sagemaker-countycensusclustering.ipynb

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    "# Analyze US census data for population segmentation using Amazon SageMaker\n",
    "\n",
    "### https://aws.amazon.com/blogs/machine-learning/analyze-us-census-data-for-population-segmentation-using-amazon-sagemaker/ ###\n",
    "\n",
    "\n",
    "## Introduction\n",
    "\n",
    "In the United States, with the 2018 midterm elections approaching, people are looking for more information about the voting process. This example notebook explores how we can apply machine learning (ML) to better integrate science into the task of understanding the electorate.\n",
    "\n",
    "Typically, for machine learning applications, clear use cases are derived from labelled data. For example, based on the attributes of a device, such as its age or model number, we can predict its likelihood of failure. We call this *supervised learning* because there is supervision or guidance towards predicting specific outcomes.\n",
    "\n",
    "However, in the real world, there are often large data sets where there is no particular outcome to predict, where clean labels are hard to define. It can be difficult to pinpoint exactly what the right outcome is to predict. This type of use case is often exploratory. It seeks to understand the makeup of a dataset and what natural patterns exist. This type of use case is known as `unsupervised learning`. One example of this is trying to group similar individuals together based on a set of attributes.\n",
    "\n",
    "The use case this blog post explores is population segmentation. We have taken publicly available, anonymized data from the US census on demographics by different US counties: https://factfinder.census.gov/faces/nav/jsf/pages/index.xhtml. (Note that this product uses the Census Bureau Data API but is not endorsed or certified by the Census Bureau.) The outcome of this analysis are natural groupings of similar counties in a transformed feature space. The cluster that a county belongs to can be leveraged to plan an election campaign, for example, to understand how to reach a group of similar counties by highlighting messages that resonate with that group. More generally, this technique can be applied by businesses in customer or user segmentation to create targeted marketing campaigns. This type of analysis has the ability to uncover similarities that may not be obvious at face value- such as counties CA-Fresno and AZ- Yuma County being grouped together. While intuitively they differ in commonly-examined attributes such as population size and racial makeup, they are more similar than different when viewed along axes such as the mix of employment type.\n",
    "\n",
    "You can follow along in this sample notebook where you can run the code and interact with the data while reading through the blog post (link is shown above).\n",
    "\n",
    "There are two goals for this exercise:\n",
    "\n",
    "1) Walk through a data science workflow using Amazon SageMaker for `unsupervised learning` using `PCA` and `KMeans` modelling techniques.\n",
    "\n",
    "2) Demonstrate how users can access the underlying models that are built within Amazon SageMaker to extract useful model attributes. Often, it can be difficult to draw conclusions from unsupervised learning, so being able to access the models for `PCA` and `KMeans` becomes even more important beyond simply generating predictions using the model.\n",
    "\n",
    "The data science workflow has 4 main steps:\n",
    "\n",
    "1. [Loading the data from Amazon S3](#Step-1:-Loading-the-data-from-Amazon-S3)\n",
    "2. [Exploratory data analysis (EDA) - Data cleaning and exploration](#Step-2:-Exploratory-data-analysis-EDA---Data-cleaning-and-exploration)\n",
    "   1. [Cleaning the data](#a.-Cleaning-the-data)\n",
    "   2. [Visualizing the data](#b.-Visualizing-the-data)\n",
    "   3. [Feature engineering](#c.-Feature-engineering)\n",
    "3. [Data modelling](#Step-3:-Data-modelling)\n",
    "   1. [Dimensionality reduction](#a.-Dimensionality-reduction)\n",
    "   2. [Accessing the PCA model attributes](#b.-Accessing-the-PCA-model-attributes)\n",
    "   3. [Deploying the PCA model](#c.-Deploying-the-PCA-model)\n",
    "   4. [Population segmentation using unsupervised clustering](#d.-Population-segmentation-using-unsupervised-clustering)\n",
    "4. [Drawing conclusions from our modelling](#Step-4:-Drawing-conclusions-from-our-modelling)\n",
    "    1. [Accessing the KMeans model attributes](#a.-Accessing-the-KMeans-model-attributes)"
   ]
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   "source": [
    "## Step 1: Loading the data from Amazon S3\n",
    "\n",
    "You need to load the dataset from an Amazon S3 bucket into the Amazon SageMaker notebook.\n",
    "\n",
    "First, we will import the relevant libraries into our Amazon SageMaker notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import os\n",
    "import boto3\n",
    "import io\n",
    "import sagemaker\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import mxnet as mx\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "import seaborn as sns\n",
    "\n",
    "matplotlib.style.use(\"ggplot\")\n",
    "import pickle, gzip, urllib, json\n",
    "import csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Amazon SageMaker integrates seamlessly with Amazon S3. During the first step in creating the notebook, we specified a `AmazonSageMakerFullAccess` role for the notebook. That gives this notebook permission to access any Amazon S3 bucket in this AWS account with \"sagemaker\" in its name.\n",
    "\n",
    "The get_execution_role function retrieves the IAM role you created at the time you created your notebook instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "nbpresent": {
     "id": "ba9ad1d9-659e-4fad-a0fd-0a23e7b56fc0"
    }
   },
   "outputs": [],
   "source": [
    "from sagemaker import get_execution_role\n",
    "\n",
    "role = get_execution_role()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see our role is an AmazonSageMaker-ExecutionRole."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'arn:aws:iam::528038902135:role/service-role/AmazonSageMaker-ExecutionRole-20220120T142266'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "role"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading the dataset\n",
    "I have previously downloaded and stored the data in a public S3 bucket that you can access. You can use the Python SDK to interact with AWS using a Boto3 client.\n",
    "\n",
    "First, start the client."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "s3_client = boto3.client(\"s3\")\n",
    "data_bucket_name = \"aws-ml-blog-sagemaker-census-segmentation\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You’ll get a list of objects that are contained within the bucket.  You can see there is one file in the bucket, 'Census_Data_for_SageMaker.csv'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Census_Data_for_SageMaker.csv']\n"
     ]
    }
   ],
   "source": [
    "obj_list = s3_client.list_objects(Bucket=data_bucket_name)\n",
    "file = []\n",
    "for contents in obj_list[\"Contents\"]:\n",
    "    file.append(contents[\"Key\"])\n",
    "print(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_data = file[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grab the data from the CSV file in the bucket."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "response = s3_client.get_object(Bucket=data_bucket_name, Key=file_data)\n",
    "response_body = response[\"Body\"].read()\n",
    "counties = pd.read_csv(io.BytesIO(response_body), header=0, delimiter=\",\", low_memory=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is what the first 5 rows of our data looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "nbpresent": {
     "id": "97a46770-dbe0-40ea-b454-b15bdec20f53"
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   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CensusId</th>\n",
       "      <th>State</th>\n",
       "      <th>County</th>\n",
       "      <th>TotalPop</th>\n",
       "      <th>Men</th>\n",
       "      <th>Women</th>\n",
       "      <th>Hispanic</th>\n",
       "      <th>White</th>\n",
       "      <th>Black</th>\n",
       "      <th>Native</th>\n",
       "      <th>...</th>\n",
       "      <th>Walk</th>\n",
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       "      <th>SelfEmployed</th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001</td>\n",
       "      <td>Alabama</td>\n",
       "      <td>Autauga</td>\n",
       "      <td>55221</td>\n",
       "      <td>26745</td>\n",
       "      <td>28476</td>\n",
       "      <td>2.6</td>\n",
       "      <td>75.8</td>\n",
       "      <td>18.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>...</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1.3</td>\n",
       "      <td>1.8</td>\n",
       "      <td>26.5</td>\n",
       "      <td>23986</td>\n",
       "      <td>73.6</td>\n",
       "      <td>20.9</td>\n",
       "      <td>5.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1003</td>\n",
       "      <td>Alabama</td>\n",
       "      <td>Baldwin</td>\n",
       "      <td>195121</td>\n",
       "      <td>95314</td>\n",
       "      <td>99807</td>\n",
       "      <td>4.5</td>\n",
       "      <td>83.1</td>\n",
       "      <td>9.5</td>\n",
       "      <td>0.6</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>26.4</td>\n",
       "      <td>85953</td>\n",
       "      <td>81.5</td>\n",
       "      <td>12.3</td>\n",
       "      <td>5.8</td>\n",
       "      <td>0.4</td>\n",
       "      <td>7.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1005</td>\n",
       "      <td>Alabama</td>\n",
       "      <td>Barbour</td>\n",
       "      <td>26932</td>\n",
       "      <td>14497</td>\n",
       "      <td>12435</td>\n",
       "      <td>4.6</td>\n",
       "      <td>46.2</td>\n",
       "      <td>46.7</td>\n",
       "      <td>0.2</td>\n",
       "      <td>...</td>\n",
       "      <td>1.8</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1.6</td>\n",
       "      <td>24.1</td>\n",
       "      <td>8597</td>\n",
       "      <td>71.8</td>\n",
       "      <td>20.8</td>\n",
       "      <td>7.3</td>\n",
       "      <td>0.1</td>\n",
       "      <td>17.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1007</td>\n",
       "      <td>Alabama</td>\n",
       "      <td>Bibb</td>\n",
       "      <td>22604</td>\n",
       "      <td>12073</td>\n",
       "      <td>10531</td>\n",
       "      <td>2.2</td>\n",
       "      <td>74.5</td>\n",
       "      <td>21.4</td>\n",
       "      <td>0.4</td>\n",
       "      <td>...</td>\n",
       "      <td>0.6</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.7</td>\n",
       "      <td>28.8</td>\n",
       "      <td>8294</td>\n",
       "      <td>76.8</td>\n",
       "      <td>16.1</td>\n",
       "      <td>6.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1009</td>\n",
       "      <td>Alabama</td>\n",
       "      <td>Blount</td>\n",
       "      <td>57710</td>\n",
       "      <td>28512</td>\n",
       "      <td>29198</td>\n",
       "      <td>8.6</td>\n",
       "      <td>87.9</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.3</td>\n",
       "      <td>...</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>34.9</td>\n",
       "      <td>22189</td>\n",
       "      <td>82.0</td>\n",
       "      <td>13.5</td>\n",
       "      <td>4.2</td>\n",
       "      <td>0.4</td>\n",
       "      <td>7.7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 37 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   CensusId    State   County  TotalPop    Men  Women  Hispanic  White  Black  \\\n",
       "0      1001  Alabama  Autauga     55221  26745  28476       2.6   75.8   18.5   \n",
       "1      1003  Alabama  Baldwin    195121  95314  99807       4.5   83.1    9.5   \n",
       "2      1005  Alabama  Barbour     26932  14497  12435       4.6   46.2   46.7   \n",
       "3      1007  Alabama     Bibb     22604  12073  10531       2.2   74.5   21.4   \n",
       "4      1009  Alabama   Blount     57710  28512  29198       8.6   87.9    1.5   \n",
       "\n",
       "   Native  ...  Walk  OtherTransp  WorkAtHome  MeanCommute  Employed  \\\n",
       "0     0.4  ...   0.5          1.3         1.8         26.5     23986   \n",
       "1     0.6  ...   1.0          1.4         3.9         26.4     85953   \n",
       "2     0.2  ...   1.8          1.5         1.6         24.1      8597   \n",
       "3     0.4  ...   0.6          1.5         0.7         28.8      8294   \n",
       "4     0.3  ...   0.9          0.4         2.3         34.9     22189   \n",
       "\n",
       "   PrivateWork  PublicWork  SelfEmployed  FamilyWork  Unemployment  \n",
       "0         73.6        20.9           5.5         0.0           7.6  \n",
       "1         81.5        12.3           5.8         0.4           7.5  \n",
       "2         71.8        20.8           7.3         0.1          17.6  \n",
       "3         76.8        16.1           6.7         0.4           8.3  \n",
       "4         82.0        13.5           4.2         0.4           7.7  \n",
       "\n",
       "[5 rows x 37 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counties.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "c2f7177c-9a56-46a7-8e51-53c1ccdac759"
    }
   },
   "source": [
    "## Step 2: Exploratory data analysis *EDA* - Data cleaning and exploration\n",
    "### a. Cleaning the data\n",
    "We can do simple data cleaning and processing right in our notebook instance, using `the compute` instance of the notebook to execute these computations.\n",
    "\n",
    "How much data are we working with?\n",
    "\n",
    "There are 3220 rows with 37 columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3220, 37)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counties.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's just drop any incomplete data to make our analysis easier. We can see that we lost 2 rows of incomplete data, we now have 3218 rows in our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "nbpresent": {
     "id": "2f809521-0a9c-4000-ba29-f6fcbb027dc9"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3218, 37)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counties.dropna(inplace=True)\n",
    "counties.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "fdd10c00-53ba-405d-8622-fbfeac17d3bb"
    }
   },
   "source": [
    "Let's combine some descriptive reference columns such as state and county and leave the numerical feature columns.\n",
    "\n",
    "We can now set the 'state-county' as the index and the rest of the numerical features become the attributes of each unique county."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr>\n",
       "      <th>Alabama-Autauga</th>\n",
       "      <td>55221</td>\n",
       "      <td>26745</td>\n",
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       "      <td>20.9</td>\n",
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       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>Alabama-Baldwin</th>\n",
       "      <td>195121</td>\n",
       "      <td>95314</td>\n",
       "      <td>99807</td>\n",
       "      <td>4.5</td>\n",
       "      <td>83.1</td>\n",
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       "      <td>0.6</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>147695</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>26.4</td>\n",
       "      <td>85953</td>\n",
       "      <td>81.5</td>\n",
       "      <td>12.3</td>\n",
       "      <td>5.8</td>\n",
       "      <td>0.4</td>\n",
       "      <td>7.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Barbour</th>\n",
       "      <td>26932</td>\n",
       "      <td>14497</td>\n",
       "      <td>12435</td>\n",
       "      <td>4.6</td>\n",
       "      <td>46.2</td>\n",
       "      <td>46.7</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>20714</td>\n",
       "      <td>...</td>\n",
       "      <td>1.8</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1.6</td>\n",
       "      <td>24.1</td>\n",
       "      <td>8597</td>\n",
       "      <td>71.8</td>\n",
       "      <td>20.8</td>\n",
       "      <td>7.3</td>\n",
       "      <td>0.1</td>\n",
       "      <td>17.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Bibb</th>\n",
       "      <td>22604</td>\n",
       "      <td>12073</td>\n",
       "      <td>10531</td>\n",
       "      <td>2.2</td>\n",
       "      <td>74.5</td>\n",
       "      <td>21.4</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>17495</td>\n",
       "      <td>...</td>\n",
       "      <td>0.6</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.7</td>\n",
       "      <td>28.8</td>\n",
       "      <td>8294</td>\n",
       "      <td>76.8</td>\n",
       "      <td>16.1</td>\n",
       "      <td>6.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Blount</th>\n",
       "      <td>57710</td>\n",
       "      <td>28512</td>\n",
       "      <td>29198</td>\n",
       "      <td>8.6</td>\n",
       "      <td>87.9</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>42345</td>\n",
       "      <td>...</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>34.9</td>\n",
       "      <td>22189</td>\n",
       "      <td>82.0</td>\n",
       "      <td>13.5</td>\n",
       "      <td>4.2</td>\n",
       "      <td>0.4</td>\n",
       "      <td>7.7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 34 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 TotalPop    Men  Women  Hispanic  White  Black  Native  \\\n",
       "Alabama-Autauga     55221  26745  28476       2.6   75.8   18.5     0.4   \n",
       "Alabama-Baldwin    195121  95314  99807       4.5   83.1    9.5     0.6   \n",
       "Alabama-Barbour     26932  14497  12435       4.6   46.2   46.7     0.2   \n",
       "Alabama-Bibb        22604  12073  10531       2.2   74.5   21.4     0.4   \n",
       "Alabama-Blount      57710  28512  29198       8.6   87.9    1.5     0.3   \n",
       "\n",
       "                 Asian  Pacific  Citizen  ...  Walk  OtherTransp  WorkAtHome  \\\n",
       "Alabama-Autauga    1.0      0.0    40725  ...   0.5          1.3         1.8   \n",
       "Alabama-Baldwin    0.7      0.0   147695  ...   1.0          1.4         3.9   \n",
       "Alabama-Barbour    0.4      0.0    20714  ...   1.8          1.5         1.6   \n",
       "Alabama-Bibb       0.1      0.0    17495  ...   0.6          1.5         0.7   \n",
       "Alabama-Blount     0.1      0.0    42345  ...   0.9          0.4         2.3   \n",
       "\n",
       "                 MeanCommute  Employed  PrivateWork  PublicWork  SelfEmployed  \\\n",
       "Alabama-Autauga         26.5     23986         73.6        20.9           5.5   \n",
       "Alabama-Baldwin         26.4     85953         81.5        12.3           5.8   \n",
       "Alabama-Barbour         24.1      8597         71.8        20.8           7.3   \n",
       "Alabama-Bibb            28.8      8294         76.8        16.1           6.7   \n",
       "Alabama-Blount          34.9     22189         82.0        13.5           4.2   \n",
       "\n",
       "                 FamilyWork  Unemployment  \n",
       "Alabama-Autauga         0.0           7.6  \n",
       "Alabama-Baldwin         0.4           7.5  \n",
       "Alabama-Barbour         0.1          17.6  \n",
       "Alabama-Bibb            0.4           8.3  \n",
       "Alabama-Blount          0.4           7.7  \n",
       "\n",
       "[5 rows x 34 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counties.index = counties[\"State\"] + \"-\" + counties[\"County\"]\n",
    "counties.head()\n",
    "drop = [\"CensusId\", \"State\", \"County\"]\n",
    "counties.drop(drop, axis=1, inplace=True)\n",
    "counties.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b. Visualizing the data\n",
    "Now we have a dataset with a mix of numerical and categorical columns. We can visualize the data for some of our numerical columns and see what the distribution looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "nbpresent": {
     "id": "7e847244-7b42-490f-8945-46e234a3af75"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "# plt.subplots(figsize=(6, 3))\n",
    "for a in [\"Professional\", \"Service\", \"Office\"]\n",
    "    sns.displot(counties[a])\n",
    "    title = \"Histogram of \" + a\n",
    "    plt.title(title, fontsize=12)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, from the figures above you can observe the distribution of counties that have a percentage of workers in Professional, Service, or Office occupations. Viewing the histograms can visually indicate characteristics of these features such as the mean or skew. The distribution of Professional workers for example reveals that the typical county has around 25-30% Professional workers, with a right skew, long tail and a Professional worker % topping out at almost 80% in some counties."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c. Feature engineering\n",
    "\n",
    "**Data Scaling**- We need to standardize the scaling of the numerical columns in order to use any distance based analytical methods so that we can compare the relative distances between different feature columns. We can use `minmaxscaler` to transform the numerical columns so that they also fall between 0 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import MinMaxScaler\n",
    "\n",
    "scaler = MinMaxScaler()\n",
    "counties_scaled = pd.DataFrame(scaler.fit_transform(counties))\n",
    "counties_scaled.columns = counties.columns\n",
    "counties_scaled.index = counties.index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that all of our numerical columns now have a min of 0 and a max of 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<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>TotalPop</th>\n",
       "      <th>Men</th>\n",
       "      <th>Women</th>\n",
       "      <th>Hispanic</th>\n",
       "      <th>White</th>\n",
       "      <th>Black</th>\n",
       "      <th>Native</th>\n",
       "      <th>Asian</th>\n",
       "      <th>Pacific</th>\n",
       "      <th>Citizen</th>\n",
       "      <th>...</th>\n",
       "      <th>Walk</th>\n",
       "      <th>OtherTransp</th>\n",
       "      <th>WorkAtHome</th>\n",
       "      <th>MeanCommute</th>\n",
       "      <th>Employed</th>\n",
       "      <th>PrivateWork</th>\n",
       "      <th>PublicWork</th>\n",
       "      <th>SelfEmployed</th>\n",
       "      <th>FamilyWork</th>\n",
       "      <th>Unemployment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "      <td>3218.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.009883</td>\n",
       "      <td>0.009866</td>\n",
       "      <td>0.009899</td>\n",
       "      <td>0.110170</td>\n",
       "      <td>0.756024</td>\n",
       "      <td>0.100942</td>\n",
       "      <td>0.018682</td>\n",
       "      <td>0.029405</td>\n",
       "      <td>0.006470</td>\n",
       "      <td>0.011540</td>\n",
       "      <td>...</td>\n",
       "      <td>0.046496</td>\n",
       "      <td>0.041154</td>\n",
       "      <td>0.124428</td>\n",
       "      <td>0.470140</td>\n",
       "      <td>0.009806</td>\n",
       "      <td>0.760810</td>\n",
       "      <td>0.194426</td>\n",
       "      <td>0.216744</td>\n",
       "      <td>0.029417</td>\n",
       "      <td>0.221775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.031818</td>\n",
       "      <td>0.031692</td>\n",
       "      <td>0.031948</td>\n",
       "      <td>0.192617</td>\n",
       "      <td>0.229682</td>\n",
       "      <td>0.166262</td>\n",
       "      <td>0.078748</td>\n",
       "      <td>0.062744</td>\n",
       "      <td>0.035446</td>\n",
       "      <td>0.033933</td>\n",
       "      <td>...</td>\n",
       "      <td>0.051956</td>\n",
       "      <td>0.042321</td>\n",
       "      <td>0.085301</td>\n",
       "      <td>0.143135</td>\n",
       "      <td>0.032305</td>\n",
       "      <td>0.132949</td>\n",
       "      <td>0.106923</td>\n",
       "      <td>0.106947</td>\n",
       "      <td>0.046451</td>\n",
       "      <td>0.112138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.001092</td>\n",
       "      <td>0.001117</td>\n",
       "      <td>0.001069</td>\n",
       "      <td>0.019019</td>\n",
       "      <td>0.642285</td>\n",
       "      <td>0.005821</td>\n",
       "      <td>0.001086</td>\n",
       "      <td>0.004808</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.001371</td>\n",
       "      <td>...</td>\n",
       "      <td>0.019663</td>\n",
       "      <td>0.023018</td>\n",
       "      <td>0.072581</td>\n",
       "      <td>0.373402</td>\n",
       "      <td>0.000948</td>\n",
       "      <td>0.697279</td>\n",
       "      <td>0.120861</td>\n",
       "      <td>0.147541</td>\n",
       "      <td>0.010204</td>\n",
       "      <td>0.150685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.002571</td>\n",
       "      <td>0.002591</td>\n",
       "      <td>0.002539</td>\n",
       "      <td>0.039039</td>\n",
       "      <td>0.842685</td>\n",
       "      <td>0.022119</td>\n",
       "      <td>0.003257</td>\n",
       "      <td>0.012019</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.003219</td>\n",
       "      <td>...</td>\n",
       "      <td>0.033708</td>\n",
       "      <td>0.033248</td>\n",
       "      <td>0.104839</td>\n",
       "      <td>0.462916</td>\n",
       "      <td>0.002234</td>\n",
       "      <td>0.785714</td>\n",
       "      <td>0.172185</td>\n",
       "      <td>0.188525</td>\n",
       "      <td>0.020408</td>\n",
       "      <td>0.208219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.006594</td>\n",
       "      <td>0.006645</td>\n",
       "      <td>0.006556</td>\n",
       "      <td>0.098098</td>\n",
       "      <td>0.933868</td>\n",
       "      <td>0.111758</td>\n",
       "      <td>0.006515</td>\n",
       "      <td>0.028846</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.008237</td>\n",
       "      <td>...</td>\n",
       "      <td>0.056180</td>\n",
       "      <td>0.048593</td>\n",
       "      <td>0.150538</td>\n",
       "      <td>0.560102</td>\n",
       "      <td>0.006144</td>\n",
       "      <td>0.853741</td>\n",
       "      <td>0.243377</td>\n",
       "      <td>0.256831</td>\n",
       "      <td>0.030612</td>\n",
       "      <td>0.271233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 34 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          TotalPop          Men        Women     Hispanic        White  \\\n",
       "count  3218.000000  3218.000000  3218.000000  3218.000000  3218.000000   \n",
       "mean      0.009883     0.009866     0.009899     0.110170     0.756024   \n",
       "std       0.031818     0.031692     0.031948     0.192617     0.229682   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.001092     0.001117     0.001069     0.019019     0.642285   \n",
       "50%       0.002571     0.002591     0.002539     0.039039     0.842685   \n",
       "75%       0.006594     0.006645     0.006556     0.098098     0.933868   \n",
       "max       1.000000     1.000000     1.000000     1.000000     1.000000   \n",
       "\n",
       "             Black       Native        Asian      Pacific      Citizen  ...  \\\n",
       "count  3218.000000  3218.000000  3218.000000  3218.000000  3218.000000  ...   \n",
       "mean      0.100942     0.018682     0.029405     0.006470     0.011540  ...   \n",
       "std       0.166262     0.078748     0.062744     0.035446     0.033933  ...   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
       "25%       0.005821     0.001086     0.004808     0.000000     0.001371  ...   \n",
       "50%       0.022119     0.003257     0.012019     0.000000     0.003219  ...   \n",
       "75%       0.111758     0.006515     0.028846     0.000000     0.008237  ...   \n",
       "max       1.000000     1.000000     1.000000     1.000000     1.000000  ...   \n",
       "\n",
       "              Walk  OtherTransp   WorkAtHome  MeanCommute     Employed  \\\n",
       "count  3218.000000  3218.000000  3218.000000  3218.000000  3218.000000   \n",
       "mean      0.046496     0.041154     0.124428     0.470140     0.009806   \n",
       "std       0.051956     0.042321     0.085301     0.143135     0.032305   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.019663     0.023018     0.072581     0.373402     0.000948   \n",
       "50%       0.033708     0.033248     0.104839     0.462916     0.002234   \n",
       "75%       0.056180     0.048593     0.150538     0.560102     0.006144   \n",
       "max       1.000000     1.000000     1.000000     1.000000     1.000000   \n",
       "\n",
       "       PrivateWork   PublicWork  SelfEmployed   FamilyWork  Unemployment  \n",
       "count  3218.000000  3218.000000   3218.000000  3218.000000   3218.000000  \n",
       "mean      0.760810     0.194426      0.216744     0.029417      0.221775  \n",
       "std       0.132949     0.106923      0.106947     0.046451      0.112138  \n",
       "min       0.000000     0.000000      0.000000     0.000000      0.000000  \n",
       "25%       0.697279     0.120861      0.147541     0.010204      0.150685  \n",
       "50%       0.785714     0.172185      0.188525     0.020408      0.208219  \n",
       "75%       0.853741     0.243377      0.256831     0.030612      0.271233  \n",
       "max       1.000000     1.000000      1.000000     1.000000      1.000000  \n",
       "\n",
       "[8 rows x 34 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counties_scaled.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3: Data modelling\n",
    "### a. Dimensionality reduction\n",
    "\n",
    "We will be using principal component analysis (PCA) to reduce the dimensionality of our data. This method decomposes the data matrix into features that are orthogonal with each other. The resultant orthogonal features are linear combinations of the original feature set. You can think of this method as taking many features and combining similar or redundant features together to form a new, smaller feature set.\n",
    "\n",
    "We can reduce dimensionality with the built-in Amazon SageMaker algorithm for PCA.\n",
    "\n",
    "We first import and call an instance of the PCA SageMaker model. Then we specify different parameters of the model. These can be resource configuration parameters, such as how many instances to use during training, or what type of instances to use. Or they can be model computation hyperparameters, such as how many components to use when performing PCA. Documentation on the PCA model can be found here: http://sagemaker.readthedocs.io/en/latest/pca.html\n",
    "\n",
    "You will use the tools provided by the Amazon SageMaker Python SDK to upload the data to a default bucket. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": [
     "parameters"
    ]
   },
   "outputs": [],
   "source": [
    "sess = sagemaker.Session()\n",
    "bucket = sess.default_bucket()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "isConfigCell": true
   },
   "outputs": [],
   "source": [
    "from sagemaker import PCA\n",
    "\n",
    "num_components = 33\n",
    "\n",
    "pca_SM = PCA(\n",
    "    role=role,\n",
    "    instance_count=1,\n",
    "    instance_type=\"ml.c4.xlarge\",\n",
    "    output_path=\"s3://\" + bucket + \"/counties/\",\n",
    "    num_components=num_components,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we prepare data for Amazon SageMaker by extracting the `numpy array` from the `DataFrame` and explicitly casting to `float32`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data = counties_scaled.values.astype(\"float32\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *record_set* function in the Amazon SageMaker `PCA` model converts a `numpy array` into a record set format that is the required format for the input data to be trained. This is a requirement for all Amazon SageMaker built-in models. The use of this data type is one of the reasons that allows training of models within Amazon SageMaker to perform faster, for larger data sets compared with other implementations of the same models, such as the `sklearn` implementation.\n",
    "\n",
    "We call the fit function on our PCA model, passing in our training data, and this spins up a training instance or cluster to perform the training job."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Defaulting to the only supported framework/algorithm version: 1. Ignoring framework/algorithm version: 1.\n",
      "Defaulting to the only supported framework/algorithm version: 1. Ignoring framework/algorithm version: 1.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2022-03-24 19:39:44 Starting - Starting the training job...\n",
      "2022-03-24 19:40:07 Starting - Preparing the instances for trainingProfilerReport-1648150783: InProgress\n",
      ".........\n",
      "2022-03-24 19:41:28 Downloading - Downloading input data...\n",
      "2022-03-24 19:42:14 Training - Training image download completed. Training in progress...\u001b[34mDocker entrypoint called with argument(s): train\u001b[0m\n",
      "\u001b[34mRunning default environment configuration script\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600 integration.py:636] worker started\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] Reading default configuration from /opt/amazon/lib/python3.7/site-packages/algorithm/resources/default-conf.json: {'algorithm_mode': 'regular', 'subtract_mean': 'true', 'extra_components': '-1', 'force_dense': 'true', 'epochs': 1, '_log_level': 'info', '_kvstore': 'dist_sync', '_num_kv_servers': 'auto', '_num_gpus': 'auto'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] Merging with provided configuration from /opt/ml/input/config/hyperparameters.json: {'feature_dim': '34', 'mini_batch_size': '500', 'num_components': '33'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] Final configuration: {'algorithm_mode': 'regular', 'subtract_mean': 'true', 'extra_components': '-1', 'force_dense': 'true', 'epochs': 1, '_log_level': 'info', '_kvstore': 'dist_sync', '_num_kv_servers': 'auto', '_num_gpus': 'auto', 'feature_dim': '34', 'mini_batch_size': '500', 'num_components': '33'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 WARNING 140082691745600] Loggers have already been setup.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] Launching parameter server for role scheduler\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] {'ENVROOT': '/opt/amazon', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION': 'cpp', 'HOSTNAME': 'ip-10-0-233-218.us-east-2.compute.internal', 'TRAINING_JOB_NAME': 'pca-2022-03-24-19-39-43-887', 'NVIDIA_REQUIRE_CUDA': 'cuda>=9.0', 'TRAINING_JOB_ARN': 'arn:aws:sagemaker:us-east-2:528038902135:training-job/pca-2022-03-24-19-39-43-887', 'AWS_CONTAINER_CREDENTIALS_RELATIVE_URI': '/v2/credentials/proxy-776335ebeb382909e6a76ba9322a055c6c68a411a45d2951354abc37b1c24dde-customer', 'CANONICAL_ENVROOT': '/opt/amazon', 'PYTHONUNBUFFERED': 'TRUE', 'NVIDIA_VISIBLE_DEVICES': 'all', 'LD_LIBRARY_PATH': '/opt/amazon/lib/python3.7/site-packages/cv2/../../../../lib:/usr/local/nvidia/lib64:/opt/amazon/lib', 'NVIDIA_DRIVER_CAPABILITIES': 'compute,utility', 'PATH': '/opt/amazon/bin:/usr/local/nvidia/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/amazon/bin:/opt/amazon/bin', 'PWD': '/', 'LANG': 'en_US.utf8', 'AWS_REGION': 'us-east-2', 'HOME': '/root', 'SHLVL': '1', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION_VERSION': '2', 'OMP_NUM_THREADS': '2', 'DMLC_INTERFACE': 'eth0', 'SAGEMAKER_HTTP_PORT': '8080', 'SAGEMAKER_DATA_PATH': '/opt/ml'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] envs={'ENVROOT': '/opt/amazon', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION': 'cpp', 'HOSTNAME': 'ip-10-0-233-218.us-east-2.compute.internal', 'TRAINING_JOB_NAME': 'pca-2022-03-24-19-39-43-887', 'NVIDIA_REQUIRE_CUDA': 'cuda>=9.0', 'TRAINING_JOB_ARN': 'arn:aws:sagemaker:us-east-2:528038902135:training-job/pca-2022-03-24-19-39-43-887', 'AWS_CONTAINER_CREDENTIALS_RELATIVE_URI': '/v2/credentials/proxy-776335ebeb382909e6a76ba9322a055c6c68a411a45d2951354abc37b1c24dde-customer', 'CANONICAL_ENVROOT': '/opt/amazon', 'PYTHONUNBUFFERED': 'TRUE', 'NVIDIA_VISIBLE_DEVICES': 'all', 'LD_LIBRARY_PATH': '/opt/amazon/lib/python3.7/site-packages/cv2/../../../../lib:/usr/local/nvidia/lib64:/opt/amazon/lib', 'NVIDIA_DRIVER_CAPABILITIES': 'compute,utility', 'PATH': '/opt/amazon/bin:/usr/local/nvidia/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/amazon/bin:/opt/amazon/bin', 'PWD': '/', 'LANG': 'en_US.utf8', 'AWS_REGION': 'us-east-2', 'HOME': '/root', 'SHLVL': '1', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION_VERSION': '2', 'OMP_NUM_THREADS': '2', 'DMLC_INTERFACE': 'eth0', 'SAGEMAKER_HTTP_PORT': '8080', 'SAGEMAKER_DATA_PATH': '/opt/ml', 'DMLC_ROLE': 'scheduler', 'DMLC_PS_ROOT_URI': '10.0.233.218', 'DMLC_PS_ROOT_PORT': '9000', 'DMLC_NUM_SERVER': '1', 'DMLC_NUM_WORKER': '1'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] Launching parameter server for role server\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] {'ENVROOT': '/opt/amazon', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION': 'cpp', 'HOSTNAME': 'ip-10-0-233-218.us-east-2.compute.internal', 'TRAINING_JOB_NAME': 'pca-2022-03-24-19-39-43-887', 'NVIDIA_REQUIRE_CUDA': 'cuda>=9.0', 'TRAINING_JOB_ARN': 'arn:aws:sagemaker:us-east-2:528038902135:training-job/pca-2022-03-24-19-39-43-887', 'AWS_CONTAINER_CREDENTIALS_RELATIVE_URI': '/v2/credentials/proxy-776335ebeb382909e6a76ba9322a055c6c68a411a45d2951354abc37b1c24dde-customer', 'CANONICAL_ENVROOT': '/opt/amazon', 'PYTHONUNBUFFERED': 'TRUE', 'NVIDIA_VISIBLE_DEVICES': 'all', 'LD_LIBRARY_PATH': '/opt/amazon/lib/python3.7/site-packages/cv2/../../../../lib:/usr/local/nvidia/lib64:/opt/amazon/lib', 'NVIDIA_DRIVER_CAPABILITIES': 'compute,utility', 'PATH': '/opt/amazon/bin:/usr/local/nvidia/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/amazon/bin:/opt/amazon/bin', 'PWD': '/', 'LANG': 'en_US.utf8', 'AWS_REGION': 'us-east-2', 'HOME': '/root', 'SHLVL': '1', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION_VERSION': '2', 'OMP_NUM_THREADS': '2', 'DMLC_INTERFACE': 'eth0', 'SAGEMAKER_HTTP_PORT': '8080', 'SAGEMAKER_DATA_PATH': '/opt/ml'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] envs={'ENVROOT': '/opt/amazon', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION': 'cpp', 'HOSTNAME': 'ip-10-0-233-218.us-east-2.compute.internal', 'TRAINING_JOB_NAME': 'pca-2022-03-24-19-39-43-887', 'NVIDIA_REQUIRE_CUDA': 'cuda>=9.0', 'TRAINING_JOB_ARN': 'arn:aws:sagemaker:us-east-2:528038902135:training-job/pca-2022-03-24-19-39-43-887', 'AWS_CONTAINER_CREDENTIALS_RELATIVE_URI': '/v2/credentials/proxy-776335ebeb382909e6a76ba9322a055c6c68a411a45d2951354abc37b1c24dde-customer', 'CANONICAL_ENVROOT': '/opt/amazon', 'PYTHONUNBUFFERED': 'TRUE', 'NVIDIA_VISIBLE_DEVICES': 'all', 'LD_LIBRARY_PATH': '/opt/amazon/lib/python3.7/site-packages/cv2/../../../../lib:/usr/local/nvidia/lib64:/opt/amazon/lib', 'NVIDIA_DRIVER_CAPABILITIES': 'compute,utility', 'PATH': '/opt/amazon/bin:/usr/local/nvidia/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/amazon/bin:/opt/amazon/bin', 'PWD': '/', 'LANG': 'en_US.utf8', 'AWS_REGION': 'us-east-2', 'HOME': '/root', 'SHLVL': '1', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION_VERSION': '2', 'OMP_NUM_THREADS': '2', 'DMLC_INTERFACE': 'eth0', 'SAGEMAKER_HTTP_PORT': '8080', 'SAGEMAKER_DATA_PATH': '/opt/ml', 'DMLC_ROLE': 'server', 'DMLC_PS_ROOT_URI': '10.0.233.218', 'DMLC_PS_ROOT_PORT': '9000', 'DMLC_NUM_SERVER': '1', 'DMLC_NUM_WORKER': '1'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:20 INFO 140082691745600] Environment: {'ENVROOT': '/opt/amazon', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION': 'cpp', 'HOSTNAME': 'ip-10-0-233-218.us-east-2.compute.internal', 'TRAINING_JOB_NAME': 'pca-2022-03-24-19-39-43-887', 'NVIDIA_REQUIRE_CUDA': 'cuda>=9.0', 'TRAINING_JOB_ARN': 'arn:aws:sagemaker:us-east-2:528038902135:training-job/pca-2022-03-24-19-39-43-887', 'AWS_CONTAINER_CREDENTIALS_RELATIVE_URI': '/v2/credentials/proxy-776335ebeb382909e6a76ba9322a055c6c68a411a45d2951354abc37b1c24dde-customer', 'CANONICAL_ENVROOT': '/opt/amazon', 'PYTHONUNBUFFERED': 'TRUE', 'NVIDIA_VISIBLE_DEVICES': 'all', 'LD_LIBRARY_PATH': '/opt/amazon/lib/python3.7/site-packages/cv2/../../../../lib:/usr/local/nvidia/lib64:/opt/amazon/lib', 'NVIDIA_DRIVER_CAPABILITIES': 'compute,utility', 'PATH': '/opt/amazon/bin:/usr/local/nvidia/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/amazon/bin:/opt/amazon/bin', 'PWD': '/', 'LANG': 'en_US.utf8', 'AWS_REGION': 'us-east-2', 'HOME': '/root', 'SHLVL': '1', 'PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION_VERSION': '2', 'OMP_NUM_THREADS': '2', 'DMLC_INTERFACE': 'eth0', 'SAGEMAKER_HTTP_PORT': '8080', 'SAGEMAKER_DATA_PATH': '/opt/ml', 'DMLC_ROLE': 'worker', 'DMLC_PS_ROOT_URI': '10.0.233.218', 'DMLC_PS_ROOT_PORT': '9000', 'DMLC_NUM_SERVER': '1', 'DMLC_NUM_WORKER': '1'}\u001b[0m\n",
      "\u001b[34mProcess 34 is a shell:scheduler.\u001b[0m\n",
      "\u001b[34mProcess 43 is a shell:server.\u001b[0m\n",
      "\u001b[34mProcess 1 is a worker.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:21 INFO 140082691745600] Using default worker.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:21 INFO 140082691745600] Loaded iterator creator application/x-labeled-vector-protobuf for content type ('application/x-labeled-vector-protobuf', '1.0')\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:21 INFO 140082691745600] Loaded iterator creator application/x-recordio-protobuf for content type ('application/x-recordio-protobuf', '1.0')\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:21 INFO 140082691745600] Loaded iterator creator protobuf for content type ('protobuf', '1.0')\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:21 INFO 140082691745600] Checkpoint loading and saving are disabled.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:21 INFO 140082691745600] Create Store: dist_sync\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] nvidia-smi: took 0.054 seconds to run.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] nvidia-smi identified 0 GPUs.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] Number of GPUs being used: 0\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] The default executor is <PCAExecutor on cpu(0)>.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] 34 feature(s) found in 'data'.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] <PCAExecutor on cpu(0)> is assigned to batch slice from 0 to 499.\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648150941.2386668, \"EndTime\": 1648150942.1872294, \"Dimensions\": {\"Algorithm\": \"PCA\", \"Host\": \"algo-1\", \"Operation\": \"training\"}, \"Metrics\": {\"initialize.time\": {\"sum\": 933.5856437683105, \"count\": 1, \"min\": 933.5856437683105, \"max\": 933.5856437683105}}}\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648150942.187475, \"EndTime\": 1648150942.187538, \"Dimensions\": {\"Algorithm\": \"PCA\", \"Host\": \"algo-1\", \"Operation\": \"training\", \"Meta\": \"init_train_data_iter\"}, \"Metrics\": {\"Total Records Seen\": {\"sum\": 0.0, \"count\": 1, \"min\": 0, \"max\": 0}, \"Total Batches Seen\": {\"sum\": 0.0, \"count\": 1, \"min\": 0, \"max\": 0}, \"Max Records Seen Between Resets\": {\"sum\": 0.0, \"count\": 1, \"min\": 0, \"max\": 0}, \"Max Batches Seen Between Resets\": {\"sum\": 0.0, \"count\": 1, \"min\": 0, \"max\": 0}, \"Reset Count\": {\"sum\": 0.0, \"count\": 1, \"min\": 0, \"max\": 0}, \"Number of Records Since Last Reset\": {\"sum\": 0.0, \"count\": 1, \"min\": 0, \"max\": 0}, \"Number of Batches Since Last Reset\": {\"sum\": 0.0, \"count\": 1, \"min\": 0, \"max\": 0}}}\u001b[0m\n",
      "\u001b[34m[2022-03-24 19:42:22.187] [tensorio] [info] epoch_stats={\"data_pipeline\": \"/opt/ml/input/data/train\", \"epoch\": 0, \"duration\": 948, \"num_examples\": 1, \"num_bytes\": 82000}\u001b[0m\n",
      "\u001b[34m[2022-03-24 19:42:22.257] [tensorio] [info] epoch_stats={\"data_pipeline\": \"/opt/ml/input/data/train\", \"epoch\": 1, \"duration\": 58, \"num_examples\": 7, \"num_bytes\": 527752}\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648150942.1873982, \"EndTime\": 1648150942.2578907, \"Dimensions\": {\"Algorithm\": \"PCA\", \"Host\": \"algo-1\", \"Operation\": \"training\"}, \"Metrics\": {\"epochs\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}, \"update.time\": {\"sum\": 69.88382339477539, \"count\": 1, \"min\": 69.88382339477539, \"max\": 69.88382339477539}}}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] #progress_metric: host=algo-1, completed 100.0 % of epochs\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648150942.187968, \"EndTime\": 1648150942.2583528, \"Dimensions\": {\"Algorithm\": \"PCA\", \"Host\": \"algo-1\", \"Operation\": \"training\", \"epoch\": 0, \"Meta\": \"training_data_iter\"}, \"Metrics\": {\"Total Records Seen\": {\"sum\": 3218.0, \"count\": 1, \"min\": 3218, \"max\": 3218}, \"Total Batches Seen\": {\"sum\": 7.0, \"count\": 1, \"min\": 7, \"max\": 7}, \"Max Records Seen Between Resets\": {\"sum\": 3218.0, \"count\": 1, \"min\": 3218, \"max\": 3218}, \"Max Batches Seen Between Resets\": {\"sum\": 7.0, \"count\": 1, \"min\": 7, \"max\": 7}, \"Reset Count\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}, \"Number of Records Since Last Reset\": {\"sum\": 3218.0, \"count\": 1, \"min\": 3218, \"max\": 3218}, \"Number of Batches Since Last Reset\": {\"sum\": 7.0, \"count\": 1, \"min\": 7, \"max\": 7}}}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] #throughput_metric: host=algo-1, train throughput=45625.3981097124 records/second\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648150942.2580156, \"EndTime\": 1648150942.296419, \"Dimensions\": {\"Algorithm\": \"PCA\", \"Host\": \"algo-1\", \"Operation\": \"training\"}, \"Metrics\": {\"finalize.time\": {\"sum\": 37.58096694946289, \"count\": 1, \"min\": 37.58096694946289, \"max\": 37.58096694946289}}}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600] Test data is not provided.\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648150942.296527, \"EndTime\": 1648150942.3040993, \"Dimensions\": {\"Algorithm\": \"PCA\", \"Host\": \"algo-1\", \"Operation\": \"training\"}, \"Metrics\": {\"setuptime\": {\"sum\": 25.897979736328125, \"count\": 1, \"min\": 25.897979736328125, \"max\": 25.897979736328125}, \"totaltime\": {\"sum\": 1336.9038105010986, \"count\": 1, \"min\": 1336.9038105010986, \"max\": 1336.9038105010986}}}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:42:22 INFO 140082691745600 integration.py:636] worker closed\u001b[0m\n",
      "\n",
      "2022-03-24 19:42:40 Uploading - Uploading generated training model\n",
      "2022-03-24 19:42:40 Completed - Training job completed\n",
      "Training seconds: 78\n",
      "Billable seconds: 78\n",
      "CPU times: user 610 ms, sys: 39.9 ms, total: 650 ms\n",
      "Wall time: 3min 12s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "pca_SM.fit(pca_SM.record_set(train_data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b. Accessing the PCA model attributes\n",
    "\n",
    "After the model is created, we can also access the underlying model parameters.\n",
    "\n",
    "Now that the training job is complete, you can find the job under **Jobs** in the **Training** subsection in the Amazon SageMaker console.\n",
    "\n",
    "Model artifacts are stored in Amazon S3 after they have been trained. This is the same model artifact that is used to deploy a trained model using Amazon SageMaker. Since many of the Amazon SageMaker algorithms use MXNet for computational speed, the model artifact is stored as an ND array. For an output path that was specified during the training call, the model resides in `<training_job_name>/output/model.tar.gz` file, which is a TAR archive file compressed with GNU zip (`gzip`) compression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job_name = pca_SM.latest_training_job.name\n",
    "model_key = \"counties/\" + job_name + \"/output/model.tar.gz\"\n",
    "\n",
    "boto3.resource(\"s3\").Bucket(bucket).download_file(model_key, \"model.tar.gz\")\n",
    "os.system(\"tar -zxvf model.tar.gz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the model is decompressed, we can load the ND array using MXNet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mxnet as mx\n",
    "\n",
    "pca_model_params = mx.ndarray.load(\"model_algo-1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Three groups of model parameters are contained within the PCA model.**\n",
    "\n",
    "`mean` is optional and is only available if the “subtract_mean” hyperparameter is true when calling the training step from the original PCA SageMaker function.\n",
    "\n",
    "`v` contains the principal components (same as ‘components_’ in the `sklearn PCA` model).\n",
    "\n",
    "`s` the singular values of the components for the PCA transformation. This does not exactly give the % variance from the original feature space, but can give the % variance from the projected feature space.\n",
    "\n",
    "`explained-variance-ratio` ~= square(s) / sum(square(s))\n",
    "\n",
    "To calculate the exact `explained-variance-ratio` vector if needed, it simply requires saving the sum of squares of the original data (call that N) and computing explained-variance-ratio = square(s) / N."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = pd.DataFrame(pca_model_params[\"s\"].asnumpy())\n",
    "v = pd.DataFrame(pca_model_params[\"v\"].asnumpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now calculate the variance explained by the largest n components that we want to keep. For this example, let's take the top 5 components.\n",
    "\n",
    "We can see that the largest 5 components explain ~72% of the total variance in our dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.717983\n",
       "dtype: float32"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.iloc[28:, :].apply(lambda x: x * x).sum() / s.apply(lambda x: x * x).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After we have decided to keep the top 5 components, we can take only the 5 largest components from our original s and v matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_5 = s.iloc[28:, :]\n",
    "v_5 = v.iloc[:, 28:]\n",
    "v_5.columns = [0, 1, 2, 3, 4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now examine the makeup of each PCA component based on the weightings of the original features that are included in the component. For example, the following code shows the first component. We can see that this component describes an attribute of a county that has high poverty and unemployment, low income and income per capita, and high Hispanic/Black population and low White population.\n",
    "\n",
    "Note that this is v_5[4] or last component of the list of components in v_5, but is actually the largest component because the components are ordered from smallest to largest. So v_5[0] would be the smallest component. Similarly, change the value of component_num to cycle through the makeup of each component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "component_num = 1\n",
    "\n",
    "first_comp = v_5[5 - component_num]\n",
    "comps = pd.DataFrame(\n",
    "    list(zip(first_comp, counties_scaled.columns)), columns=[\"weights\", \"features\"]\n",
    ")\n",
    "comps[\"abs_weights\"] = comps[\"weights\"].apply(lambda x: np.abs(x))\n",
    "ax = sns.barplot(\n",
    "    data=comps.sort_values(\"abs_weights\", ascending=False).head(10),\n",
    "    x=\"weights\",\n",
    "    y=\"features\",\n",
    "    palette=\"Blues_d\",\n",
    ")\n",
    "ax.set_title(\"PCA Component Makeup: #\" + str(component_num))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, you can go through and examine the makeup of each PCA components and try to understand what the key positive and negative attributes are for each component. The following code names the components, but feel free to change them as you gain insight into the unique makeup of each component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "PCA_list = [\"comp_1\", \"comp_2\", \"comp_3\", \"comp_4\", \"comp_5\"]\n",
    "\n",
    "# PCA_list=[\"Poverty/Unemployment\", \"Self Employment/Public Workers\", \"High Income/Professional & Office Workers\", \\\n",
    "#         \"Black/Native Am Populations & Public/Professional Workers\", \"Construction & Commuters\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c. Deploying the PCA model\n",
    "\n",
    "We can now deploy this model endpoint and use it to make predictions. This model is now live and hosted on an instance_type that we specify."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Defaulting to the only supported framework/algorithm version: 1. Ignoring framework/algorithm version: 1.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------!CPU times: user 198 ms, sys: 27.7 ms, total: 225 ms\n",
      "Wall time: 5min 31s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "pca_predictor = pca_SM.deploy(initial_instance_count=1, instance_type=\"ml.t2.medium\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also pass our original dataset to the model so that we can transform the data using the model we created. Then we can take the largest 5 components and this will reduce the dimensionality of our data from 34 to 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 182 ms, sys: 6.25 ms, total: 188 ms\n",
      "Wall time: 561 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result = pca_predictor.predict(train_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "counties_transformed = pd.DataFrame()\n",
    "for a in result:\n",
    "    b = a.label[\"projection\"].float32_tensor.values\n",
    "    counties_transformed = counties_transformed.append([list(b)])\n",
    "counties_transformed.index = counties_scaled.index\n",
    "counties_transformed = counties_transformed.iloc[:, 28:]\n",
    "counties_transformed.columns = PCA_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have created a dataset where each county is described by the 5 principal components that we analyzed earlier. Each of these 5 components is a linear combination of the original feature space. We can interpret each of these 5 components by analyzing the makeup of the component shown previously."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<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>comp_1</th>\n",
       "      <th>comp_2</th>\n",
       "      <th>comp_3</th>\n",
       "      <th>comp_4</th>\n",
       "      <th>comp_5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama-Autauga</th>\n",
       "      <td>-0.010824</td>\n",
       "      <td>0.120480</td>\n",
       "      <td>-0.088356</td>\n",
       "      <td>0.160527</td>\n",
       "      <td>-0.060274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Baldwin</th>\n",
       "      <td>-0.068677</td>\n",
       "      <td>-0.023092</td>\n",
       "      <td>-0.145743</td>\n",
       "      <td>0.185969</td>\n",
       "      <td>-0.149684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Barbour</th>\n",
       "      <td>0.093111</td>\n",
       "      <td>0.297829</td>\n",
       "      <td>0.146258</td>\n",
       "      <td>0.296662</td>\n",
       "      <td>0.506202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Bibb</th>\n",
       "      <td>0.283526</td>\n",
       "      <td>0.011757</td>\n",
       "      <td>0.224402</td>\n",
       "      <td>0.190861</td>\n",
       "      <td>0.069224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Blount</th>\n",
       "      <td>0.100738</td>\n",
       "      <td>-0.193824</td>\n",
       "      <td>0.022714</td>\n",
       "      <td>0.254403</td>\n",
       "      <td>-0.091030</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   comp_1    comp_2    comp_3    comp_4    comp_5\n",
       "Alabama-Autauga -0.010824  0.120480 -0.088356  0.160527 -0.060274\n",
       "Alabama-Baldwin -0.068677 -0.023092 -0.145743  0.185969 -0.149684\n",
       "Alabama-Barbour  0.093111  0.297829  0.146258  0.296662  0.506202\n",
       "Alabama-Bibb     0.283526  0.011757  0.224402  0.190861  0.069224\n",
       "Alabama-Blount   0.100738 -0.193824  0.022714  0.254403 -0.091030"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counties_transformed.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d. Population segmentation using unsupervised clustering\n",
    "\n",
    "Now, we’ll use the `KMeans` algorithm to segment the population of counties by the 5 `PCA` attributes we have created. `KMeans` is a clustering algorithm that identifies clusters of similar counties based on their attributes. Since we have ~3000 counties and 34 attributes in our original dataset, the large feature space may have made it difficult to cluster the counties effectively. Instead, we have reduced the feature space to 5 PCA components, and we’ll cluster on this transformed dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data = counties_transformed.values.astype(\"float32\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we call and define the hyperparameters of our `KMeans` model as we have done with our `PCA` model. The `KMeans` algorithm allows the user to specify how many clusters to identify. In this instance, let's try to find the top 7 clusters from our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sagemaker import KMeans\n",
    "\n",
    "num_clusters = 7\n",
    "kmeans = KMeans(\n",
    "    role=role,\n",
    "    instance_count=1,\n",
    "    instance_type=\"ml.c4.xlarge\",\n",
    "    output_path=\"s3://\" + bucket + \"/counties/\",\n",
    "    k=num_clusters,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we train the model on our training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Defaulting to the only supported framework/algorithm version: 1. Ignoring framework/algorithm version: 1.\n",
      "Defaulting to the only supported framework/algorithm version: 1. Ignoring framework/algorithm version: 1.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2022-03-24 19:50:58 Starting - Starting the training job...\n",
      "2022-03-24 19:51:14 Starting - Preparing the instances for trainingProfilerReport-1648151458: InProgress\n",
      ".........\n",
      "2022-03-24 19:52:57 Downloading - Downloading input data...\n",
      "2022-03-24 19:53:17 Training - Downloading the training image..\u001b[34mDocker entrypoint called with argument(s): train\u001b[0m\n",
      "\u001b[34mRunning default environment configuration script\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:41 INFO 139950812604224] Reading default configuration from /opt/amazon/lib/python3.7/site-packages/algorithm/resources/default-input.json: {'init_method': 'random', 'mini_batch_size': '5000', 'epochs': '1', 'extra_center_factor': 'auto', 'local_lloyd_max_iter': '300', 'local_lloyd_tol': '0.0001', 'local_lloyd_init_method': 'kmeans++', 'local_lloyd_num_trials': 'auto', 'half_life_time_size': '0', 'eval_metrics': '[\"msd\"]', 'force_dense': 'true', '_disable_wait_to_read': 'false', '_enable_profiler': 'false', '_kvstore': 'auto', '_log_level': 'info', '_num_gpus': 'auto', '_num_kv_servers': '1', '_num_slices': '1', '_tuning_objective_metric': ''}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:41 INFO 139950812604224] Merging with provided configuration from /opt/ml/input/config/hyperparameters.json: {'feature_dim': '5', 'force_dense': 'True', 'k': '7'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:41 INFO 139950812604224] Final configuration: {'init_method': 'random', 'mini_batch_size': '5000', 'epochs': '1', 'extra_center_factor': 'auto', 'local_lloyd_max_iter': '300', 'local_lloyd_tol': '0.0001', 'local_lloyd_init_method': 'kmeans++', 'local_lloyd_num_trials': 'auto', 'half_life_time_size': '0', 'eval_metrics': '[\"msd\"]', 'force_dense': 'True', '_disable_wait_to_read': 'false', '_enable_profiler': 'false', '_kvstore': 'auto', '_log_level': 'info', '_num_gpus': 'auto', '_num_kv_servers': '1', '_num_slices': '1', '_tuning_objective_metric': '', 'feature_dim': '5', 'k': '7'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 WARNING 139950812604224] Loggers have already been setup.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224 integration.py:636] worker started\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Final configuration: {'init_method': 'random', 'mini_batch_size': '5000', 'epochs': '1', 'extra_center_factor': 'auto', 'local_lloyd_max_iter': '300', 'local_lloyd_tol': '0.0001', 'local_lloyd_init_method': 'kmeans++', 'local_lloyd_num_trials': 'auto', 'half_life_time_size': '0', 'eval_metrics': '[\"msd\"]', 'force_dense': 'True', '_disable_wait_to_read': 'false', '_enable_profiler': 'false', '_kvstore': 'auto', '_log_level': 'info', '_num_gpus': 'auto', '_num_kv_servers': '1', '_num_slices': '1', '_tuning_objective_metric': '', 'feature_dim': '5', 'k': '7'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 WARNING 139950812604224] Loggers have already been setup.\u001b[0m\n",
      "\u001b[34mProcess 1 is a worker.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Using default worker.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Loaded iterator creator application/x-recordio-protobuf for content type ('application/x-recordio-protobuf', '1.0')\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Create Store: local\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] nvidia-smi: took 0.031 seconds to run.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] nvidia-smi identified 0 GPUs.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Number of GPUs being used: 0\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Checkpoint loading and saving are disabled.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Setting up with params: {'init_method': 'random', 'mini_batch_size': '5000', 'epochs': '1', 'extra_center_factor': 'auto', 'local_lloyd_max_iter': '300', 'local_lloyd_tol': '0.0001', 'local_lloyd_init_method': 'kmeans++', 'local_lloyd_num_trials': 'auto', 'half_life_time_size': '0', 'eval_metrics': '[\"msd\"]', 'force_dense': 'True', '_disable_wait_to_read': 'false', '_enable_profiler': 'false', '_kvstore': 'auto', '_log_level': 'info', '_num_gpus': 'auto', '_num_kv_servers': '1', '_num_slices': '1', '_tuning_objective_metric': '', 'feature_dim': '5', 'k': '7'}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] 'extra_center_factor' was set to 'auto', evaluated to 10.\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Number of GPUs being used: 0\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] number of center slices 1\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 WARNING 139950812604224] Batch size 5000 is bigger than the first batch data. Effective batch size used to initialize is 3218\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648151624.3319883, \"EndTime\": 1648151624.332019, \"Dimensions\": {\"Algorithm\": \"AWS/KMeansWebscale\", \"Host\": \"algo-1\", \"Operation\": \"training\", \"Meta\": \"init_train_data_iter\"}, \"Metrics\": {\"Total Records Seen\": {\"sum\": 3218.0, \"count\": 1, \"min\": 3218, \"max\": 3218}, \"Total Batches Seen\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}, \"Max Records Seen Between Resets\": {\"sum\": 3218.0, \"count\": 1, \"min\": 3218, \"max\": 3218}, \"Max Batches Seen Between Resets\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}, \"Reset Count\": {\"sum\": 0.0, \"count\": 1, \"min\": 0, \"max\": 0}, \"Number of Records Since Last Reset\": {\"sum\": 3218.0, \"count\": 1, \"min\": 3218, \"max\": 3218}, \"Number of Batches Since Last Reset\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}}}\u001b[0m\n",
      "\u001b[34m[2022-03-24 19:53:44.332] [tensorio] [info] epoch_stats={\"data_pipeline\": \"/opt/ml/input/data/train\", \"epoch\": 0, \"duration\": 42, \"num_examples\": 1, \"num_bytes\": 141592}\u001b[0m\n",
      "\u001b[34m[2022-03-24 19:53:44.421] [tensorio] [info] epoch_stats={\"data_pipeline\": \"/opt/ml/input/data/train\", \"epoch\": 1, \"duration\": 86, \"num_examples\": 1, \"num_bytes\": 141592}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] processed a total of 3218 examples\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] #progress_metric: host=algo-1, completed 100.0 % of epochs\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648151624.3323638, \"EndTime\": 1648151624.42163, \"Dimensions\": {\"Algorithm\": \"AWS/KMeansWebscale\", \"Host\": \"algo-1\", \"Operation\": \"training\", \"epoch\": 0, \"Meta\": \"training_data_iter\"}, \"Metrics\": {\"Total Records Seen\": {\"sum\": 6436.0, \"count\": 1, \"min\": 6436, \"max\": 6436}, \"Total Batches Seen\": {\"sum\": 2.0, \"count\": 1, \"min\": 2, \"max\": 2}, \"Max Records Seen Between Resets\": {\"sum\": 3218.0, \"count\": 1, \"min\": 3218, \"max\": 3218}, \"Max Batches Seen Between Resets\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}, \"Reset Count\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}, \"Number of Records Since Last Reset\": {\"sum\": 3218.0, \"count\": 1, \"min\": 3218, \"max\": 3218}, \"Number of Batches Since Last Reset\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}}}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] #throughput_metric: host=algo-1, train throughput=35994.35246931194 records/second\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 WARNING 139950812604224] wait_for_all_workers will not sync workers since the kv store is not running distributed\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] shrinking 70 centers into 7\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #0. Current mean square distance 0.066840\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #1. Current mean square distance 0.059967\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #2. Current mean square distance 0.066656\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #3. Current mean square distance 0.059408\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #4. Current mean square distance 0.069589\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #5. Current mean square distance 0.065964\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #6. Current mean square distance 0.060301\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #7. Current mean square distance 0.059562\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #8. Current mean square distance 0.067816\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] local kmeans attempt #9. Current mean square distance 0.059022\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] finished shrinking process. Mean Square Distance = 0\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] #quality_metric: host=algo-1, train msd <loss>=0.059022292494773865\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] compute all data-center distances: inner product took: 40.5564%, (0.038601 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] gradient: cluster center took: 10.3686%, (0.009869 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] batch data loading with context took: 8.8341%, (0.008408 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] gradient: one_hot took: 7.8621%, (0.007483 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] collect from kv store took: 7.3982%, (0.007041 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] compute all data-center distances: point norm took: 7.3441%, (0.006990 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] splitting centers key-value pair took: 7.2562%, (0.006906 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] predict compute msd took: 5.2196%, (0.004968 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] update state and report convergance took: 2.6643%, (0.002536 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] gradient: cluster size  took: 1.8675%, (0.001777 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] update set-up time took: 0.3512%, (0.000334 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] compute all data-center distances: center norm took: 0.2370%, (0.000226 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] predict minus dist took: 0.0408%, (0.000039 secs)\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] TOTAL took: 0.09517788887023926\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Number of GPUs being used: 0\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648151624.2896078, \"EndTime\": 1648151624.8193247, \"Dimensions\": {\"Algorithm\": \"AWS/KMeansWebscale\", \"Host\": \"algo-1\", \"Operation\": \"training\"}, \"Metrics\": {\"initialize.time\": {\"sum\": 33.69402885437012, \"count\": 1, \"min\": 33.69402885437012, \"max\": 33.69402885437012}, \"epochs\": {\"sum\": 1.0, \"count\": 1, \"min\": 1, \"max\": 1}, \"update.time\": {\"sum\": 89.05911445617676, \"count\": 1, \"min\": 89.05911445617676, \"max\": 89.05911445617676}, \"_shrink.time\": {\"sum\": 391.64280891418457, \"count\": 1, \"min\": 391.64280891418457, \"max\": 391.64280891418457}, \"finalize.time\": {\"sum\": 393.55969429016113, \"count\": 1, \"min\": 393.55969429016113, \"max\": 393.55969429016113}, \"model.serialize.time\": {\"sum\": 3.766775131225586, \"count\": 1, \"min\": 3.766775131225586, \"max\": 3.766775131225586}}}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224] Test data is not provided.\u001b[0m\n",
      "\u001b[34m#metrics {\"StartTime\": 1648151624.8194828, \"EndTime\": 1648151624.8197656, \"Dimensions\": {\"Algorithm\": \"AWS/KMeansWebscale\", \"Host\": \"algo-1\", \"Operation\": \"training\"}, \"Metrics\": {\"setuptime\": {\"sum\": 3.6301612854003906, \"count\": 1, \"min\": 3.6301612854003906, \"max\": 3.6301612854003906}, \"totaltime\": {\"sum\": 587.8574848175049, \"count\": 1, \"min\": 587.8574848175049, \"max\": 587.8574848175049}}}\u001b[0m\n",
      "\u001b[34m[03/24/2022 19:53:44 INFO 139950812604224 integration.py:636] worker closed\u001b[0m\n",
      "\n",
      "2022-03-24 19:53:58 Uploading - Uploading generated training model\n",
      "2022-03-24 19:54:18 Completed - Training job completed\n",
      "Training seconds: 87\n",
      "Billable seconds: 87\n",
      "CPU times: user 518 ms, sys: 44.5 ms, total: 563 ms\n",
      "Wall time: 3min 43s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "kmeans.fit(kmeans.record_set(train_data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we deploy the model, and we can pass in the original training set to get the labels for each entry. This will give us which cluster each county belongs to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Defaulting to the only supported framework/algorithm version: 1. Ignoring framework/algorithm version: 1.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------------!CPU times: user 368 ms, sys: 27.1 ms, total: 395 ms\n",
      "Wall time: 6min 32s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "kmeans_predictor = kmeans.deploy(initial_instance_count=1, instance_type=\"ml.t2.medium\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 223 ms, sys: 11 ms, total: 234 ms\n",
      "Wall time: 1.23 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result = kmeans_predictor.predict(train_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the breakdown of cluster counts and the distribution of clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "cluster_labels = [r.label[\"closest_cluster\"].float32_tensor.values[0] for r in result]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0    979\n",
       "3.0    778\n",
       "4.0    460\n",
       "2.0    366\n",
       "6.0    321\n",
       "5.0    207\n",
       "1.0    107\n",
       "Name: 0, dtype: int64"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(cluster_labels)[0].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(cluster_labels, kde=False, aspect=2)\n",
    "title = \"Histogram of Cluster Counts\"\n",
    "plt.title(title, fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, to improve `explainability`, we need to access the underlying model to get the cluster centers. These centers will help describe which features characterize each cluster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Drawing conclusions from our modelling\n",
    "\n",
    "Explaining the result of the modelling is an important step in making use of our analysis. By combining `PCA` and `KMeans`, and the information contained in the model attributes within an Amazon SageMaker trained model, we can form concrete conclusions based on the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a. Accessing the KMeans model attributes\n",
    "\n",
    "First, we will go into the bucket where the `KMeans` model is stored and extract it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job_name = kmeans.latest_training_job.name\n",
    "model_key = \"counties/\" + job_name + \"/output/model.tar.gz\"\n",
    "\n",
    "boto3.resource(\"s3\").Bucket(bucket).download_file(model_key, \"model.tar.gz\")\n",
    "os.system(\"tar -zxvf model.tar.gz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "Kmeans_model_params = mx.ndarray.load(\"model_algo-1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**There is 1 set of model parameters that is contained within the KMeans model.**\n",
    "\n",
    "**Cluster Centroid Locations**: The location of the centers of each cluster identified by the `KMeans` algorithm. The cluster location is given in our `PCA` transformed space with 5 components, since we passed the transformed `PCA` data into the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "cluster_centroids = pd.DataFrame(Kmeans_model_params[0].asnumpy())\n",
    "cluster_centroids.columns = counties_transformed.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>comp_1</th>\n",
       "      <th>comp_2</th>\n",
       "      <th>comp_3</th>\n",
       "      <th>comp_4</th>\n",
       "      <th>comp_5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.032364</td>\n",
       "      <td>-0.055323</td>\n",
       "      <td>0.123491</td>\n",
       "      <td>0.099215</td>\n",
       "      <td>-0.041350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.108374</td>\n",
       "      <td>-0.368914</td>\n",
       "      <td>-0.173843</td>\n",
       "      <td>-0.266890</td>\n",
       "      <td>1.224936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.110373</td>\n",
       "      <td>0.295335</td>\n",
       "      <td>0.077772</td>\n",
       "      <td>0.254567</td>\n",
       "      <td>0.399202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.057882</td>\n",
       "      <td>-0.042858</td>\n",
       "      <td>-0.094169</td>\n",
       "      <td>0.082907</td>\n",
       "      <td>-0.228334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.060140</td>\n",
       "      <td>0.054856</td>\n",
       "      <td>0.062290</td>\n",
       "      <td>-0.294689</td>\n",
       "      <td>-0.276882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.009336</td>\n",
       "      <td>0.129696</td>\n",
       "      <td>-0.531469</td>\n",
       "      <td>0.037357</td>\n",
       "      <td>-0.099570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.061187</td>\n",
       "      <td>-0.037701</td>\n",
       "      <td>-0.007477</td>\n",
       "      <td>-0.228988</td>\n",
       "      <td>0.242238</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     comp_1    comp_2    comp_3    comp_4    comp_5\n",
       "0 -0.032364 -0.055323  0.123491  0.099215 -0.041350\n",
       "1 -0.108374 -0.368914 -0.173843 -0.266890  1.224936\n",
       "2  0.110373  0.295335  0.077772  0.254567  0.399202\n",
       "3 -0.057882 -0.042858 -0.094169  0.082907 -0.228334\n",
       "4  0.060140  0.054856  0.062290 -0.294689 -0.276882\n",
       "5  0.009336  0.129696 -0.531469  0.037357 -0.099570\n",
       "6  0.061187 -0.037701 -0.007477 -0.228988  0.242238"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster_centroids"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot a heatmap of the centroids and their location in the transformed feature space. This gives us insight into what characteristics define each cluster. Often with unsupervised learning, results are hard to interpret. This is one way to make use of the results of PCA plus clustering techniques together. Since we were able to examine the makeup of each PCA component, we can understand what each centroid represents in terms of the `PCA` components that we interpreted previously.\n",
    "\n",
    "For example, we can see that cluster 1 has the highest value in the \"Construction & Commuters\" attribute while it has the lowest value in the \"Self Employment/Public Workers\" attribute compared with other clusters. Similarly, cluster 4 has high values in \"Construction & Commuters,\" \"High Income/Professional & Office Workers,\" and \"Self Employment/Public Workers.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 6))\n",
    "ax = sns.heatmap(cluster_centroids.T, cmap=\"YlGnBu\")\n",
    "ax.set_xlabel(\"Cluster\")\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xticks(fontsize=16)\n",
    "ax.set_title(\"Attribute Value by Centroid\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also map the cluster labels back to each individual county and examine which counties were naturally grouped together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<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",
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       "      <th>comp_1</th>\n",
       "      <th>comp_2</th>\n",
       "      <th>comp_3</th>\n",
       "      <th>comp_4</th>\n",
       "      <th>comp_5</th>\n",
       "      <th>labels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama-Autauga</th>\n",
       "      <td>-0.010824</td>\n",
       "      <td>0.120480</td>\n",
       "      <td>-0.088356</td>\n",
       "      <td>0.160527</td>\n",
       "      <td>-0.060274</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Baldwin</th>\n",
       "      <td>-0.068677</td>\n",
       "      <td>-0.023092</td>\n",
       "      <td>-0.145743</td>\n",
       "      <td>0.185969</td>\n",
       "      <td>-0.149684</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Barbour</th>\n",
       "      <td>0.093111</td>\n",
       "      <td>0.297829</td>\n",
       "      <td>0.146258</td>\n",
       "      <td>0.296662</td>\n",
       "      <td>0.506202</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Bibb</th>\n",
       "      <td>0.283526</td>\n",
       "      <td>0.011757</td>\n",
       "      <td>0.224402</td>\n",
       "      <td>0.190861</td>\n",
       "      <td>0.069224</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alabama-Blount</th>\n",
       "      <td>0.100738</td>\n",
       "      <td>-0.193824</td>\n",
       "      <td>0.022714</td>\n",
       "      <td>0.254403</td>\n",
       "      <td>-0.091030</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   comp_1    comp_2    comp_3    comp_4    comp_5  labels\n",
       "Alabama-Autauga -0.010824  0.120480 -0.088356  0.160527 -0.060274       3\n",
       "Alabama-Baldwin -0.068677 -0.023092 -0.145743  0.185969 -0.149684       3\n",
       "Alabama-Barbour  0.093111  0.297829  0.146258  0.296662  0.506202       2\n",
       "Alabama-Bibb     0.283526  0.011757  0.224402  0.190861  0.069224       0\n",
       "Alabama-Blount   0.100738 -0.193824  0.022714  0.254403 -0.091030       0"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counties_transformed[\"labels\"] = list(map(int, cluster_labels))\n",
    "counties_transformed.head()"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can examine one of the clusters in more detail, like cluster 1 for example. A cursory glance at the location of the centroid tells us that it has the highest value for the \"Construction & Commuters\" attribute. We can now see which counties fit that description."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
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       "      <th>comp_4</th>\n",
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       "      <th>labels</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Arizona-Santa Cruz</th>\n",
       "      <td>-0.014149</td>\n",
       "      <td>-0.347113</td>\n",
       "      <td>-0.386305</td>\n",
       "      <td>-0.284937</td>\n",
       "      <td>0.753071</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California-Imperial</th>\n",
       "      <td>-0.015831</td>\n",
       "      <td>-0.291125</td>\n",
       "      <td>-0.296619</td>\n",
       "      <td>-0.279273</td>\n",
       "      <td>0.885126</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>New Mexico-Doña Ana</th>\n",
       "      <td>-0.132046</td>\n",
       "      <td>-0.219981</td>\n",
       "      <td>-0.244511</td>\n",
       "      <td>-0.247713</td>\n",
       "      <td>0.706542</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico-Luna</th>\n",
       "      <td>-0.004152</td>\n",
       "      <td>-0.319118</td>\n",
       "      <td>-0.041910</td>\n",
       "      <td>-0.204971</td>\n",
       "      <td>0.724001</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico-Mora</th>\n",
       "      <td>0.062434</td>\n",
       "      <td>-0.124934</td>\n",
       "      <td>-0.162434</td>\n",
       "      <td>-0.637112</td>\n",
       "      <td>0.829913</td>\n",
       "      <td>1</td>\n",
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      ],
      "text/plain": [
       "                       comp_1    comp_2    comp_3    comp_4    comp_5  labels\n",
       "Arizona-Santa Cruz  -0.014149 -0.347113 -0.386305 -0.284937  0.753071       1\n",
       "California-Imperial -0.015831 -0.291125 -0.296619 -0.279273  0.885126       1\n",
       "New Mexico-Doña Ana -0.132046 -0.219981 -0.244511 -0.247713  0.706542       1\n",
       "New Mexico-Luna     -0.004152 -0.319118 -0.041910 -0.204971  0.724001       1\n",
       "New Mexico-Mora      0.062434 -0.124934 -0.162434 -0.637112  0.829913       1"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster = counties_transformed[counties_transformed[\"labels\"] == 1]\n",
    "cluster.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "You have just walked through a data science workflow for unsupervised learning, specifically clustering a dataset using KMeans after reducing the dimensionality using PCA. By accessing the underlying models created within Amazon SageMaker, we were able to improve the `explainability` of our modelling and draw actionable conclusions. Using these techniques, we have been able to better understand the essential characteristics of different counties in the US and segment the electorate into groupings accordingly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Because endpoints are persistent, let’s delete our endpoints now that we’re done to avoid any excess charges on our AWS bill."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_predictor.delete_endpoint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans_predictor.delete_endpoint()"
   ]
  }
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