FMML_CLF1_Lab1_2022.ipynb

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      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/harika136/IIIT_IHUB_HYD/blob/main/FMML_CLF1_Lab1_2022.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
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        "id": "mqB80fpFv6b8"
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      "source": [
        "# **FOUNDATIONS OF MODERN MACHINE LEARNING, IIIT Hyderabad**\n",
        "### MODULE 3: CLASSIFICATION-1\n",
        "### LAB-1 : Understanding Distance metrics and Introduction to KNN\n",
        "#### Module Coordinator: Tanvi Kamble\n",
        "\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "## **SECTION - 1 : Distance metrics**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J4l3wwMnxLFd"
      },
      "source": [
        "# Importing Required Libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import math\n",
        "from scipy.spatial import distance\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      },
      "source": [
        "### **Euclidean Distance**"
      ]
    },
    {
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      "source": [
        "There is more than one way to define distance. The most familiar distance metric is probably _Euclidean distance_, which is the straight-line distance between the two points. The formula for calculating this distance is a generalization of the Pythagorean theorem:\n",
        "\n",
        "$$ d({\\bf x}, {\\bf x'}) = \\sqrt{\\sum_{j=1}^D (x_j - x'_j)^2} $$\n",
        "  \n",
        "    \n",
        "                            \n",
        "\n",
        "                              \n",
        "                              \n",
        "\n",
        "![euclidean.png](data:image/png;base64,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)\n",
        "\n",
        "[Image Source](https://www.google.com/imgres?imgurl=https%3A%2F%2Fwww.tutorialexample.com%2Fwp-content%2Fuploads%2F2020%2F05%2FEuclidean-distance-in-tensorflow.png&imgrefurl=https%3A%2F%2Fwww.tutorialexample.com%2Fcalculate-euclidean-distance-in-tensorflow-a-step-guide-tensorflow-tutorial%2F&tbnid=xB3LUnhOEpdklM&vet=12ahUKEwj_qrjI3dfxAhXTJCsKHX_7DDgQMygDegUIARDLAQ..i&docid=AIcC7trk2GUB6M&w=521&h=329&q=euclidean%20distance&ved=2ahUKEwj_qrjI3dfxAhXTJCsKHX_7DDgQMygDegUIARDLAQ)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "35sMuIGQvzJe"
      },
      "source": [
        "# Simple 2D example\n",
        "x_1 = np.array((1, 2))\n",
        "x_2 = np.array((4, 6))"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oRT3hc0PzhZt",
        "outputId": "333f3492-21e5-4885-a173-185cbf182f5a"
      },
      "source": [
        "# Naive approach to calculating Euclidean distance (not-vectorized)\n",
        "sumv = 0\n",
        "for i in range(len(x_1)):\n",
        "  sumv += ((x_1[i]-x_2[i])**2)\n",
        "dist = math.sqrt(sumv)\n",
        "print(dist)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FYfCNWCryC-1",
        "outputId": "f00207ee-9614-43a5-cea4-9c394cf6678f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "## TASK-1\n",
        "## Write a vectorized version of computing Euclidean distance (using numpy) in the space given below\n",
        "## (Expected number of lines ~ 1). Your answer should be stored in the variable 'euclidean_dist'\n",
        "## Verify this result with what you saw above\n",
        "\n",
        "# Write your code below and uncomment the lines below in order to run the cell.\n",
        "\n",
        "euclidean_dist = np.sqrt(np.sum((x_1-x_2)**2))\n",
        "print(euclidean_dist)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IMgLfH5XIivU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "50c9c36f-950f-47ca-cc76-d01c621440f1"
      },
      "source": [
        "#@title Answer to Task-1\n",
        "# Answer:\n",
        "euclidean_dist = np.sqrt(np.sum((x_1-x_2)**2))\n",
        "print(euclidean_dist)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aAgS7NcF2J_9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a5317029-5e65-4d57-8c49-a0cbbc8a8e4b"
      },
      "source": [
        "# Libraries such as SciPy provide functions to compute different kinds of distance metrics between points\n",
        "euclidean_dist = distance.euclidean(x_1, x_2)\n",
        "print(euclidean_dist)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pCGh72MWWpmE"
      },
      "source": [
        "# 3-D Visualization\n",
        "plotx = np.linspace(-10,10,50)\n",
        "meshx, meshy = np.meshgrid(plotx,plotx)"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wpCmZVYgYWDD"
      },
      "source": [
        "tempeuclid = np.sqrt((meshx**2 + meshy**2))"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "VpwgcTtsWPLk",
        "outputId": "27363c7c-60d1-43c7-adb5-d7fe98bd3a52"
      },
      "source": [
        "import plotly.graph_objects as go\n",
        "\n",
        "fig = go.Figure(data=[go.Surface(z=tempeuclid, x=plotx, y=plotx)])\n",
        "fig.update_layout(title='Euclidean Distance from origin', autosize=False,\n",
        "                  width=1000, height=1000,\n",
        "                  margin=dict(l=65, r=50, b=65, t=90))\n",
        "fig.show()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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      "source": [
        "### **Manhattan Distance**"
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      "source": [
        "Euclidean distance is not the only way to measure how far apart two points are. [**Manhattan distance**](https://en.wikipedia.org/wiki/Taxicab_geometry) (also called _taxicab distance_) measures the distance a taxicab in would have to drive to travel from A to B. Taxicabs cannot travel in a straight line because they have to follow the street grid. But there are multiple paths along the street grid that all have exactly the same length; the Manhattan distance is the length of any one of these shortest paths.\n",
        "The formula for Manhattan distance is as follows:\n",
        "$$ d({\\bf x}, {\\bf x'}) = \\sum_{j=1}^D |x_j - x'_j| $$  \n",
        "  \n",
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)  \n",
        "\n",
        "\n",
        "[Image Source](https://www.google.com/url?sa=i&url=https%3A%2F%2Faigents.co%2Fblog%2Fpublication%2Fdistance-metrics-for-machine-learning&psig=AOvVaw3oUdVhaRKBIADWyXWDUoLZ&ust=1625576456552000&source=images&cd=vfe&ved=0CAoQjRxqFwoTCOC6pa3-y_ECFQAAAAAdAAAAABAD)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Agx5Cmm34ub6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9c44ba50-3331-4d42-b3a0-f41f77cf7d88"
      },
      "source": [
        "# Libraries such as SciPy provide functions to compute different kinds of distance metrics between points\n",
        "# x_1 = np.array((1, 2))\n",
        "# x_2 = np.array((4, 6))\n",
        "manhattan_dist = distance.cityblock(x_1, x_2)\n",
        "print(manhattan_dist)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZQD9nRk03IRw",
        "outputId": "715fe1af-92e3-48b3-d569-22f845733e29",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "## TASK-2\n",
        "## Write a vectorized version of computing Manhattan distance (using numpy) in the space given below\n",
        "## (Expected number of lines ~ 1). Your answer should be stored in the variable 'manhattan_dist'\n",
        "## Verify your result with the output of the scipy function in the previous cell.\n",
        "\n",
        "# Write your code below and uncomment the lines below in order to run the cell.\n",
        "\n",
        "manhattan_dist = np.sum(np.abs((x_1 - x_2)))\n",
        "print(manhattan_dist)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gzT3M83oI8O6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d0fff8f1-cd22-4a3a-a950-607225ffdbc2"
      },
      "source": [
        "#@title Answer to Task-2\n",
        "# Answer:\n",
        "manhattan_dist = np.sum(np.abs((x_1 - x_2)))\n",
        "print(manhattan_dist)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h4D0UKaebUcW"
      },
      "source": [
        "# 3-D visualization\n",
        "plotx = np.linspace(-10,10,50)\n",
        "meshx, meshy = np.meshgrid(plotx,plotx)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ty-wxEkqbYry"
      },
      "source": [
        "tempmanhattan = np.abs(meshx) + np.abs(meshy)"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "4RIaYB2Fbda3",
        "outputId": "c3352cf9-27e3-4bcb-b58d-dd7a20b82294"
      },
      "source": [
        "import plotly.graph_objects as go\n",
        "\n",
        "fig = go.Figure(data=[go.Surface(z=tempmanhattan, x=plotx, y=plotx)])\n",
        "fig.update_layout(title='Manhattan Distance from origin', autosize=False,\n",
        "                  width=1000, height=1000,\n",
        "                  margin=dict(l=65, r=50, b=65, t=90))\n",
        "fig.show()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5aBtFZKL46mz"
      },
      "source": [
        "### **Minkowski Distance**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BtjF_jww5DKs"
      },
      "source": [
        "Minkowski distance is a generalized form of Euclidean and Manhattan distance. We can raise the absolute difference to any power $p$ and take the $p$th root. The formula for Minkowski distance is:\n",
        "$$ d({\\bf x}, {\\bf x'}) = \\left(\\sum_{j=1}^D |x_j - x'_j|^p\\right)^{1/p}. $$\n",
        "Manhattan distance and Euclidean distance are special cases of Minkowski distance for $p=1$ and $p=2$, respectively."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tYJW9RRp5coB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aaa3798c-7ddf-40ea-9685-facd378b951d"
      },
      "source": [
        "# x_1 = np.array((1, 2))\n",
        "# x_2 = np.array((4, 6))\n",
        "minkowski_distance = distance.minkowski(x_1, x_2, p=3)\n",
        "print(\"Minkowski distance when p=3 is \",minkowski_distance)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Minkowski distance when p=3 is  4.497941445275415\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S4Y7gKoW6ZOa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cbc1e729-95ae-4337-c605-b677a40ca55d"
      },
      "source": [
        "# You can verify that this distance is the same as Manhattan dist when p=1,\n",
        "# and Euclidean dist when p=2\n",
        "\n",
        "minkowski_dist_p1 = distance.minkowski(x_1,x_2,p=1)\n",
        "print(\"Minkowski distance when p=1 is \",minkowski_dist_p1)\n",
        "minkowski_dist_p2 = distance.minkowski(x_1,x_2,p=2)\n",
        "print(\"Minkowski distance when p=2 is \",minkowski_dist_p2)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Minkowski distance when p=1 is  7.0\n",
            "Minkowski distance when p=2 is  5.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dPaqFnNLXnl8"
      },
      "source": [
        "### **Hamming Distance**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zunLh6BWXuPq"
      },
      "source": [
        "Hamming distance is slightly different from the distance metrics previously discussed, and is applied in certain kinds of machine learning problems. It measures similarity between two strings of the same length.\n",
        "The Hamming Distance between two strings of **the same length** is the number of positions at which the corresponding characters are different."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o7QqV_YTYHWv",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d37a862c-9775-4a2a-f63c-ae87968a01e4"
      },
      "source": [
        "str_1 = 'euclidean'\n",
        "str_2 = 'manhattan'\n",
        "hamming_dist = distance.hamming(list(str_1), list(str_2)) * len(str_1)\n",
        "print(hamming_dist)\n",
        "\n",
        "# Note that the answer will be 7, as except for the last two letters ('a' and 'n'), all\n",
        "# the other corresponding letters in the two strings are different."
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BaWnfZ6ZfZ_X"
      },
      "source": [
        "### **Cosine Similarity**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OUsZxAj7GPg_"
      },
      "source": [
        "This is a measure of \"similarity\" (note that this is different from distance) between two non-zero vectors of an inner product space. Range: [-1,1].  \n",
        "$$ \\text{cosine similarity}(A,B)  = \\frac{A \\cdot B}{\\lVert A \\rVert \\lVert B \\rVert}$$\n",
        "  \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zulSnU0GfeLE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "062d8062-0781-4b2d-e06f-f5abe5a4e1f8"
      },
      "source": [
        "from numpy.linalg import norm\n",
        "\n",
        "# x_1 = np.array((1, 2))\n",
        "# x_2 = np.array((4, 6))\n",
        "\n",
        "cosine_similarity = 1 - distance.cosine(x_1,x_2)\n",
        "print(cosine_similarity)\n",
        "\n",
        "cosine_similarity = np.dot(x_1, x_2)/(norm(x_1)*norm(x_2))\n",
        "print(cosine_similarity)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.9922778767136677\n",
            "0.9922778767136677\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nndOIHk6fekM"
      },
      "source": [
        "### **Chebyshev Distance**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6gG9yOKAIBmO"
      },
      "source": [
        "Chebyshev distance is also called the L∞ metric. It is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. Simply explained, it is the maximum distance along one axis.  \n",
        "$$ d_{chebyshev}(x,y) = \\max_{i}(\\lvert x_i - y_i \\rvert) $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0x8iyHWUhGsW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5eaf08f7-be67-4978-8924-a5d8a40c8b78"
      },
      "source": [
        "# x_1 = np.array((1, 2))\n",
        "# x_2 = np.array((4, 6))\n",
        "\n",
        "chebyshev_distance = distance.chebyshev(x_1,x_2)\n",
        "print(chebyshev_distance)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MjQ47HbqqIhC"
      },
      "source": [
        "### **Jaccard Distance**\n",
        "The Jaccard distance is a metric that measures dissimilarity between sample sets.  \n",
        "$$ \\text{Jaccard Index ie, } J(A,B) = \\frac{\\lvert A \\cap B \\rvert}{\\lvert A \\cup B \\rvert}$$\n",
        "$$ \\text{Jaccard Distance ie, } d_{J}(A,B) = 1 - J(A,B) = 1 -\\frac{\\lvert A \\cap B \\rvert}{\\lvert A \\cup B \\rvert}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EYh42i48qXB1",
        "outputId": "dbe0d5c9-91ca-43db-a759-18f88ac82a7e"
      },
      "source": [
        "## In the context of binary vectors, let's say:\n",
        "## a = no. of indices where vector1[i] == 1 == vector2[i]\n",
        "## b = no. of indices where vector1[i] == 0 and vector2[i] == 1\n",
        "## c = no. of indices where vector1[i] == 1 and vector2[i] == 0\n",
        "## d = no. of indices where vector1[i] == 0 == vector2[i]\n",
        "## Jaccard-distance = 1 - [a/(a+b+c)]\n",
        "\n",
        "print(distance.jaccard([1, 0, 0], [0, 1, 0]))\n",
        "print(distance.jaccard([1, 0, 0], [1, 1, 0]))\n",
        "print(distance.jaccard([1, 0, 0], [1, 1, 1]))"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.0\n",
            "0.5\n",
            "0.6666666666666666\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LKMdC249xDDK",
        "outputId": "8566a0bf-2f21-46cc-e5c4-d03b1e1c3439"
      },
      "source": [
        "def jaccard_similarity(a, b):\n",
        "    c = a.intersection(b)\n",
        "    return float(len(c)) / (len(a) + len(b) - len(c))\n",
        "\n",
        "list1 = ['dog', 'cat', 'rat']\n",
        "list2 = ['dog', 'cat', 'mouse', 'rabbit']\n",
        "# The intersection is ['dog', 'cat']\n",
        "# union is ['dog', 'cat', 'rat', 'mouse, 'rabbit']\n",
        "words1 = set(list1)\n",
        "words2 = set(list2)\n",
        "print(\"Jaccard similarity is :\",jaccard_similarity(words1, words2))\n",
        "print(\"Jaccard distance is :\", 1-jaccard_similarity(words1, words2))"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Jaccard similarity is : 0.4\n",
            "Jaccard distance is : 0.6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_pEGB4hYf8ih"
      },
      "source": [
        "### **How to decide the appropriate distance metric ?**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VlvfcA1xgPeE"
      },
      "source": [
        "1. **Euclidean distance**: The most widely used metric in KNN classification problems, since it calculates the straight line distance between two points.  \n",
        "\n",
        "2. **Manhattan distance**: In some cases, Manhattan distance maybe preferable over Euclidean distances. For eg: For data with high dimensionality, Manhattan distance maybe more useful. When Euclidean distance is defined using many coordinates, there is not a lot of difference in the distances between different pairs of points. This is due to the **Curse of Dimensionality**, ie, \"*when the dimensionality increases, the volume of the space increases so fast that the available data become sparse*\".  \n",
        "Manhattan distance is a more appropriate metric to use if the data is, for example, in the form of a grid. For instance, if the data consists of several houses that are arranged in the form of a grid and connected by roads, Euclidean distance is not an appropriate indicator of the distance between the houses, as in real-life, one would take the roads to travel between two points, thus making Manhattan distance a more suitable metric.  \n",
        "\n",
        "3. **Cosine Similarity**: Cosine similarity is commonly used in text-analytics and document comparison problems. It is also used in collaborative filtering-based recommendation systems.  It is used when the magnitude of the vectors is not of importance.\n",
        "\n",
        "4. **Hamming Distance**: It is commonly used to measure the distance between categorical variables.  \n",
        "\n",
        "5. **Jaccard Index**: The Jaccard index is often used in applications where binary data is used. It can also be used in text similarity analysis to measure how much word choice overlap there is between documents"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **SECTION - 2 : KNN**"
      ],
      "metadata": {
        "id": "gmBBvmJx_jRo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### What is KNN ?\n",
        "\n",
        "K-NN (K- Nearest Neighbours) is a classification technique where the output is a class membership.  \n",
        "An object is classified by a **plurality vote of its neighbors**, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small). If k = 1, then the object is simply assigned to the class of that single nearest neighbor.  \n",
        "\n",
        "### What is so unique about KNN ?  \n",
        "First off, KNN is a **supervised learning** algorithm, ie, the idea is to learn a function that can map an input to an output given some example pairs.  \n",
        "\n",
        "It is a **non-parametric** algorithm, since it doesn't assume anything about the form of the mapping function, which makes it very flexible to use. Certain algorithms are parametric (such as Naive Bayes), which are constrained as they require a specified form. KNN can, thus, be a good algorithm to try if the form is unknown.  \n",
        "\n",
        "Moreover, KNN is an **instance-based algorithm**, since it compares new problems/inputs with those which were seen during model training and that were stored in memory. "
      ],
      "metadata": {
        "id": "GgIfFiVPJUTE"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tjBH8Fd7gG4d"
      },
      "source": [
        "### **SECTION - 2.1: KNN on a Synthetic Dataset**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KQ0EUgnbgQXy"
      },
      "source": [
        "In the previous section, you saw different kinds of distance metrics and their values on two sample 2-dimensional points.   \n",
        "This section covers use of distance metrics in a KNN classifier for synthetic two-dimensional data. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fyXurJobpSEI"
      },
      "source": [
        "import random\n",
        "import scipy.stats as ss\n",
        "from sklearn.neighbors import KNeighborsClassifier"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "_lrY1BLhpdzK",
        "outputId": "4d569904-7850-4adf-d097-936b792f3631"
      },
      "source": [
        "def generate_synth_data(n = 50):\n",
        "    points = np.concatenate((ss.norm(0, 1).rvs((n, 2)), ss.norm(1, 1).rvs((n, 2))), axis = 0)\n",
        "    outcomes = np.concatenate((np.repeat(0, n), np.repeat(1, n)))\n",
        "    return (points, outcomes)\n",
        "\n",
        "n = 50\n",
        "pts,tgts = generate_synth_data(n) #generates 100 points\n",
        "# print(tgts)\n",
        "plt.figure()\n",
        "plt.plot(pts[:n, 0], pts[:n, 1], \"ro\")\n",
        "plt.plot(pts[n:, 0], pts[n:, 1], \"bo\")\n",
        "plt.show()"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "_sE0OBTMrDx2",
        "outputId": "75bb450a-46fa-4058-fdf7-f67f64e4cfae"
      },
      "source": [
        "n = 15\n",
        "test_pts,test_tgts = generate_synth_data(n)\n",
        "# print(test_tgts)\n",
        "plt.figure()\n",
        "plt.plot(test_pts[:n, 0], test_pts[:n, 1], \"ro\")\n",
        "plt.plot(test_pts[n:, 0], test_pts[n:, 1], \"bo\")\n",
        "plt.show()"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "j7_rEYusq3gx",
        "outputId": "b2b6f78a-b618-45ce-d906-d78315189e96"
      },
      "source": [
        "## TASK - 3\n",
        "## The code given below is that of a KNN classifier, provided by Scikit-learn.\n",
        "## The parameter 'metric' includes various distance metric options, including those \n",
        "## we learnt above- manhattan, euclidean, minkowski,chebyshev, hamming, etc.\n",
        "\n",
        "## Try out different metrics and observe changes in the accuracy, if any. Don't change value of 'k'\n",
        "## Also, experiment with different metrics and observe if they are applicable for this kind of data.\n",
        "## If there are any additional parameters needed, for instance, 'p' in case of Minkowski distance, include them.\n",
        "\n",
        "knn = KNeighborsClassifier(n_neighbors = 3)\n",
        "knn.fit(pts, tgts)\n",
        "our_predictions = knn.predict(test_pts)\n",
        "print(\"Prediction Accuracy: \")\n",
        "print(100 * np.mean(our_predictions == test_tgts))"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Prediction Accuracy: \n",
            "80.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EI_EKcQbpSfc"
      },
      "source": [
        "### **SECTION - 2.2: KNN on a Real World dataset**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zajt-k7v7qbW"
      },
      "source": [
        "The Iris flower data set or Fisher's Iris data set is a multivariate data set that consists of 50 samples from each of three species of Iris (*Iris setosa, Iris virginica and Iris versicolor*). Four features were measured from each sample: the length and the width of the sepals and petals, in centimeters."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "jJNUUOszgKop",
        "outputId": "76065b68-2f13-4ea1-adf9-553129877693"
      },
      "source": [
        "from sklearn.datasets import load_iris\n",
        "iris = load_iris()\n",
        "data = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
        "# data['species'] = pd.Categorical.from_codes(iris.target, iris.target_names)\n",
        "data['target'] = pd.Series(iris.target)\n",
        "data.head(10)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \\\n",
              "0                5.1               3.5                1.4               0.2   \n",
              "1                4.9               3.0                1.4               0.2   \n",
              "2                4.7               3.2                1.3               0.2   \n",
              "3                4.6               3.1                1.5               0.2   \n",
              "4                5.0               3.6                1.4               0.2   \n",
              "5                5.4               3.9                1.7               0.4   \n",
              "6                4.6               3.4                1.4               0.3   \n",
              "7                5.0               3.4                1.5               0.2   \n",
              "8                4.4               2.9                1.4               0.2   \n",
              "9                4.9               3.1                1.5               0.1   \n",
              "\n",
              "   target  \n",
              "0       0  \n",
              "1       0  \n",
              "2       0  \n",
              "3       0  \n",
              "4       0  \n",
              "5       0  \n",
              "6       0  \n",
              "7       0  \n",
              "8       0  \n",
              "9       0  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-9593df55-2d2a-49d2-bd73-e0e0da0eddf0\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5.4</td>\n",
              "      <td>3.9</td>\n",
              "      <td>1.7</td>\n",
              "      <td>0.4</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.4</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.3</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.4</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>4.4</td>\n",
              "      <td>2.9</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-9593df55-2d2a-49d2-bd73-e0e0da0eddf0')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-9593df55-2d2a-49d2-bd73-e0e0da0eddf0 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-9593df55-2d2a-49d2-bd73-e0e0da0eddf0');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UVLp3aPcmHpd"
      },
      "source": [
        "np.random.seed(123)\n",
        "indices = np.random.permutation(data.shape[0])\n",
        "div = int(0.65 * len(indices))\n",
        "train_idx, test_idx = indices[:div], indices[div:]\n",
        "\n",
        "train_set, test_set = data.loc[train_idx,:], data.loc[test_idx,:]\n",
        "test_class = list(test_set.iloc[:,-1])\n",
        "train_class = list(train_set.iloc[:,-1])"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-wJLdSdgTH3c"
      },
      "source": [
        "def dist_euclidean(X1,X2):           \n",
        "    return distance.euclidean(X1,X2)"
      ],
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DJZA2cEXUnsS"
      },
      "source": [
        "def dist_cosine(X1,X2):           \n",
        "    return distance.cosine(X1,X2)"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gSG6q9qEoV0M"
      },
      "source": [
        "def dist_manhattan(X1,X2):           \n",
        "    return distance.cityblock(X1,X2)"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hJ-8j3NyooWR"
      },
      "source": [
        "def dist_chebyshev(X1,X2):           \n",
        "    return distance.chebyshev(X1,X2)"
      ],
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TOyqbdGCmTOa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f1cd31be-1c46-4426-c0d3-f52f2c05a111"
      },
      "source": [
        "metrics_list = [dist_euclidean,dist_cosine, dist_manhattan, dist_chebyshev]\n",
        "for dist_metric in metrics_list:\n",
        "  knn = KNeighborsClassifier(n_neighbors = 3, metric=dist_metric)\n",
        "  knn.fit(train_set, train_class)\n",
        "  our_predictions = knn.predict(test_set)\n",
        "  print(dist_metric.__name__)\n",
        "  print(\"Prediction Accuracy: \")\n",
        "  print(100 * np.mean(our_predictions == test_class))\n",
        "  print()"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "dist_euclidean\n",
            "Prediction Accuracy: \n",
            "100.0\n",
            "\n",
            "dist_cosine\n",
            "Prediction Accuracy: \n",
            "100.0\n",
            "\n",
            "dist_manhattan\n",
            "Prediction Accuracy: \n",
            "100.0\n",
            "\n",
            "dist_chebyshev\n",
            "Prediction Accuracy: \n",
            "100.0\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mrl4bMze0UpK"
      },
      "source": [
        "---\n",
        "### Questions to Think About and Answer: \n",
        "\n",
        "1. How are similarity and distance different from each other?  \n",
        "\n",
        "2. Are there any conditions for a particular distance to be considered a \"distance metric\"? \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Answer for Question 1**\n",
        "\n",
        "A distance is a measure of the difference between two points or vectors whereas similarity is an amount that reflects the strength of relationship between two data items.If the distance is high the similarity of features becomes low and if distance is low the similarity of features becomes high."
      ],
      "metadata": {
        "id": "tJ4ZrSNntBn4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Answer for Question 2**\n",
        "\n",
        "Distance metrics are the important part of several machine learning algorithms. These distance metrics are used in both supervised and unsupervised learning, generally to calculate the similarity between data points. There are 4 types of distance matrices in machine learning:\n",
        "\n",
        "  1. Euclidean distance:To calculate the straight line distance between two points.\n",
        "  2. Manhattan distance:To calculate sum of absolute differences of their coordinates in which distances are measured in the form of grid.\n",
        "  3. Cosine Similarity:Used for text-analytics,document comparison problems and in collaborative filtering-based recommendation systems.\n",
        "  4. Hamming Distance:To measure the distance between categorical variables.\n",
        "\n",
        "I think there are no conditions for a particular distance to be considered a distance metrics."
      ],
      "metadata": {
        "id": "Ew5n0kCNueVo"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DsCOj-JbyFk0"
      },
      "source": [
        "\n",
        "### Useful Resources for further reading\n",
        "1.   [Analytics Vidhya: Distance metrics](https://www.analyticsvidhya.com/blog/2020/02/4-types-of-distance-metrics-in-machine-learning/)\n",
        "2.   [Scikit learn distance metric documentation](https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.DistanceMetric.html)\n",
        "\n"
      ]
    }
  ]
}