFY4rJ0h2H+NvHy0g86jltKTRYePzytgzt3sDm8xpThonIUlVN8C73t2f8T+B/wA4R+RJnxa3awCU42w32KZ4wjTG+qCofLNzBU1+uzTcFqU6VCF4f2pmzGtgKV8aUV/4u+rHYtUnDY8DFQCxwCGdq01Oq+nvJhWhMxZaakcU/Z/yet6a0u3OaVueV686yEcvGlHMns+jHKuDqEozFGONlW1IKt3+4lA2Jx/Idu6NPU+67sAUhwf7uhGqMKasKTMYiEgRcCmwraFEP10IgjVT1ixKKz5gK67s1+7hv6kqOpWd5lMeEh/Cvazryl3a1AxSZMaa4FfaRehgwGShstv8xYLKIXFesURlTgWXnKOO/Xc+tHy7Nl4hb1Iph1qieloiNOcMUdpl6GPCeqm4rqIKqbheRd4DhOInbGHMaDqVkcPfk5czfnJTv2OUd6/LcVe2J9nP3JGNM+VHY/+rOwKt+nGMuMLR4wjGm4lqxK5m/fbQ03+pWIUHCw5e25qZzGtm0JWPOUIUl40o4m0EU5bCrrjHmFKgqkxfvYuysNWRke25rWKNSOK8P7UzXRrEBis4YUxoKS8ZJQENgfhHnaOCqa4w5SWmZ2Tz639VMW7o737FujWJ57fqzqFk5IgCRGWNKU2HJeD7OveCPizjHTRSdsI0xXtIys7ll0hKf94dv7tWYf/RvRahNWzKmQigsGb8MzBeRl4AHVdVjJXgRCQXGA/2AXiUXojFnnrTMbEZ+kD8RR4UF88LVHbisQ90ARWaMCYQCk7GqLhSR+4AXgaEi8h2ww3W4IXAhUB24T1UXlXikxpwh0rOyuf2jpfy8yTMRN4mL5o0butC8lg3BMKaiKXSOhKq+LCLLgAeBgUCk69AJnLWqn1PVn0s0QmPOIOlZ2dzx0TL+t+GAR3nLWpX4ZGR3qtuylsZUSEVOWFTVn4CfXCtyxbmKD6pqdiHNjDFeMrJyuPPj5fywfr9HefOaMXxsidiYCs3v0SGqmqOq+11fp5yIRaS+iEwXkSMiclREZohIAz/bNhCRSSKyU0ROiMhGEXnatZVjbp06IvKsiCwRkWQROSAi34tIbx/ne19E1MfXy6f6+ozxJTM7h7smL2PuukSP8qY1ovlk/2oZWAAAHGBJREFUZA/b6MGYCq5Ul/IRkSic/Y/TcUZqK/A0ME9EOqhqgUtvuhLuXCAUeBTYCXQFngCaA4NdVbu4fn4PWASEAX8D/iciA1T1S69THwAGeJXtPdXXaIy3zOwc7p68nG/XeCbiJnHRTB7ZgxqVLBEbU9GV9rp6I4EmQEtV3QwgIquATcBtwIRC2vbESboXq+p3rrJ5IhIL3C8iUaqaijPNqoWq5i3qKyLfAmuAMYB3Ms6wAWimpGRl53DPlBXMXr3Po7xxXDSTb+1hc4iNMcBJXKYuJgOARbmJGMC19vUC4Ioi2oa5vh/1Kk/GeR3iOl+yeyJ2lWUBK4D4Uw/dmJOTlZ3DvVNX8tUqzwstDatHMXlkD2pZIjbGuJR2Mm4L/9/enYdJVZ15HP/+uptVkB0VAQERAkYlsQUUdyNookmciZOocYILxkycuESjieK4LyOGxKgB4kKCBI0aRqNEEBQQxQUjqKBsiqCCsu97v/PHuSW3i+ru6qa7bnfxfp6nnqo699xb76nqrrfOveeeS6bLMc4Gelaw7kRCD/puST0lNZF0MnA5MKyCXdz1gaOBDzIsbitphaQd0THoayUVZtUa58qws8S45ql3eXbW56XKO7RsxJhBfdm/mSdi59wuud5N3ZLM812vAlqUt6KZbZF0LPA0IXmnPARcVsHr3gS0Z/cLWswE3o6215Bw+tadhN3hF2fakKRLgEsAOnbMatyZ28vsLDF+9dS7jH3ns1Ll7VuERNyueaMy1nTO7a3qzLXYJDUEngDaAucTBnD1Bm4EdgA/K2O9c4HrgFvTz4k2s/RR0+MkbQCukHS3mc1P356ZjQBGABQXF9seNcrlnZIS47qn3+Xpf5Wea/rA5iERt2/ROKHInHO1Wa6T8Woy94DL6jHHXQScCHQ1s4VR2VRJa4ERkoaZ2az4CpLOBEYCD5vZ/2QZ4xjgCqCYsFvcuayUlBi/Gfvebhd9aNesIWMG9aVDS0/EzrnMcn3MeDbhuHG6nsCcCtY9DFgdS8Qpb0b3PeKFkk4BngTGEkZqV5b3el3WzIzBz7zP428tKVW+/74N+eugvnRs5YnYOVe2XCfjZ4G+krqkCiR1Ipy29GwF6y4DWkjqmlbeJ7r/6gCdpKOBZ4BJwI/NrITsnUdIxG9VYh23FzMzbnxmNqPfWFyqvG3TBoy5pC+dWu9TxprOORfILHcdwGjijlmEua1vICS9W4GmwOFmtiGqdxCwELjFzG6JyjoB7xKS8u2EY8bFhAlA5gG9zaxE0teA1winQA0EtsRjSJ1THL3GKOBxYAHQgDCAayAw3MwyHoOOKy4uthkzZlTlrXB5wsy4+R9zGPnaolLlbZo24PFL+nJwmybJBOacq5UkvW1mxenlOT1mbGYbo9ORhhISoQi91ytSiTgioJBYz93MFknqSxgZfRthnuwlhMFUt8d6v30Jx6VbAC9nCEPR/XrCKO5rgf2AEuBD4BfAg3vaVpf/zIzbnv9gt0TcukkDxgzq44nYOZe1nPaM8433jPdeZsad//yQEVM/KlXeap/6jLmkL938MojOuQzK6hnn+pixc3WemXH3C3N3S8Qt96nP6EF9PBE75yrNk7FzlWBmDJkwl2FTSg/qb964Ho9d1Iev7b9vQpE55+oyT8bOVcLQifN54OXSibhZo3qMvrgPPdt5InbOVY0nY+ey9PuJ87lvUul5YPZtWMToi/twaLtmCUXlnMsHnoydy8L9L81n6MR5pcqaNixi1EV9+PqBnoidc3vGk7FzFfjj5IUMmZCWiBsU8ZcLe3NEh+YJReWcyyeejJ0rx4ipC7n7hQ9Lle1Tv5CRF/bmGx3LvdCYc85lzZOxc2V46JWPuGNc6UTcOErERx7kidg5V33qzCUUncuVdz9dwz3j5/LK/BWlyhvVK+TRgUdxVKeWCUXmnMtXnoydiyz4cj1Dxs/jhdnLdlvWsF4Bjww8ij5dWiUQmXMu33kydnu9Jas28buJ8xn7zqeUZJgdtkFRAY/85CiOPtgTsXOuZngydnut5eu38sDLCxj9xids35l5jva+XVoy+Iyefh6xc65GeTJ2e521m7czYupCHpm2iM3bd2asc3j7ZlwzoDvHdm2NpIx1nHOuungydnuNzdt28uhrHzNs8kLWbdmRsU7Xtk24un83Bhy6vydh51zOeDJ2eW/bjhKeeGsx9720gOXrt2asc2DzRlx5ajfO+saBFBZ4EnbO5ZYnY5e3dpYYz8z8jKET57Fk1eaMdVo3qc9lJ3XlnD4daVBUmOMInXMu8GTs8o6ZMWHOF9w7YS7zvtiQsU7ThkVcesLBXNCvE43r+7+Bcy5Z/i3k8sprC1bwv+PnMnPJmozLG9Yr4IJ+nbn0+INp1rhejqNzzrnMPBm7vDBzyRruGf8hry5YmXF5vUJxTu+OXHZSV9ru2zDH0TnnXPk8Gee59Vu289ArH/P8e0tZt3k7bZo2oHWTcAuP69OmaQPaNGlA6+i+eeN6dWYk8bwv1jNk/FwmzPki43IJzup1IFd8qxsdWzXOcXTOOZcdT8Z5avO2nfx5+iKGTVnImk3bvyr/sozRxHFFBQoJu2n9kLRjibp1lMDbRkm9WaNkEveSVZsY+uI8xs78DMs8Xwf9e+7H1QO6022/prkNzjnnKsmTcZ7ZtqOEx99azB/KOY2nIjtKjGXrtrBs3ZYK69Yr1G497cKCAsyMnSVGiUGJGSXRczOi8l1l6XVKDEqiOjuN0tsqMXaa8cnKjWXOmnXMwa24ZkB3v8Shc67O8GScJ3bsLGHsO5/xu4nz+WxN5tN4asL2ncbStVtYurbixF3TjujQnF8N6E6/rq2TDsU55yrFk3EdV1JijHt/Kb99cR4fLd+YsU7TBkUMOr4L3z2iHWs2b2fF+q0s37B11/2GraxYv+2rsvVbM89OVVsd0rYJVw/oTv+e+9WZY93OOReX82QsqQMwFDgVEDARuMLMFmexbkfgVuAkoA2wBPgbcKeZbUyrOwj4JdAZWAQMNbNhGbb5feB/gB7AF8Cfou1lnrS4ljAzXp77JUPGz2PO0nUZ6zSsV8DAYzpz6QldaN64ftbb3rJ9J8tjCXvFhm0sXx+Sduo+9XjjtuTepg4tG3HFKd34vs+a5Zyr43KajCU1Bl4CtgI/AQy4DXhZ0uHpCTVt3X0IibseMBhYDBwF3AwcAvwwVncQMBy4M1rnFOBBSTKzP8bqDQCeBh4GrgK+AdwBNAWurZ5WV7/pC1cyZMJc3v5kdcbl9QrFub078vMqnsbTsF4hHVo2pkPLikcfb9q246te9fL1W1m1cRslZhQWiAJBgUSBRGGBkIjKU7fY8wJRGJUVFKTWASlVLgoK+GpbDYsK6dCykfeEnXN5Idc940FAF6C7mS0AkPQuMB/4KfDbctbtR0i6A8xsQlT2sqSWwNWSGpvZJklFwO3AKDO7PlavHXCrpIfMLDW8+C5gmpldEqvXBLhB0lAz2/0q8wmauWQNQ8bPZdqCFRmXFwh+cGR7fnHKIbRvkZvTeBrXL6JjqyI/bcg55/ZArpPxd4HXU4kYwMw+lvQq8D3KT8ap/azp+2TXAAWEXd4ARxN2YT+WVm8UcAFwLCHpdgB6AZdkqHczcDrwaBZtqnEfLlvHvRPm8WIZ59ICnHH4AVx5ajcObtMkh5E555yrDrlOxocCz2Qonw2cXcG6Ewk96Lsl/Yywm7o3cDkwLLaL+9Do/v0MrwHQE3i5rHrRj4NNUb1EfbxiI0NfnMc/3v28zHNpT/laW67q341D2zXLbXDOOeeqTa6TcUsg04HOVUC5J4Wa2RZJxxKO8c6OLXoIuCztNcjwOqvSlpdVL1XWMkM5ki4h6k137NixvJCr7PM1m7lv0nyefPtTdpaUfS7tL/t358iD/Fxa55yr6+rMqU2SGgJPAG2B89nVM74R2AH8LBdxmNkIYARAcXFxGf3Vqlm+fisPTl7A6NcXs21nScY6vTo05xo/l9Y55/JKrpPxajL3gMvqMcddBJwIdDWzhVHZVElrgRGShpnZrNh2WgBL014DdvWQ4/XStYjVq3FrN21nxCsLeWTaIjZvz3yq0Nf2b8rV/btzSo+2PoLYOefyTK6T8Wx2HauN6wnMqWDdw4DVsUSc8mZ03wOYxa5d2IdSOhmnjgGnXideb3qqkqROQOMs4tljG7fu4NFXP2bE1I9YtyXzRBudW+/Dlad244zDDqDAz6V1zrm8lOtk/CwwRFIXM/sIvkp+/YDrKlh3GdBCUtf4aGygT3T/WXQ/HVgBnEcY9JXyY0Jv91UAM1ssaVZU76G0etuBf1aqZZX0wvtLuX7s+6zcuC3j8nbNGnL5tw7h37/ZnqLCgpoMxTnnXMJynYz/RBhs9YykGwiTftxKmElreKqSpIOAhcAtZnZLVDySMDHHOEm3E44ZFxMmAHmbXUl2u6TBhEk+PiMk5JOBC4H/NrN49vsN8Jyk4cAYwqQfNwC/r+lzjFvu0yBjIm7dpD4/P6kr5/bpSIOiwpoMwTnnXC2R02RsZhslnUyYDnMU4dzgSYTpMDfEqgooJJw/nFp3kaS+wE2EWbtaE5L4COB2MyuJ1R0myQjTYV5DSNyXmdmDafGMk/QDwnSYAwnTYd5BmDSkRvXu3JITurVhyrzlAOzbsIhLTzyYgcd0onH9OjOuzjnnXDWQlXUCq6tQcXGxzZgxo8rrv/fpWs750+tc0K8TFx/XhWaN6lVjdM4552obSW+bWXF6uXfBEnRY+2a8/ptTaNLAPwbnnNub+cighHkids4558nYOeecS5gnY+eccy5hnoydc865hHkyds455xLmydg555xLmCdj55xzLmGejJ1zzrmE+Qxce0DScuCTpOOohNaEi2jkg3xqC3h7arN8agt4e5J2kJm1SS/0ZLwXkTQj0zRsdVE+tQW8PbVZPrUFvD21le+mds455xLmydg555xLmCfjvcuIpAOoRvnUFvD21Gb51Bbw9tRKfszYOeecS5j3jJ1zzrmEeTJ2zjnnEubJeC8g6duSpkraIGmdpBmSTk46rsqS1E/SBElfSlov6V+SLkw6rmxIai/pD5KmS9okySR1ylCvoaR7JC2VtDmqf3zuIy5bNm2RVCxphKQPozqLJY2W1DmZqMuW7WeTts51Ub1puYkye5Vpj6Qekp6UtCL6e5sr6fLcRly2SvzfdJT05+jvbLOkeZJuk7RP7qOuGk/GeU7ST4FngLeBs4CzgSeBxknGVVmSDgcmAvWAQcC/AW8BD0v6WZKxZakr8B/AauCVcuo9TGjfjcAZwFJgvKReNR5h9rJpy4+AQ4H7gNOB64BvAjMkdchFkJWQ7WcDgKQuwA3AlzUcV1Vl1R5JxcAbQAPgYuDbwL1AYQ5izFaFbYkS7kTgeGAwoR0PAb8EHslNmNXAzPyWpzegE7AZuCLpWKqhLXcA24AmaeXTgelJx5dF/AWxxxcDBnRKq3NEVH5BrKwImAs8m3QbKtmWNhnWOwgoAW5Jug2VbU9a/fHAcGAyMC3p+Kv4+RQAc4CxScdbDW3pH5X3Tyu/C9gBNE66HdncvGec3y4kfPkNSzqQalAf2E74cRG3ljqwh8fMSrKo9l1CG5+IrbcDeBwYIKlBDYVXKdm0xcyWZyj7BFgOHFgTcVVVlp8NAJLOJfTwf11zEe2ZLNtzItAD+G3NRrNnsmxL/eh+XVr5GsJ3g6o1qBpS67/E3B45FvgQ+JGkhZJ2SFog6edJB1YFI6P7+yS1k9Rc0iDgFGBocmFVq0OBj81sU1r5bMIXTtfch1R9JPUA2gIfJB1LVUhqQfhb+5WZrUo6nj10bHTfUNLrkrZHYzHuk9Qo0cgqbyIwH7hbUk9JTaIxMZcDw8xsY7LhZceTcX5rBxwC3EPYZdMfeBG4vzYN0siGmb1P+DX/PeAzwjGkB4BLzezxBEOrTi0J7Uq3Kra8TpJURNhDs5xwXLwuugeYx64fhnVZu+j+CWACcCrwv4RdwX9NKqiqMLMthB8XBYQfruuBScBzwGUJhlYpRUkH4GpUAdAUGGhmf4/KXopGI/5a0n0WHVyp7SQdAjxN+Ge7lLC7+nvAMElbzGx0kvG5Ct0PHAN8x8wy/eCo1SQdB/wn8M268j9TgVRH7DEzuzF6PFlSIXCXpB5mVif2YEhqSPhR0RY4H1gM9CYMgtwB1IUBnp6M89xKQs/4xbTyCcBpwAHA57kOqoruIBxPPcPMtkdlkyS1An4vaUxljv3VUqsJg5zSpXrEdXLXqKS7gEuAn5jZhKTjqaLhhB79p5KaR2VFQGH0fLOZbU0suspbGd1n+m64C/gGdedwwkWEvWZdzWxhVDZV0lpghKRhZjYrseiy5Lup89vsCpbXpeR1GDArlohT3gRaEX4V13Wzgc6S0k8760kYSb4g9yHtGUnXA9cCvzCzUUnHswd6EPbIrI7d+gF9o8d1ovcVk2/fDatjiTjlzei+R47jqRJPxvltbHQ/IK38NOBTM1uW43j2xDKgl6T6aeV9gC3U0V5jmn8QzqM+O1UQHWv9ITChjvW8kPQL4DbgejO7P+l49tBJGW6zgPejx08lF1qV/BPYSubvBoAZuQ1njywDWkhKH+DYJ7r/LMfxVInvps5v44CXgeGSWgMfEb7o+wMXJBlYFdxPmKzkH5IeJBwz/i5wDjDUzLYlGVw2JP0genhkdH+6pOXAcjObYmbvSHoC+J2kesDHhB5XZ+C83EdctoraIulHwO+AFwjjFPrGVl9nZnNyGG6FsvhsJmdYZw1QlGlZ0rJoz0pJdwKDJa0DXgKKCcdZ/2xmtWYvTEVtIQyouwoYJ+l2wjHjYsIEIG8Dr+Y24ipK+kRnv9XsDdiXMOr4C8KuzneBc5OOq4ptOZ0w0cJywojJmcB/AYVJx5Zl/FbGbXKsTiPCuZ/LCD3+N4ATk469sm0hfEFW2N7acqtKrNTSST8q8bcmQhJbEH03fALcAtRLOv4qtKUn8DdgCeGH+jxgCNAi6fizvfklFJ1zzrmE+TFj55xzLmGejJ1zzrmEeTJ2zjnnEubJ2DnnnEuYJ2PnnHMuYZ6MnXPOuYR5MnauHJLOl7Q49nyOpP+q5tc4WtIbkjZKMkm9qnP71UnSIkkjk44jCZKukPRvScfh8pMnY+fKdyRhFh8kNQG6p55Xo4cJs+GdCRxNmLDA1T5XAJ6MXY3wZOxc+b5KxsA3CRPoV9sVYCQVEBL882b2kpm9bmabKrF+g+qKxeWef34uxZOxc2WIEmUvdiXjYmCOhYuZZ7P+vpLul/S5pK2S5kq6UpKi5QOBnYT/w8HRLupF5WzvpqjO1yWNl7SBMAUgkvpLGidpqaRNkt6X9Mvo+rTxbSyS9JikH0n6INo1PkPSsRle7/Ko/paoznFlxNVb0kRJG6LtTZLUO63OSEmfSiqW9JqkzdH78Z1o+VXRa62T9IykNhW8t89L+leG8gMk7ZB0Zayss6TRkpZHn8NMSWdlWPcISWMlrYzF9+vU+0a4vOV50Wdg8d31kk6TND1ab62k/5PUPW37kyVNk3SmpHckbSVM55p6rz+I1l8dvd+7xejyl18owrk0sS/elHFR/kwtT80h29nMFpWxjQLgeUJv+kbgPeA7hHmn2wC/iZYfC0wj7Kp+iHAlnYo8E9W/m12XuusCTAL+QJjTuhi4KXqt69LWP47QGx8c1b0VeE5SJzNbE8V/EeFCDyMJF27vCowBmqa183BgCjAHGEiYM/g6YIqkvlb6OrL7An8hzBn8OXA98LSkB4BuwM+B/aLXfQD4j3Leg1HAGEk9rfRFJ86N7v8axdeBML/3l8CVhHnNfxi97vfN7NmoXm/CXNMLonqfEq4Ffni0vbMIF16ZRXhfibaFpNMIn+VL0babEOZ4niapl5nFrxrUDbiP8J5/BKySdB5wb7TOK4T5yQ9n13Ws3d4g6cmx/ea32nYjTDrfi5A4Z0ePewHrCF/Uqef1y9nGGYTENDCtPJVwW0fPi6J6N2UR101R3csrqKdou9cTrrVbEFu2KCprESsrjrZ7bvS8gDDh/gtp2/1hVG9krOwpYA3QPFa2L+GSln+PlY2M1j0+VnZ4VDaX2MU+ovd9O+VcAISQsNYCd6aVzwTGxZ4/TEiardLqvQjMjD2fGrW5cTmvuQh4LEP5DGA+4QpOqbLOURt+GyubTPjx1Ctt/fuBfyX9d++3ZG++m9q5NGY2x8xmAh0IV4aZCWwk9AqfNLOZ0a28yzYeT/ji/Wta+WNAfcJAraoam14Q7Z4dLukTwhV4thOuJdwcaJtWfbqZrY49fy+67xjdt49uf0tb72lgR1rZ8cBzFvWoAcxsHfAscEJa3Y1mNjX2/MPofqKZ7UwrLwIOSG9n7DU2E34InBfb7X8YcASh15xyGqFHu1ZSUeoGjAeOiA4lNAb6AaOtEsfro9fch7D34wkz++q9MbOPCZfuS38PFkV/T3FvEa7V/QdJ34ricXsZT8bOxUgqjH1h9wOmR4+PI1ykfFm0XOVuKOxiXJUhYS+LLa+qpWkxFxCS3xmEBHwycBRwe1SlYdr6q+JPzGxrWr1UEvwird4OYGXatlqmxxNZBrRIK1sTfxJ7b1an1UuVp8edbhThB9OJ0fPzCZfW/L9YnbbAfxJ+nMRv90TLW0VxFhB2TVdWC8KeiLLeg/TPOVO9vxCuW92H8CNhlaS/S+pUhXhcHeXHjJ0rbRKlezOjKN3T2h7dn0TY7ViWVUBLSfXTEvL+seVVlX7d04MJu5rPN7PHUoWSzqzi9lMJY794YfSjpFVa3VXsalPc/uyeZKvbFMKF5H8saQrhePFTUa85ZSXhOOzdZWzjc6CQsBfjwCrEsJrweZT1HqR/zrtds9bMDBgODJfUAuhPOIb8BCFBu72A94ydK+2nhF7lEMJgnqOi23Lghtjzis41nkL4/zo7rfw8Qs9vevWFTGq3ZuqHApLqRa9VFZ8Sjp+mD6D6d3b/AT8F+LakrwZ2RY/PpPwfK3ssSmKPAT8Avk1IpqPSqr1AODY928xmZLhtjXZNTyMk9UblvORWwrHqeAwbCX8LZ8dHrks6CDiGSr4HZrbazJ4gHCL4emXWdXWb94ydizGzuQCSBhPO/Z0RnaLSGnjYzJaVu4Fd/kn4gh8WnaYzm5AwLiYMOlpRjWF/AHwC3C5pJyEpX1n+KmUzsxJJNwMPSXoUeJwwmvo6wiC2uFsJu8cnSbqb0PO7lvAD4ZaqxlAJowgj04cResmT05bfCLwJTJV0P2EQVgtCoutiZhdG9a4m/LCYLulewg+SLoTBVv8d1ZkDHCfpDMIu6BUWRtMPJoymfk7Sg4TR1DcTBpjdW1EDJI0g7F6fThj13Y2wy31CJd4HV8d5z9i5NJLqA6cQelUApwPvVCIRY2YlhFOZ/kxITs9Hz68ijHKuNtFu8O8TEsRfCKcFTQXu2oNtPkyYcepkwqlUFwDnkLbr2czeJRyzXUdo6yhgA3CClT6tqUaY2YeE0cwHEgZgWdryxYRd+LOAOwijqP9IOBTxUqzeW4QxAksIp4eNA66h9HHkXxNGfv+NMOjqpmjdFwifbfNo2TDCD6RjzezzLJrxKmFymQej+K4n9Ph/ktWb4PKC0v52nXPOOZdj3jN2zjnnEubJ2DnnnEuYJ2PnnHMuYZ6MnXPOuYR5MnbOOecS5snYOeecS5gnY+eccy5hnoydc865hP0/sqrDbBKZfLoAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x324 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G1mSNpEng-LE"
      },
      "source": [
        "We see a similar trade-off between quality and performance: as the number of random vectors increases, the query time goes down as each bin contains fewer documents on average, but on average the neighbors are likewise placed farther from the query. On the other hand, when using a small enough number of random vectors, LSH becomes very similar brute-force search: Many documents appear in a single bin, so searching the query bin alone covers a lot of the corpus; then, including neighboring bins might result in searching all documents, just as in the brute-force approach."
      ]
    }
  ]
}