24-EX-Unsuper-Reduction-v1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creative Commons CC BY 4.0 Lynd Bacon & Associates, Ltd. Not warranted to be suitable for any particular purpose. (You're on your own!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised Learning\n",
    "\n",
    "Many ML applications involve _supervised_ learning.  There's a target variable to be predicted, and \"labels\" (values) on the target are available.\n",
    "\n",
    "_Unsupervised_ learning problems are those in which there is no target variable with labels.  In a sense the problem consists of trying to predict labels a set of observations that indicate membership in a particular group or, \"cluster,\" of observations.  The number of such classes is usually known a priori.  Discovering what it most likely is for a particular set of data is a critical part of the learning problem. \n",
    "\n",
    "_Clustering methods_ are the class of algorithms that are used for unsupervised learning problems.  There are many, including:\n",
    "\n",
    "* K-centroids clustering\n",
    "* Hierarchical clustering\n",
    "* Model-based, or mixture, clustering\n",
    "* Copula-based clustering\n",
    "* Ensemble clustering\n",
    "\n",
    "See [What's available in scikit-learn](https://scikit-learn.org/stable/modules/clustering.html).\n",
    "\n",
    "Clustering methods can be used for data reduction, and for solving _semi-supervised learning_ problems.  The latter consist of the situation in which you have a lot of data, and labels for a small proportion of it.\n",
    "\n",
    "In the following we'll apply k-means clustering, a widely used _partitioning_ algorithm, to the diabetes dataset in the file `dataset_37_diabetes.csv`.   We examine results, and try to pick the \"best\" number of clusters.  We'll then apply _principal components analysis_ (PCA) to the data, cluster it again, and note any differences in results. PCA is a frequently used _data reduction_ technique which can be used to represent a set of features in a space of smaller dimensions based on covariations between the features, and perhaps at some loss of information about the set. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get Some Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n",
    "from IPython.display import display, Markdown\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import scikitplot as skplt\n",
    "from sklearn import linear_model\n",
    "from sklearn.model_selection import KFold, StratifiedShuffleSplit\n",
    "from sklearn.model_selection import cross_val_predict, train_test_split\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn import preprocessing\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, roc_auc_score\n",
    "from sklearn.metrics import roc_curve, precision_score, recall_score\n",
    "from sklearn.metrics import classification_report\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_score, silhouette_samples\n",
    "from sklearn.decomposition import PCA\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get the Data\n",
    "\n",
    "The path to the file may need modification:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(768, 9)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Index(['preg', 'plas', 'pres', 'skin', 'insu', 'mass', 'pedi', 'age', 'class'], dtype='object')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diabetes=pd.read_csv('DATA/dataset_37_diabetes.csv')\n",
    "diabetes.shape\n",
    "diabetes.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Data, Other Than \"Class\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>preg</th>\n",
       "      <th>plas</th>\n",
       "      <th>pres</th>\n",
       "      <th>skin</th>\n",
       "      <th>insu</th>\n",
       "      <th>mass</th>\n",
       "      <th>pedi</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>768.000000</td>\n",
       "      <td>768.000000</td>\n",
       "      <td>768.000000</td>\n",
       "      <td>768.000000</td>\n",
       "      <td>768.000000</td>\n",
       "      <td>768.000000</td>\n",
       "      <td>768.000000</td>\n",
       "      <td>768.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.845052</td>\n",
       "      <td>120.894531</td>\n",
       "      <td>69.105469</td>\n",
       "      <td>20.536458</td>\n",
       "      <td>79.799479</td>\n",
       "      <td>31.992578</td>\n",
       "      <td>0.471876</td>\n",
       "      <td>33.240885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.369578</td>\n",
       "      <td>31.972618</td>\n",
       "      <td>19.355807</td>\n",
       "      <td>15.952218</td>\n",
       "      <td>115.244002</td>\n",
       "      <td>7.884160</td>\n",
       "      <td>0.331329</td>\n",
       "      <td>11.760232</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>0.078000</td>\n",
       "      <td>21.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>99.000000</td>\n",
       "      <td>62.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>27.300000</td>\n",
       "      <td>0.243750</td>\n",
       "      <td>24.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>117.000000</td>\n",
       "      <td>72.000000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>30.500000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>0.372500</td>\n",
       "      <td>29.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>140.250000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>127.250000</td>\n",
       "      <td>36.600000</td>\n",
       "      <td>0.626250</td>\n",
       "      <td>41.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>17.000000</td>\n",
       "      <td>199.000000</td>\n",
       "      <td>122.000000</td>\n",
       "      <td>99.000000</td>\n",
       "      <td>846.000000</td>\n",
       "      <td>67.100000</td>\n",
       "      <td>2.420000</td>\n",
       "      <td>81.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             preg        plas        pres        skin        insu        mass  \\\n",
       "count  768.000000  768.000000  768.000000  768.000000  768.000000  768.000000   \n",
       "mean     3.845052  120.894531   69.105469   20.536458   79.799479   31.992578   \n",
       "std      3.369578   31.972618   19.355807   15.952218  115.244002    7.884160   \n",
       "min      0.000000    0.000000    0.000000    0.000000    0.000000    0.000000   \n",
       "25%      1.000000   99.000000   62.000000    0.000000    0.000000   27.300000   \n",
       "50%      3.000000  117.000000   72.000000   23.000000   30.500000   32.000000   \n",
       "75%      6.000000  140.250000   80.000000   32.000000  127.250000   36.600000   \n",
       "max     17.000000  199.000000  122.000000   99.000000  846.000000   67.100000   \n",
       "\n",
       "             pedi         age  \n",
       "count  768.000000  768.000000  \n",
       "mean     0.471876   33.240885  \n",
       "std      0.331329   11.760232  \n",
       "min      0.078000   21.000000  \n",
       "25%      0.243750   24.000000  \n",
       "50%      0.372500   29.000000  \n",
       "75%      0.626250   41.000000  \n",
       "max      2.420000   81.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diabClusDat=diabetes.drop('class',axis=1)\n",
    "diabClusDat.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(768, 8)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=diabClusDat.to_numpy()\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-means\n",
    "\n",
    "[Kmeans documentation on scikit-learn.org](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dry Run : 3 Cluster K-Means Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "km3=KMeans(3,random_state=99)\n",
    "yPred=km3.fit_predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Three Cluster Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cluster Centers:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.981818</td>\n",
       "      <td>114.008081</td>\n",
       "      <td>67.771717</td>\n",
       "      <td>14.997980</td>\n",
       "      <td>14.400000</td>\n",
       "      <td>30.805455</td>\n",
       "      <td>0.431931</td>\n",
       "      <td>33.759596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.527660</td>\n",
       "      <td>129.327660</td>\n",
       "      <td>71.446809</td>\n",
       "      <td>30.306383</td>\n",
       "      <td>159.102128</td>\n",
       "      <td>33.989362</td>\n",
       "      <td>0.540277</td>\n",
       "      <td>31.902128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.026316</td>\n",
       "      <td>158.447368</td>\n",
       "      <td>72.000000</td>\n",
       "      <td>32.263158</td>\n",
       "      <td>441.289474</td>\n",
       "      <td>35.107895</td>\n",
       "      <td>0.569211</td>\n",
       "      <td>34.763158</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0           1          2          3           4          5  \\\n",
       "0  3.981818  114.008081  67.771717  14.997980   14.400000  30.805455   \n",
       "1  3.527660  129.327660  71.446809  30.306383  159.102128  33.989362   \n",
       "2  4.026316  158.447368  72.000000  32.263158  441.289474  35.107895   \n",
       "\n",
       "          6          7  \n",
       "0  0.431931  33.759596  \n",
       "1  0.540277  31.902128  \n",
       "2  0.569211  34.763158  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"cluster Centers:\")\n",
    "pd.DataFrame(km3.cluster_centers_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Summary of Cluster Labels:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0    495\n",
       "1    235\n",
       "2     38\n",
       "dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Summary of Cluster Labels:')\n",
    "pd.Series(yPred).value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inertia: 2913322.58  Number of Iterations:  11\n"
     ]
    }
   ],
   "source": [
    "print(\"Inertia: {:6.2f}  Number of Iterations: {:3d}\".format(\n",
    "    km3.inertia_,km3.n_iter_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"Inertia\" is the sum of squared distances of samples to their closest cluster center."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering Biplot\n",
    "\n",
    "Sometimes, a clustering solution can be visualized in a couple of dimensions.  here's our 3 cluster solution projected into a 2D space that accounts for the largest proportion of the total variation in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=None, random_state=99,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fbde88814a8>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "km3pca=PCA(random_state=99)\n",
    "km3pca.fit(X)\n",
    "skplt.decomposition.plot_pca_2d_projection(km3pca,X,yPred,\n",
    "        biplot=True,\n",
    "        figsize=(8,8),\n",
    "        text_fontsize='large')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Choosing the \"Correct\" Number of Clusters: Elbow Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "km=KMeans(random_state=99)\n",
    "skplt.cluster.plot_elbow_curve(km,X,cluster_ranges=range(1,20),\n",
    "                              figsize=(7,7),\n",
    "                               text_fontsize='large')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How Good Is That Clustering Solution: Silhouette Coefficient\n",
    "\n",
    "**_Compared to what?_**\n",
    "\n",
    "_Inertia_ here is sum of squared within cluster differences.\n",
    "\n",
    "_Silhouette coefficients_ can be used to describe cluster homogeneity. See:\n",
    "\n",
    "[Silhouette Method](https://en.wikipedia.org/wiki/Determining_the_number_of_clusters_in_a_data_set#The_silhouette_method).\n",
    "\n",
    "[Silhouettes: A graphical aid to the interpretation and validation of cluster analysis](https://www.sciencedirect.com/science/article/pii/0377042787901257).\n",
    "\n",
    "The range of possible values for the silhouette coefficient is $\\big[-1,1\\big]$.  larger is better.  Values $\\lt$ 0 indicate observations in the \"wrong\" cluster.  A \"good\" cluster has no coefficients $\\lt$ 0, and and average of cluster coefficients that's positive and \"large.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Silhouette Coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Silhouette Coefficient: 0.510\n"
     ]
    }
   ],
   "source": [
    "print(\"Average Silhouette Coefficient: {:3.3f}\".format(\n",
    "      silhouette_score(X,yPred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Describing Silhouette Coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"8\" halign=\"left\">silcoef</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yPred</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>495.0</td>\n",
       "      <td>0.548746</td>\n",
       "      <td>0.163807</td>\n",
       "      <td>-0.008809</td>\n",
       "      <td>0.496852</td>\n",
       "      <td>0.622992</td>\n",
       "      <td>0.665629</td>\n",
       "      <td>0.699211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>235.0</td>\n",
       "      <td>0.444012</td>\n",
       "      <td>0.173055</td>\n",
       "      <td>0.034683</td>\n",
       "      <td>0.309339</td>\n",
       "      <td>0.511324</td>\n",
       "      <td>0.589442</td>\n",
       "      <td>0.642188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>38.0</td>\n",
       "      <td>0.422027</td>\n",
       "      <td>0.205847</td>\n",
       "      <td>-0.019027</td>\n",
       "      <td>0.235653</td>\n",
       "      <td>0.502882</td>\n",
       "      <td>0.609062</td>\n",
       "      <td>0.630150</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      silcoef                                                              \\\n",
       "        count      mean       std       min       25%       50%       75%   \n",
       "yPred                                                                       \n",
       "0       495.0  0.548746  0.163807 -0.008809  0.496852  0.622992  0.665629   \n",
       "1       235.0  0.444012  0.173055  0.034683  0.309339  0.511324  0.589442   \n",
       "2        38.0  0.422027  0.205847 -0.019027  0.235653  0.502882  0.609062   \n",
       "\n",
       "                 \n",
       "            max  \n",
       "yPred            \n",
       "0      0.699211  \n",
       "1      0.642188  \n",
       "2      0.630150  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get coefficients for each observation\n",
    "\n",
    "silCoefs=silhouette_samples(X,yPred)\n",
    "silDF=pd.DataFrame({'yPred':yPred,'silcoef':silCoefs})\n",
    "silDF.groupby('yPred').describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These coefficients can be plotted by cluster to help visualize a clustering solution.  More on this, below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Search for Number of Clusters Using Average Silhouette Coefficient\n",
    "\n",
    "One way to find a \"best\" number of clusters is to compare one or more cluster quality measures across solutions that differ in their number of clusters.  Here's a K-means example using the average silhouette coefficient, from above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Little Search for the Largest Average Silhouette Coefficient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kmeanSilSearch(X,minN,maxN):\n",
    "    '''\n",
    "    Calculates mean sihouette scores for a range of kmeans solutions.\n",
    "    Returns a Pandas DataFrame of results.\n",
    "    Does no error checking or exception trapping.\n",
    "    User beware!\n",
    "    '''\n",
    "    nClusters=range(minN,maxN+1)  # number of clusters range\n",
    "    clustRes=[]   # results dict holder\n",
    "    for nClust in nClusters:\n",
    "        cRes=KMeans(nClust, random_state=99)\n",
    "        yPred=cRes.fit_predict(X)\n",
    "        resDict={'nclus':nClust,\n",
    "                'meanSilScore':silhouette_score(X,yPred)\n",
    "                }\n",
    "        clustRes.append(resDict)\n",
    "    return pd.DataFrame(clustRes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "clustResDF=kmeanSilSearch(X,2,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering Results, Sorted in Descending Value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "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>meanSilScore</th>\n",
       "      <th>nclus</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.568790</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.510429</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.427819</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.393654</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.352629</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.338606</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.333512</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.333353</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.289905</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   meanSilScore  nclus\n",
       "0      0.568790      2\n",
       "1      0.510429      3\n",
       "2      0.427819      4\n",
       "3      0.393654      5\n",
       "6      0.352629      8\n",
       "7      0.338606      9\n",
       "4      0.333512      6\n",
       "5      0.333353      7\n",
       "8      0.289905     10"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clustResDF.sort_values('meanSilScore',ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Plot of the Average Silhouette Coefficient By Number of Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "ax=sns.lineplot(\"nclus\",\"meanSilScore\",data=clustResDF,color=\"purple\")\n",
    "ax.set(xlabel='no. of kmeans clusters',ylabel='ave sil score')\n",
    "plt.title('Mean Sil Score vs Number of Kmeans Clusters')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# UDU: Repeat the Above \"Search for Best K\" using different Cluster Quality Measures\n",
    "\n",
    "Modify the function, above.  Also, if you can, add in the capability to return the \"best\" solution based on the metric you use.\n",
    "\n",
    "You can find scikit-learn's clustering metrics [here](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.metrics.cluster)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rescaling Features\n",
    "\n",
    "Some clustering algorithms will work better if the features are _scaled_ so as to have similar variances or ranges. This has sometimes been called \"sphering the data.\"  Here we'll standardize the data (mean = 0, sd = 1), and then try clustering again.\n",
    "\n",
    "See [StandardScaler on scikit-learn.org](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standardizing X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(768, 8)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stdScaler=preprocessing.StandardScaler()\n",
    "XS=stdScaler.fit_transform(X)\n",
    "XS.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering Using Standardized Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "clustSResDF=kmeanSilSearch(XS,2,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "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>meanSilScore</th>\n",
       "      <th>nclus</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.201749</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.195654</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.189125</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.180360</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.168094</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.167942</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.162820</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.156201</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.148446</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   meanSilScore  nclus\n",
       "2      0.201749      4\n",
       "0      0.195654      2\n",
       "3      0.189125      5\n",
       "1      0.180360      3\n",
       "5      0.168094      7\n",
       "4      0.167942      6\n",
       "6      0.162820      8\n",
       "7      0.156201      9\n",
       "8      0.148446     10"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clustSResDF.sort_values('meanSilScore',ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Question__:  Are these silhouette coefficients comparable to those obtained above before standardizing the features?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "ax=sns.lineplot(\"nclus\",\"meanSilScore\",data=clustSResDF,color=\"purple\")\n",
    "ax.set(xlabel='no. of kmeans clusters',ylabel='ave sil score')\n",
    "plt.title('Mean Sil Score vs Number of Kmeans Clusters: Std Features')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Components Analysis (PCA) for Data Reduction\n",
    "\n",
    "PCA is used in ML applications as a _data reduction_ method.  It is also sometimes used as a preliminary processing step before clustering.  That's called \"tandem clustering,\" and has been criticized by some based on the possibility that information will be lost.  But here we'll go ahead and \"try it at home\" just to see how it's done."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA in a Nutshell\n",
    "\n",
    "\"Conventional\" PCA is done using a matrix decomposition method called _singular value decomposition_ (SVD), or by eigenvalue decomposition, depending on whether the matrix is a rectangular data matrix, or a covariance or correlation matrix, respectively.  The result is a series of orthogonal vectors, or components, that are each weighted linear combinations of the data.  These components account for decreasing amounts of the total variation in the original data, from the most to the least. There can be as many components are there are features, or as there are observations, whichever is less.\n",
    "\n",
    "Data reduction is accomplished by selecting up to some number of components that account for a specified total percentage of the variation in the data, or by selecting those components that have eigenvalues $\\ge$ 1.0, given that the correlation matrix of the features is the input data.  The selected subset of components, and the scores on them, are used as features in subsequent analyses.\n",
    "\n",
    "Here's where you can find PCA information on [scikit-learn](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A complete PCA solution:\n",
    "pca=PCA()\n",
    "#\n",
    "Xpca=pca.fit(XS)  # Note that here we are using the correlation matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scree Plot\n",
    "\n",
    "This is a plot of eigenvalue vs. component number.\n",
    "\n",
    "A component with an eigenvalue = 1 accounts for as much variance as the average input feature. The sum of these eigenvalues should equal the number of features, rounding and truncation errors notwithstanding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.09711056, 1.73346726, 1.03097228, 0.87667054, 0.76333832,\n",
       "       0.68351839, 0.42036353, 0.40498938])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "8.010430247718384"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xpca.explained_variance_\n",
    "(Xpca.explained_variance_).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenDF=pd.DataFrame({'eigenvalue':Xpca.explained_variance_,\n",
    "                     'component':range(1,9)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "ax=sns.lineplot(\"component\",\"eigenvalue\",data=eigenDF,color=\"blue\")\n",
    "plt.axhline(1.0,color='grey',linestyle='--')\n",
    "plt.title(\"Eigenvalue vs. Component: Standardized Features\")\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Another Kind of Plot for Choosing the Number of Components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pcar=PCA(random_state=99)\n",
    "pcar.fit(XS)\n",
    "skplt.decomposition.plot_pca_component_variance(pcar,\n",
    "                    figsize=(7,7),\n",
    "                    text_fontsize='large',\n",
    "                    target_explained_variance=0.80)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extracting Components\n",
    "\n",
    "It appears that the number of components we should use is 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(768, 3)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca3=PCA(3)\n",
    "XS3=pca3.fit_transform(XS)\n",
    "XS3.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# UDU:  K Means Clustering Using Reduced Data\n",
    "\n",
    "Find your \"best\" clustering solution using the above PCA results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting Silhouette Coefficients\n",
    "\n",
    "I've grabbed some example code for producing silhouette plots.  One example is from [scikit-learn](https://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html), and versions of it can be found here in the notebook \"plot_kmeans_silhouette_analysis.ipynb,\" and in a Python script file \"plot_kmeans_silhouette_analysis.py.\"  They are the same code, from what I can tell.\n",
    "\n",
    "Another example is here in the script file \"another_plot_kmeans_silhouette_analysis.py.\"\n",
    "\n",
    "And yet another is in the file \"kmeansplots.py.\""
   ]
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    "# UDU:  Produce a K Means Silhouette Plot\n",
    "\n",
    "Adapt the code provided in one of the examples, above, and produce silhouette plots for a range of cluster numbers.  Use either the original or standardized diabetes data."
   ]
  }
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