unsupervised_learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unsupervised learning describes a collection of techniques that attempt to find structure in data.\n",
    "\n",
    "Examples include:\n",
    "\n",
    "* __Clustering__: attempts to divide data into groups based off a definition of similarity, such as distance in univariate or multidimensional space.\n",
    "* __Dimensionality Reduction__: Attempts to encode high dimensional data (e.g. tens of thousands of variables) into a smaller set of variables\n",
    "\n",
    "This is in contrast to supervised learning, where, given an input $x$ and output $y$ we attempt to learn a function $f(x)$ = $y$, where $x$ and $y$ can be scalars (numbers) , vectors (lines of numbers), or matrices (2D array of numbers). In unsupervised learning, we are only given $x$ and no output, and the goal is to find structure in a collection of data points.\n",
    "\n",
    "Here, we'll go over 2 Techniques: dimensionality reduction and clustering."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dimensionality Reduction\n",
    "\n",
    "Often we can deal with datasets that exist in high dimensional spaces (e.g $d$ = 10,000, where $d$ is the number of variables in the data). The breast cancer dataset we shall explore has 30 dimensions for 'input data' features  plus 1 for 'target' label (i.e. whether or not the example is benign or malignant). Not only is it impossible for people to visualize data beyond 3 dimensions, but when we use supervised learning techniques such as K-nearest neighbor classification or an unsupervised method such as K-means clustering, the assumption that similar datapoints are closer to one another than dissimilar points in terms of Euclidean distance is violated<sup>1</sup>. The violation of this assumption is called the _curse of dimensionality_. A further discussion of this topic can be found [here](https://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/lecturenote02_kNN.html).\n",
    "\n",
    "What dimensionality reduction can accomplish is to pick up neat properties of your data in high dimensional space and express them in a much lower dimensional space. This allows an automated fashion of finding those neat properties while also expressing data in a way better suited for downstream applications such as clustering or classification. Examples include Princpal Components Analysis (PCA), Factor Analysis, Locally Linear Embedding, and more. Today we'll go over PCA.\n",
    "\n",
    "1. For 2D and 3D data, Euclidean distance is just the length of a line drawn between two points $p$ and $q$ if you plotted them in 2 or 3D, and its formula is $\\sqrt{\\sum_{d=1}^D (p_d - q_d)^2} $, where $d$ denotes an individual variable and $D$ is the total number of variables. Here's an example in 2D from Wikipedia:\n",
    "\n",
    "![Euclidean Distance in 2D (Wikipedia)](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)\n",
    "\n",
    "### Overview of PCA:\n",
    "\n",
    "Without diving into linear algebra, what PCA tries to do at the end of the day is express the data as weighted sums of the data's variables.\n",
    "\n",
    "The procedure is as follows:\n",
    "\n",
    "1. Standard Normalize Data. Part of the reason we do this is so the procedure doesn't give too much weight to certain variables based on certain variables having a wider range of values.\n",
    "\n",
    "    Formula is as follows: $b_{id} = (x_{id} - \\bar{x_d})/\\sigma_d$, where $i$ denotes sample, $d$ denotes variable,  $\\bar{x_d}$ denotes mean for the variable among all $x_{id}$, and $\\sigma_d$ denotes the standard deviation for variable d\n",
    "\n",
    "2. calculate a variable $v_1$ = $\\sum_{d=1}^{D} a_d b_d$ such that $Var[v_1]$ (variance of the new variable) is maximized, with the constraint that $\\sum_{d=1}^{D} a_d^2$ = 1\n",
    "\n",
    "3. repeat step 2, but subject to the constraint that the new variable, $v_2$ is uncorrelated with $v_1$, i.e correlation between the two variables = 0.\n",
    "\n",
    "4. Repeat step 3, again and again, subject to the constraint that any new variable $v_k$ computed for iteration $l$ is not correlated with any variables $v_{k'}$ where $k' < k$ (i.e not correlated with any previously computed variables).\n",
    "\n",
    "There's an upper limit on the amount of PCs that can be computed, but we're not discussing that today as it requires knowledge of linear algebra.\n",
    "\n",
    "For a more in depth discussion of PCA, here's a reference you can look into:\n",
    "\n",
    "* [Stanford Engineering Everywhere, CS229 PCA Notes](https://see.stanford.edu/materials/aimlcs229/cs229-notes10.pdf)\n",
    "\n",
    "Let's dive into the data!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA on Breast Cancer Dataset\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn import preprocessing\n",
    "from ipywidgets import interact, fixed\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn\n",
    "import pandas as pd\n",
    "\n",
    "data = load_breast_cancer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Data\n",
    "\n",
    "The data we're using consists of attributes obtained from imaging data undergoing screening for breast cancer. Features correspond to geometric qualities of cell nuclei (objects that hold the DNA in a cell).\n",
    "\n",
    "for more details, see (sklearn website)[https://scikit-learn.org/stable/datasets/index.html] and (original source)[https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+(Diagnostic)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(569, 30)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dimensions of data: 569 examples x 30 features\n",
    "data['data'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Examine Data\n",
    "breast_cancer_df = pd.DataFrame(data = data['data'], columns = data.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>radius error</th>\n",
       "      <th>texture error</th>\n",
       "      <th>perimeter error</th>\n",
       "      <th>area error</th>\n",
       "      <th>smoothness error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.3001</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>0.2419</td>\n",
       "      <td>0.07871</td>\n",
       "      <td>1.0950</td>\n",
       "      <td>0.9053</td>\n",
       "      <td>8.589</td>\n",
       "      <td>153.40</td>\n",
       "      <td>0.006399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.0869</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>0.1812</td>\n",
       "      <td>0.05667</td>\n",
       "      <td>0.5435</td>\n",
       "      <td>0.7339</td>\n",
       "      <td>3.398</td>\n",
       "      <td>74.08</td>\n",
       "      <td>0.005225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.1974</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>0.2069</td>\n",
       "      <td>0.05999</td>\n",
       "      <td>0.7456</td>\n",
       "      <td>0.7869</td>\n",
       "      <td>4.585</td>\n",
       "      <td>94.03</td>\n",
       "      <td>0.006150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.2414</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>0.2597</td>\n",
       "      <td>0.09744</td>\n",
       "      <td>0.4956</td>\n",
       "      <td>1.1560</td>\n",
       "      <td>3.445</td>\n",
       "      <td>27.23</td>\n",
       "      <td>0.009110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.1980</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>0.1809</td>\n",
       "      <td>0.05883</td>\n",
       "      <td>0.7572</td>\n",
       "      <td>0.7813</td>\n",
       "      <td>5.438</td>\n",
       "      <td>94.44</td>\n",
       "      <td>0.011490</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
       "0        17.99         10.38          122.80     1001.0          0.11840   \n",
       "1        20.57         17.77          132.90     1326.0          0.08474   \n",
       "2        19.69         21.25          130.00     1203.0          0.10960   \n",
       "3        11.42         20.38           77.58      386.1          0.14250   \n",
       "4        20.29         14.34          135.10     1297.0          0.10030   \n",
       "\n",
       "   mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
       "0           0.27760          0.3001              0.14710         0.2419   \n",
       "1           0.07864          0.0869              0.07017         0.1812   \n",
       "2           0.15990          0.1974              0.12790         0.2069   \n",
       "3           0.28390          0.2414              0.10520         0.2597   \n",
       "4           0.13280          0.1980              0.10430         0.1809   \n",
       "\n",
       "   mean fractal dimension  radius error  texture error  perimeter error  \\\n",
       "0                 0.07871        1.0950         0.9053            8.589   \n",
       "1                 0.05667        0.5435         0.7339            3.398   \n",
       "2                 0.05999        0.7456         0.7869            4.585   \n",
       "3                 0.09744        0.4956         1.1560            3.445   \n",
       "4                 0.05883        0.7572         0.7813            5.438   \n",
       "\n",
       "   area error  smoothness error  \n",
       "0      153.40          0.006399  \n",
       "1       74.08          0.005225  \n",
       "2       94.03          0.006150  \n",
       "3       27.23          0.009110  \n",
       "4       94.44          0.011490  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Columns 1-15 (0-14 in 0 based indexing)\n",
    "breast_cancer_df.iloc[:, 0:15].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>compactness error</th>\n",
       "      <th>concavity error</th>\n",
       "      <th>concave points error</th>\n",
       "      <th>symmetry error</th>\n",
       "      <th>fractal dimension error</th>\n",
       "      <th>worst radius</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.04904</td>\n",
       "      <td>0.05373</td>\n",
       "      <td>0.01587</td>\n",
       "      <td>0.03003</td>\n",
       "      <td>0.006193</td>\n",
       "      <td>25.38</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.1622</td>\n",
       "      <td>0.6656</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.01308</td>\n",
       "      <td>0.01860</td>\n",
       "      <td>0.01340</td>\n",
       "      <td>0.01389</td>\n",
       "      <td>0.003532</td>\n",
       "      <td>24.99</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.1238</td>\n",
       "      <td>0.1866</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.04006</td>\n",
       "      <td>0.03832</td>\n",
       "      <td>0.02058</td>\n",
       "      <td>0.02250</td>\n",
       "      <td>0.004571</td>\n",
       "      <td>23.57</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.1444</td>\n",
       "      <td>0.4245</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.07458</td>\n",
       "      <td>0.05661</td>\n",
       "      <td>0.01867</td>\n",
       "      <td>0.05963</td>\n",
       "      <td>0.009208</td>\n",
       "      <td>14.91</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.2098</td>\n",
       "      <td>0.8663</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.02461</td>\n",
       "      <td>0.05688</td>\n",
       "      <td>0.01885</td>\n",
       "      <td>0.01756</td>\n",
       "      <td>0.005115</td>\n",
       "      <td>22.54</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.1374</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   compactness error  concavity error  concave points error  symmetry error  \\\n",
       "0            0.04904          0.05373               0.01587         0.03003   \n",
       "1            0.01308          0.01860               0.01340         0.01389   \n",
       "2            0.04006          0.03832               0.02058         0.02250   \n",
       "3            0.07458          0.05661               0.01867         0.05963   \n",
       "4            0.02461          0.05688               0.01885         0.01756   \n",
       "\n",
       "   fractal dimension error  worst radius  worst texture  worst perimeter  \\\n",
       "0                 0.006193         25.38          17.33           184.60   \n",
       "1                 0.003532         24.99          23.41           158.80   \n",
       "2                 0.004571         23.57          25.53           152.50   \n",
       "3                 0.009208         14.91          26.50            98.87   \n",
       "4                 0.005115         22.54          16.67           152.20   \n",
       "\n",
       "   worst area  worst smoothness  worst compactness  worst concavity  \\\n",
       "0      2019.0            0.1622             0.6656           0.7119   \n",
       "1      1956.0            0.1238             0.1866           0.2416   \n",
       "2      1709.0            0.1444             0.4245           0.4504   \n",
       "3       567.7            0.2098             0.8663           0.6869   \n",
       "4      1575.0            0.1374             0.2050           0.4000   \n",
       "\n",
       "   worst concave points  worst symmetry  worst fractal dimension  \n",
       "0                0.2654          0.4601                  0.11890  \n",
       "1                0.1860          0.2750                  0.08902  \n",
       "2                0.2430          0.3613                  0.08758  \n",
       "3                0.2575          0.6638                  0.17300  \n",
       "4                0.1625          0.2364                  0.07678  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Columns 16-30 (15-29 in 0 based indexing)\n",
    "breast_cancer_df.iloc[:, 15:30].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7bbc29fdcaf94cafb5f6b39c8e92ed6e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='var_name', options=('mean radius', 'mean texture', 'mean perimeter…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact\n",
    "# Interactive Histogram, using interact decorator function from ipywidgets\n",
    "def do_hist(var_name = data.feature_names, df = fixed(breast_cancer_df)):\n",
    "    # Inputs:\n",
    "    #       var_name: variable name. change variable name in menu to change variable displaed\n",
    "    #       df = data.frame to use. this is fixed\n",
    "    plt.hist(df[var_name].to_numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that variables denote either continuous or count data. PCA will help us find correlated structure. However, we note that the data is not centered and scaled, and while the sklearn PCA workflow does automatic centering of data, it does not scale data such that it's standard normalized. let's scale and center it now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_scaled = preprocessing.scale(data['data'])\n",
    "data_scaled_df = pd.DataFrame(data = data_scaled, columns = data.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a4a23b2e8fd247a0bb76c9d05b43acb4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='var_name', options=('mean radius', 'mean texture', 'mean perimeter…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact\n",
    "# Interactive Histogram, using interact decorator function from ipywidgets\n",
    "def do_hist(var_name = data.feature_names, df = fixed(data_scaled_df)):\n",
    "    # Inputs:\n",
    "    #       var_name: variable name. change variable name in menu to change variable displaed\n",
    "    #       df = data.frame to use. this is fixed\n",
    "    plt.hist(df[var_name].to_numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check actual numerical values of variance. here we see that we have variance = 1 for \n",
    "np.var(data_scaled, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.16286735e-15, -6.53060890e-15, -7.07889127e-16, -8.79983452e-16,\n",
       "        6.13217737e-15, -1.12036918e-15, -4.42138027e-16,  9.73249991e-16,\n",
       "       -1.97167024e-15, -1.45363120e-15, -9.07641468e-16, -8.85349205e-16,\n",
       "        1.77367396e-15, -8.29155139e-16, -7.54180940e-16, -3.92187747e-16,\n",
       "        7.91789988e-16, -2.73946068e-16, -3.10823423e-16, -3.36676596e-16,\n",
       "       -2.33322442e-15,  1.76367415e-15, -1.19802625e-15,  5.04966114e-16,\n",
       "       -5.21317026e-15, -2.17478837e-15,  6.85645643e-16, -1.41265636e-16,\n",
       "       -2.28956670e-15,  2.57517109e-15])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check actual numerical values of mean\n",
    "np.mean(data_scaled, axis = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variances are all = 1, means are all very close to 0. The latter result is likely a consequencec of numerical stability issues with very small numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Labels (Not Used Here for PCA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['malignant', 'benign'], dtype='<U9')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.target_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(data['target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0,\n",
       "       1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0,\n",
       "       1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0,\n",
       "       0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1,\n",
       "       1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0,\n",
       "       0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0,\n",
       "       1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1,\n",
       "       1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0,\n",
       "       0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0,\n",
       "       0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0,\n",
       "       1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1,\n",
       "       1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1,\n",
       "       1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,\n",
       "       1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,\n",
       "       1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1,\n",
       "       1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['target']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Labels here just denote a known class of the object for a category, in this case whether or not a case is malignant or benign. Somewhat counterintuitively, they've chosen to label benign samples as 1, malignant samples as 0 (this was spot checked against source dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### PCA of Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import decomposition\n",
    "# setup object\n",
    "pca_obj = decomposition.PCA()\n",
    "# fit PCA, i.e. perform PCA algorithm on data\n",
    "pca_obj.fit(data_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# explained variance per PC\n",
    "pcs_plot = np.arange(0,20)\n",
    "plt.plot(pcs_plot, pca_obj.explained_variance_ratio_[pcs_plot])\n",
    "plt.xticks(pcs_plot)\n",
    "plt.xlabel('PC')\n",
    "plt.ylabel('Fraction Variance Explained')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.44272026, 0.18971182, 0.09393163, 0.06602135, 0.05495768,\n",
       "       0.04024522, 0.02250734, 0.01588724, 0.01389649, 0.01168978,\n",
       "       0.00979719, 0.00870538, 0.00804525, 0.00523366, 0.00313783,\n",
       "       0.00266209, 0.00197997, 0.00175396, 0.00164925, 0.00103865])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_obj.explained_variance_ratio_[pcs_plot]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variance explained = variance of PC divided by sum of all variances across all input variables. Note that with 0 indexing, PC 0 is actually the first PC computed. it explains about 45% of variance in the data. PC 1 explains about 20%,a and PC 2 10%, for a total of about 72% of variance in the data. For the sake of simplicity and time, we'll just look at PCs 0 through 2.\n",
    "\n",
    "We can look at which features are important for each PC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f79c8280400>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# get loadings for PC, i.e. association of input features with each PC. Do for PC0, PC1, PC2\n",
    "loadings_mat = pca_obj.components_[0:3, :]\n",
    "# 3 components x 30 features\n",
    "loadings_mat.shape\n",
    "\n",
    "loadings_df = pd.DataFrame(data = np.transpose(loadings_mat), \n",
    "                           index = data.feature_names, \n",
    "                           columns = np.arange(0,3).astype('str'))\n",
    "loadings_df.shape\n",
    "seaborn.heatmap(loadings_df, xticklabels = True, yticklabels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean concave points</th>\n",
       "      <td>0.260854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean concavity</th>\n",
       "      <td>0.258400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst concave points</th>\n",
       "      <td>0.250886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean compactness</th>\n",
       "      <td>0.239285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst perimeter</th>\n",
       "      <td>0.236640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst concavity</th>\n",
       "      <td>0.228768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst radius</th>\n",
       "      <td>0.227997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean perimeter</th>\n",
       "      <td>0.227537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst area</th>\n",
       "      <td>0.224871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean area</th>\n",
       "      <td>0.220995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean radius</th>\n",
       "      <td>0.218902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>perimeter error</th>\n",
       "      <td>0.211326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst compactness</th>\n",
       "      <td>0.210096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>radius error</th>\n",
       "      <td>0.205979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>area error</th>\n",
       "      <td>0.202870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>concave points error</th>\n",
       "      <td>0.183417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compactness error</th>\n",
       "      <td>0.170393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>concavity error</th>\n",
       "      <td>0.153590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean smoothness</th>\n",
       "      <td>0.142590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean symmetry</th>\n",
       "      <td>0.138167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <td>0.131784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst smoothness</th>\n",
       "      <td>0.127953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst symmetry</th>\n",
       "      <td>0.122905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst texture</th>\n",
       "      <td>0.104469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean texture</th>\n",
       "      <td>0.103725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fractal dimension error</th>\n",
       "      <td>0.102568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <td>0.064363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>symmetry error</th>\n",
       "      <td>0.042498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>texture error</th>\n",
       "      <td>0.017428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smoothness error</th>\n",
       "      <td>0.014531</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                0\n",
       "mean concave points      0.260854\n",
       "mean concavity           0.258400\n",
       "worst concave points     0.250886\n",
       "mean compactness         0.239285\n",
       "worst perimeter          0.236640\n",
       "worst concavity          0.228768\n",
       "worst radius             0.227997\n",
       "mean perimeter           0.227537\n",
       "worst area               0.224871\n",
       "mean area                0.220995\n",
       "mean radius              0.218902\n",
       "perimeter error          0.211326\n",
       "worst compactness        0.210096\n",
       "radius error             0.205979\n",
       "area error               0.202870\n",
       "concave points error     0.183417\n",
       "compactness error        0.170393\n",
       "concavity error          0.153590\n",
       "mean smoothness          0.142590\n",
       "mean symmetry            0.138167\n",
       "worst fractal dimension  0.131784\n",
       "worst smoothness         0.127953\n",
       "worst symmetry           0.122905\n",
       "worst texture            0.104469\n",
       "mean texture             0.103725\n",
       "fractal dimension error  0.102568\n",
       "mean fractal dimension   0.064363\n",
       "symmetry error           0.042498\n",
       "texture error            0.017428\n",
       "smoothness error         0.014531"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# features ranked by association with PC 0\n",
    "loadings_df.sort_values(by = '0', ascending = False).iloc[:, np.arange(0,1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <td>0.366575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fractal dimension error</th>\n",
       "      <td>0.280092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <td>0.275339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compactness error</th>\n",
       "      <td>0.232716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smoothness error</th>\n",
       "      <td>0.204430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>concavity error</th>\n",
       "      <td>0.197207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean symmetry</th>\n",
       "      <td>0.190349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean smoothness</th>\n",
       "      <td>0.186113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>symmetry error</th>\n",
       "      <td>0.183848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst smoothness</th>\n",
       "      <td>0.172304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean compactness</th>\n",
       "      <td>0.151892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst compactness</th>\n",
       "      <td>0.143593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst symmetry</th>\n",
       "      <td>0.141883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>concave points error</th>\n",
       "      <td>0.130322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst concavity</th>\n",
       "      <td>0.097964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>texture error</th>\n",
       "      <td>0.089980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean concavity</th>\n",
       "      <td>0.060165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst concave points</th>\n",
       "      <td>-0.008257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean concave points</th>\n",
       "      <td>-0.034768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst texture</th>\n",
       "      <td>-0.045467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean texture</th>\n",
       "      <td>-0.059706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>perimeter error</th>\n",
       "      <td>-0.089457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>radius error</th>\n",
       "      <td>-0.105552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>area error</th>\n",
       "      <td>-0.152293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst perimeter</th>\n",
       "      <td>-0.199878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean perimeter</th>\n",
       "      <td>-0.215181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst area</th>\n",
       "      <td>-0.219352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst radius</th>\n",
       "      <td>-0.219866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean area</th>\n",
       "      <td>-0.231077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean radius</th>\n",
       "      <td>-0.233857</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                1\n",
       "mean fractal dimension   0.366575\n",
       "fractal dimension error  0.280092\n",
       "worst fractal dimension  0.275339\n",
       "compactness error        0.232716\n",
       "smoothness error         0.204430\n",
       "concavity error          0.197207\n",
       "mean symmetry            0.190349\n",
       "mean smoothness          0.186113\n",
       "symmetry error           0.183848\n",
       "worst smoothness         0.172304\n",
       "mean compactness         0.151892\n",
       "worst compactness        0.143593\n",
       "worst symmetry           0.141883\n",
       "concave points error     0.130322\n",
       "worst concavity          0.097964\n",
       "texture error            0.089980\n",
       "mean concavity           0.060165\n",
       "worst concave points    -0.008257\n",
       "mean concave points     -0.034768\n",
       "worst texture           -0.045467\n",
       "mean texture            -0.059706\n",
       "perimeter error         -0.089457\n",
       "radius error            -0.105552\n",
       "area error              -0.152293\n",
       "worst perimeter         -0.199878\n",
       "mean perimeter          -0.215181\n",
       "worst area              -0.219352\n",
       "worst radius            -0.219866\n",
       "mean area               -0.231077\n",
       "mean radius             -0.233857"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# features ranked by association with PC 1\n",
    "loadings_df.sort_values(by = '1', ascending = False).iloc[:, np.arange(1,2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>texture error</th>\n",
       "      <td>0.374634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smoothness error</th>\n",
       "      <td>0.308839</td>\n",
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       "    <tr>\n",
       "      <th>symmetry error</th>\n",
       "      <td>0.288584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>radius error</th>\n",
       "      <td>0.268481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>perimeter error</th>\n",
       "      <td>0.266645</td>\n",
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       "    <tr>\n",
       "      <th>concave points error</th>\n",
       "      <td>0.224658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>area error</th>\n",
       "      <td>0.216007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fractal dimension error</th>\n",
       "      <td>0.211504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>concavity error</th>\n",
       "      <td>0.176464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compactness error</th>\n",
       "      <td>0.154780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean texture</th>\n",
       "      <td>0.064550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean area</th>\n",
       "      <td>0.028700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean concavity</th>\n",
       "      <td>0.002734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean radius</th>\n",
       "      <td>-0.008531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean perimeter</th>\n",
       "      <td>-0.009314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst area</th>\n",
       "      <td>-0.011902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <td>-0.022574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean concave points</th>\n",
       "      <td>-0.025564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean symmetry</th>\n",
       "      <td>-0.040240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst texture</th>\n",
       "      <td>-0.042298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst radius</th>\n",
       "      <td>-0.047507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst perimeter</th>\n",
       "      <td>-0.048547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean compactness</th>\n",
       "      <td>-0.074092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean smoothness</th>\n",
       "      <td>-0.104292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst concave points</th>\n",
       "      <td>-0.170344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst concavity</th>\n",
       "      <td>-0.173057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <td>-0.232791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst compactness</th>\n",
       "      <td>-0.236076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst smoothness</th>\n",
       "      <td>-0.259798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst symmetry</th>\n",
       "      <td>-0.271313</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                2\n",
       "texture error            0.374634\n",
       "smoothness error         0.308839\n",
       "symmetry error           0.288584\n",
       "radius error             0.268481\n",
       "perimeter error          0.266645\n",
       "concave points error     0.224658\n",
       "area error               0.216007\n",
       "fractal dimension error  0.211504\n",
       "concavity error          0.176464\n",
       "compactness error        0.154780\n",
       "mean texture             0.064550\n",
       "mean area                0.028700\n",
       "mean concavity           0.002734\n",
       "mean radius             -0.008531\n",
       "mean perimeter          -0.009314\n",
       "worst area              -0.011902\n",
       "mean fractal dimension  -0.022574\n",
       "mean concave points     -0.025564\n",
       "mean symmetry           -0.040240\n",
       "worst texture           -0.042298\n",
       "worst radius            -0.047507\n",
       "worst perimeter         -0.048547\n",
       "mean compactness        -0.074092\n",
       "mean smoothness         -0.104292\n",
       "worst concave points    -0.170344\n",
       "worst concavity         -0.173057\n",
       "worst fractal dimension -0.232791\n",
       "worst compactness       -0.236076\n",
       "worst smoothness        -0.259798\n",
       "worst symmetry          -0.271313"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# features ranked by association with PC 2\n",
    "loadings_df.sort_values(by = '2', ascending = False).iloc[:, np.arange(2,3)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>worst radius</th>\n",
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       "      <th>0</th>\n",
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       "      <th>2</th>\n",
       "      <th>label</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>25.38</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.1622</td>\n",
       "      <td>0.6656</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.26540</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "      <td>9.192837</td>\n",
       "      <td>1.948583</td>\n",
       "      <td>-1.123166</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>24.99</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.1238</td>\n",
       "      <td>0.1866</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.18600</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "      <td>2.387802</td>\n",
       "      <td>-3.768172</td>\n",
       "      <td>-0.529293</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>23.57</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.1444</td>\n",
       "      <td>0.4245</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.24300</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "      <td>5.733896</td>\n",
       "      <td>-1.075174</td>\n",
       "      <td>-0.551748</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>14.91</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.2098</td>\n",
       "      <td>0.8663</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.25750</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "      <td>7.122953</td>\n",
       "      <td>10.275589</td>\n",
       "      <td>-3.232790</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>22.54</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.1374</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.16250</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "      <td>3.935302</td>\n",
       "      <td>-1.948072</td>\n",
       "      <td>1.389767</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>15.47</td>\n",
       "      <td>23.75</td>\n",
       "      <td>103.40</td>\n",
       "      <td>741.6</td>\n",
       "      <td>0.1791</td>\n",
       "      <td>0.5249</td>\n",
       "      <td>0.5355</td>\n",
       "      <td>0.17410</td>\n",
       "      <td>0.3985</td>\n",
       "      <td>0.12440</td>\n",
       "      <td>2.380247</td>\n",
       "      <td>3.949929</td>\n",
       "      <td>-2.934877</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>22.88</td>\n",
       "      <td>27.66</td>\n",
       "      <td>153.20</td>\n",
       "      <td>1606.0</td>\n",
       "      <td>0.1442</td>\n",
       "      <td>0.2576</td>\n",
       "      <td>0.3784</td>\n",
       "      <td>0.19320</td>\n",
       "      <td>0.3063</td>\n",
       "      <td>0.08368</td>\n",
       "      <td>2.238883</td>\n",
       "      <td>-2.690031</td>\n",
       "      <td>-1.639913</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>17.06</td>\n",
       "      <td>28.14</td>\n",
       "      <td>110.60</td>\n",
       "      <td>897.0</td>\n",
       "      <td>0.1654</td>\n",
       "      <td>0.3682</td>\n",
       "      <td>0.2678</td>\n",
       "      <td>0.15560</td>\n",
       "      <td>0.3196</td>\n",
       "      <td>0.11510</td>\n",
       "      <td>2.143299</td>\n",
       "      <td>2.340244</td>\n",
       "      <td>-0.871947</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15.49</td>\n",
       "      <td>30.73</td>\n",
       "      <td>106.20</td>\n",
       "      <td>739.3</td>\n",
       "      <td>0.1703</td>\n",
       "      <td>0.5401</td>\n",
       "      <td>0.5390</td>\n",
       "      <td>0.20600</td>\n",
       "      <td>0.4378</td>\n",
       "      <td>0.10720</td>\n",
       "      <td>3.174924</td>\n",
       "      <td>3.391813</td>\n",
       "      <td>-3.119986</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>15.09</td>\n",
       "      <td>40.68</td>\n",
       "      <td>97.65</td>\n",
       "      <td>711.4</td>\n",
       "      <td>0.1853</td>\n",
       "      <td>1.0580</td>\n",
       "      <td>1.1050</td>\n",
       "      <td>0.22100</td>\n",
       "      <td>0.4366</td>\n",
       "      <td>0.20750</td>\n",
       "      <td>6.351747</td>\n",
       "      <td>7.727174</td>\n",
       "      <td>-4.341916</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>19.19</td>\n",
       "      <td>33.88</td>\n",
       "      <td>123.80</td>\n",
       "      <td>1150.0</td>\n",
       "      <td>0.1181</td>\n",
       "      <td>0.1551</td>\n",
       "      <td>0.1459</td>\n",
       "      <td>0.09975</td>\n",
       "      <td>0.2948</td>\n",
       "      <td>0.08452</td>\n",
       "      <td>-0.810414</td>\n",
       "      <td>-2.659275</td>\n",
       "      <td>-0.488830</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>20.42</td>\n",
       "      <td>27.28</td>\n",
       "      <td>136.50</td>\n",
       "      <td>1299.0</td>\n",
       "      <td>0.1396</td>\n",
       "      <td>0.5609</td>\n",
       "      <td>0.3965</td>\n",
       "      <td>0.18100</td>\n",
       "      <td>0.3792</td>\n",
       "      <td>0.10480</td>\n",
       "      <td>2.651100</td>\n",
       "      <td>0.066568</td>\n",
       "      <td>-1.526455</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>20.96</td>\n",
       "      <td>29.94</td>\n",
       "      <td>151.70</td>\n",
       "      <td>1332.0</td>\n",
       "      <td>0.1037</td>\n",
       "      <td>0.3903</td>\n",
       "      <td>0.3639</td>\n",
       "      <td>0.17670</td>\n",
       "      <td>0.3176</td>\n",
       "      <td>0.10230</td>\n",
       "      <td>8.185034</td>\n",
       "      <td>2.700976</td>\n",
       "      <td>5.730231</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>16.84</td>\n",
       "      <td>27.66</td>\n",
       "      <td>112.00</td>\n",
       "      <td>876.5</td>\n",
       "      <td>0.1131</td>\n",
       "      <td>0.1924</td>\n",
       "      <td>0.2322</td>\n",
       "      <td>0.11190</td>\n",
       "      <td>0.2809</td>\n",
       "      <td>0.06287</td>\n",
       "      <td>0.342126</td>\n",
       "      <td>-0.968279</td>\n",
       "      <td>1.717172</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>15.03</td>\n",
       "      <td>32.01</td>\n",
       "      <td>108.80</td>\n",
       "      <td>697.7</td>\n",
       "      <td>0.1651</td>\n",
       "      <td>0.7725</td>\n",
       "      <td>0.6943</td>\n",
       "      <td>0.22080</td>\n",
       "      <td>0.3596</td>\n",
       "      <td>0.14310</td>\n",
       "      <td>4.342379</td>\n",
       "      <td>4.861083</td>\n",
       "      <td>-2.816116</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>17.46</td>\n",
       "      <td>37.13</td>\n",
       "      <td>124.10</td>\n",
       "      <td>943.2</td>\n",
       "      <td>0.1678</td>\n",
       "      <td>0.6577</td>\n",
       "      <td>0.7026</td>\n",
       "      <td>0.17120</td>\n",
       "      <td>0.4218</td>\n",
       "      <td>0.13410</td>\n",
       "      <td>4.075656</td>\n",
       "      <td>2.977061</td>\n",
       "      <td>-3.125274</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>19.07</td>\n",
       "      <td>30.88</td>\n",
       "      <td>123.40</td>\n",
       "      <td>1138.0</td>\n",
       "      <td>0.1464</td>\n",
       "      <td>0.1871</td>\n",
       "      <td>0.2914</td>\n",
       "      <td>0.16090</td>\n",
       "      <td>0.3029</td>\n",
       "      <td>0.08216</td>\n",
       "      <td>0.230055</td>\n",
       "      <td>-1.564758</td>\n",
       "      <td>-0.802519</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>20.96</td>\n",
       "      <td>31.48</td>\n",
       "      <td>136.80</td>\n",
       "      <td>1315.0</td>\n",
       "      <td>0.1789</td>\n",
       "      <td>0.4233</td>\n",
       "      <td>0.4784</td>\n",
       "      <td>0.20730</td>\n",
       "      <td>0.3706</td>\n",
       "      <td>0.11420</td>\n",
       "      <td>4.418011</td>\n",
       "      <td>1.418670</td>\n",
       "      <td>-2.270319</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>27.32</td>\n",
       "      <td>30.88</td>\n",
       "      <td>186.80</td>\n",
       "      <td>2398.0</td>\n",
       "      <td>0.1512</td>\n",
       "      <td>0.3150</td>\n",
       "      <td>0.5372</td>\n",
       "      <td>0.23880</td>\n",
       "      <td>0.2768</td>\n",
       "      <td>0.07615</td>\n",
       "      <td>4.948704</td>\n",
       "      <td>-4.114334</td>\n",
       "      <td>-0.314749</td>\n",
       "      <td>malignant</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>15.11</td>\n",
       "      <td>19.26</td>\n",
       "      <td>99.70</td>\n",
       "      <td>711.2</td>\n",
       "      <td>0.1440</td>\n",
       "      <td>0.1773</td>\n",
       "      <td>0.2390</td>\n",
       "      <td>0.12880</td>\n",
       "      <td>0.2977</td>\n",
       "      <td>0.07259</td>\n",
       "      <td>-1.237063</td>\n",
       "      <td>-0.188215</td>\n",
       "      <td>-0.593283</td>\n",
       "      <td>benign</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    worst radius  worst texture  worst perimeter  worst area  \\\n",
       "0          25.38          17.33           184.60      2019.0   \n",
       "1          24.99          23.41           158.80      1956.0   \n",
       "2          23.57          25.53           152.50      1709.0   \n",
       "3          14.91          26.50            98.87       567.7   \n",
       "4          22.54          16.67           152.20      1575.0   \n",
       "5          15.47          23.75           103.40       741.6   \n",
       "6          22.88          27.66           153.20      1606.0   \n",
       "7          17.06          28.14           110.60       897.0   \n",
       "8          15.49          30.73           106.20       739.3   \n",
       "9          15.09          40.68            97.65       711.4   \n",
       "10         19.19          33.88           123.80      1150.0   \n",
       "11         20.42          27.28           136.50      1299.0   \n",
       "12         20.96          29.94           151.70      1332.0   \n",
       "13         16.84          27.66           112.00       876.5   \n",
       "14         15.03          32.01           108.80       697.7   \n",
       "15         17.46          37.13           124.10       943.2   \n",
       "16         19.07          30.88           123.40      1138.0   \n",
       "17         20.96          31.48           136.80      1315.0   \n",
       "18         27.32          30.88           186.80      2398.0   \n",
       "19         15.11          19.26            99.70       711.2   \n",
       "\n",
       "    worst smoothness  worst compactness  worst concavity  \\\n",
       "0             0.1622             0.6656           0.7119   \n",
       "1             0.1238             0.1866           0.2416   \n",
       "2             0.1444             0.4245           0.4504   \n",
       "3             0.2098             0.8663           0.6869   \n",
       "4             0.1374             0.2050           0.4000   \n",
       "5             0.1791             0.5249           0.5355   \n",
       "6             0.1442             0.2576           0.3784   \n",
       "7             0.1654             0.3682           0.2678   \n",
       "8             0.1703             0.5401           0.5390   \n",
       "9             0.1853             1.0580           1.1050   \n",
       "10            0.1181             0.1551           0.1459   \n",
       "11            0.1396             0.5609           0.3965   \n",
       "12            0.1037             0.3903           0.3639   \n",
       "13            0.1131             0.1924           0.2322   \n",
       "14            0.1651             0.7725           0.6943   \n",
       "15            0.1678             0.6577           0.7026   \n",
       "16            0.1464             0.1871           0.2914   \n",
       "17            0.1789             0.4233           0.4784   \n",
       "18            0.1512             0.3150           0.5372   \n",
       "19            0.1440             0.1773           0.2390   \n",
       "\n",
       "    worst concave points  worst symmetry  worst fractal dimension         0  \\\n",
       "0                0.26540          0.4601                  0.11890  9.192837   \n",
       "1                0.18600          0.2750                  0.08902  2.387802   \n",
       "2                0.24300          0.3613                  0.08758  5.733896   \n",
       "3                0.25750          0.6638                  0.17300  7.122953   \n",
       "4                0.16250          0.2364                  0.07678  3.935302   \n",
       "5                0.17410          0.3985                  0.12440  2.380247   \n",
       "6                0.19320          0.3063                  0.08368  2.238883   \n",
       "7                0.15560          0.3196                  0.11510  2.143299   \n",
       "8                0.20600          0.4378                  0.10720  3.174924   \n",
       "9                0.22100          0.4366                  0.20750  6.351747   \n",
       "10               0.09975          0.2948                  0.08452 -0.810414   \n",
       "11               0.18100          0.3792                  0.10480  2.651100   \n",
       "12               0.17670          0.3176                  0.10230  8.185034   \n",
       "13               0.11190          0.2809                  0.06287  0.342126   \n",
       "14               0.22080          0.3596                  0.14310  4.342379   \n",
       "15               0.17120          0.4218                  0.13410  4.075656   \n",
       "16               0.16090          0.3029                  0.08216  0.230055   \n",
       "17               0.20730          0.3706                  0.11420  4.418011   \n",
       "18               0.23880          0.2768                  0.07615  4.948704   \n",
       "19               0.12880          0.2977                  0.07259 -1.237063   \n",
       "\n",
       "            1         2      label  \n",
       "0    1.948583 -1.123166  malignant  \n",
       "1   -3.768172 -0.529293  malignant  \n",
       "2   -1.075174 -0.551748  malignant  \n",
       "3   10.275589 -3.232790  malignant  \n",
       "4   -1.948072  1.389767  malignant  \n",
       "5    3.949929 -2.934877  malignant  \n",
       "6   -2.690031 -1.639913  malignant  \n",
       "7    2.340244 -0.871947  malignant  \n",
       "8    3.391813 -3.119986  malignant  \n",
       "9    7.727174 -4.341916  malignant  \n",
       "10  -2.659275 -0.488830  malignant  \n",
       "11   0.066568 -1.526455  malignant  \n",
       "12   2.700976  5.730231  malignant  \n",
       "13  -0.968279  1.717172  malignant  \n",
       "14   4.861083 -2.816116  malignant  \n",
       "15   2.977061 -3.125274  malignant  \n",
       "16  -1.564758 -0.802519  malignant  \n",
       "17   1.418670 -2.270319  malignant  \n",
       "18  -4.114334 -0.314749  malignant  \n",
       "19  -0.188215 -0.593283     benign  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can plot features and visualize both the distribution fo data and association of features with data\n",
    "\n",
    "# PCA coordinates derived from scaled data\n",
    "pca_coords = pca_obj.fit_transform(data_scaled)[:, 0:3]\n",
    "pca_coords_df = pd.DataFrame(data = pca_coords, columns = np.arange(0,3).astype('str'))\n",
    "# combine coordinates with other data\n",
    "combined_df = pd.concat([breast_cancer_df, pca_coords_df], axis = 1)\n",
    "lab_vect = np.repeat('malignant', combined_df.shape[0])\n",
    "lab_vect[data['target'] == 1] = 'benign'\n",
    "combined_df['label'] = lab_vect\n",
    "# we see that PCA coords + case label are appended to end\n",
    "combined_df.iloc[:, 20:34].head(20)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# helper function for pca plots. Don't worry too much about code here\n",
    "def pca_plots(df, feature):\n",
    "    # Create two subplots and unpack the output array immediately\n",
    "    \n",
    "    # notes on matplotlibe for future reference: https://jakevdp.github.io/mpl_tutorial/tutorial_pages/tut3.html\n",
    "    \n",
    "    f, (ax1, ax2) = plt.subplots(1, 2)\n",
    "    # get data for plotting\n",
    "    feat_vect = df[feature].to_numpy()\n",
    "    x1 = df['0'].to_numpy()\n",
    "    x2 = df['1'].to_numpy()\n",
    "    x3 = df['2'].to_numpy()\n",
    "    \n",
    "    if np.issubdtype(feat_vect.dtype, np.number):\n",
    "        cmap_use = None\n",
    "        categorical = False\n",
    "        col_vect = feat_vect\n",
    "    else:\n",
    "        if not type(feat_vect.dtype) == np.string_:\n",
    "            try:\n",
    "                feat_vect = feat_vect.astype('str')\n",
    "            except:\n",
    "                raise ValueError('feature maps to a variable that is neither string nor numeric')\n",
    "        unique_cats = np.unique(feat_vect)\n",
    "        num_cats = len(unique_cats)\n",
    "        cmap_use=plt.cm.get_cmap('Pastel2', num_cats)\n",
    "        # since c must be numeric for scatter method,\n",
    "        # convert to numeric labels, which are mapped back to string labels\n",
    "        # when plotting\n",
    "        col_vect = np.zeros(len(feat_vect))\n",
    "        for i in range(0, num_cats):\n",
    "            col_vect[feat_vect == unique_cats[i]] = i\n",
    "        categorical = True\n",
    "        \n",
    "    # make plots\n",
    "    ax1.scatter(x1, x2, c = col_vect, cmap = cmap_use)\n",
    "    ax1.set_xlabel('PC 0')\n",
    "    ax1.set_ylabel('PC 1')\n",
    "    im = ax2.scatter(x2, x3, c = col_vect, cmap = cmap_use)\n",
    "    ax2.set_xlabel('PC 1')\n",
    "    ax2.set_ylabel('PC 2')\n",
    "    # add colorbar\n",
    "    if categorical:\n",
    "        formatter = plt.FuncFormatter(lambda val, loc: unique_cats[val])\n",
    "        f.colorbar(im, ax = ax2, ticks=np.arange(0, num_cats), format=formatter)\n",
    "    else:\n",
    "        f.colorbar(im, ax = ax2)\n",
    "    # set width + height\n",
    "    f.set_figheight(5)\n",
    "    f.set_figwidth(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f4ce000b02064940ac1f60c464502680",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='feature', options=('mean radius', 'mean texture', 'mean perimeter'…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Interactive PCA plot\n",
    "@interact\n",
    "# PCA plots\n",
    "def pca_interactive(df = fixed(combined_df), feature = combined_df.columns):\n",
    "    pca_plots(df = df, feature = feature)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering\n",
    "\n",
    "### Overview\n",
    "\n",
    "Suppose you want to discover if there are groups of samples that are similar to one another, but don't know where to start? Manually examining numbers and grouping things together is not something people are great at, unless it's points in 2D and 3D space. Even then, you want to have a definition of how you got those groups. Clustering refers to automated procedures by which we can find groups given a bunch of samples defined by numbers.\n",
    "\n",
    "### Kmeans\n",
    "\n",
    "One example of clustering is kmeans, which attempts to find groups of samples where samples in the same group are closer to one another than they are to other samples.\n",
    "\n",
    "The function it tries to minimize is as follows:\n",
    "\n",
    "$\\sum_{i=1}^{N}\\sum_{k=1}^K r_{ik} \\cdot dist(x_i, \\mu_k)^2$\n",
    "\n",
    "where $x_i$ is a datapoint, $r_{ik}$ = 1 if $x_i$ is in cluster $k$ and = 0 otherwise, and $dist(x_i, \\mu_k)$ is the Euclidean distance between the datapoint and the mean of all datapoints in cluster k.\n",
    "\n",
    "More details on kmeans algorithm [here](https://see.stanford.edu/materials/aimlcs229/cs229-notes7a.pdf).\n",
    "\n",
    "We can try clustering with a varying number of clusters. For this exercise, we're going to use the first 2 PCs we found in the breast cancer dataset, as it will be easier to visualize what kmeans is doing.\n",
    "\n",
    "Let's try k = 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>label</th>\n",
       "      <th>k2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "      <td>9.192837</td>\n",
       "      <td>1.948583</td>\n",
       "      <td>-1.123166</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "      <td>2.387802</td>\n",
       "      <td>-3.768172</td>\n",
       "      <td>-0.529293</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "      <td>5.733896</td>\n",
       "      <td>-1.075174</td>\n",
       "      <td>-0.551748</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "      <td>7.122953</td>\n",
       "      <td>10.275589</td>\n",
       "      <td>-3.232790</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "      <td>3.935302</td>\n",
       "      <td>-1.948072</td>\n",
       "      <td>1.389767</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   worst symmetry  worst fractal dimension         0          1         2  \\\n",
       "0          0.4601                  0.11890  9.192837   1.948583 -1.123166   \n",
       "1          0.2750                  0.08902  2.387802  -3.768172 -0.529293   \n",
       "2          0.3613                  0.08758  5.733896  -1.075174 -0.551748   \n",
       "3          0.6638                  0.17300  7.122953  10.275589 -3.232790   \n",
       "4          0.2364                  0.07678  3.935302  -1.948072  1.389767   \n",
       "\n",
       "       label k2  \n",
       "0  malignant  1  \n",
       "1  malignant  1  \n",
       "2  malignant  1  \n",
       "3  malignant  1  \n",
       "4  malignant  1  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import cluster\n",
    "\n",
    "# function to do kmeans and add data to dataframe\n",
    "\n",
    "def do_kmeans(df, feats_use, k = 2, col_name = 'cluster'):\n",
    "    # df = pandas DataFrame with numeric features\n",
    "    # feats_use = list or array features columns to subset\n",
    "    # modifies dataframe to contain cluster labels\n",
    "    data_use = df[feats_use].to_numpy().astype('float64')\n",
    "    # setup + run kmeans\n",
    "    kmeans_obj = cluster.KMeans(n_clusters = k, random_state = 42)\n",
    "    clust_labs = kmeans_obj.fit_predict(data_use)\n",
    "    # conver clust_labs to string (categorical)\n",
    "    clust_labs = clust_labs.astype('str')\n",
    "    df[col_name] = clust_labs\n",
    "    \n",
    "do_kmeans(combined_df, feats_use = ['0', '1'], k = 2, col_name = 'k2')\n",
    "\n",
    "combined_df.iloc[:,28:combined_df.shape[1]].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca_plots(combined_df, 'k2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca_plots(combined_df, 'label')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the data's been partitioned into two clusters of samples that are close to one another? Also notice how in our particular dataset, clustering with k = 2 nicely partitions data into 2 groups separated perfectly in the space of PC 0 and PC 1?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try k = 3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>label</th>\n",
       "      <th>k2</th>\n",
       "      <th>k3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "      <td>9.192837</td>\n",
       "      <td>1.948583</td>\n",
       "      <td>-1.123166</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "      <td>2.387802</td>\n",
       "      <td>-3.768172</td>\n",
       "      <td>-0.529293</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "      <td>5.733896</td>\n",
       "      <td>-1.075174</td>\n",
       "      <td>-0.551748</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "      <td>7.122953</td>\n",
       "      <td>10.275589</td>\n",
       "      <td>-3.232790</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "      <td>3.935302</td>\n",
       "      <td>-1.948072</td>\n",
       "      <td>1.389767</td>\n",
       "      <td>malignant</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   worst symmetry  worst fractal dimension         0          1         2  \\\n",
       "0          0.4601                  0.11890  9.192837   1.948583 -1.123166   \n",
       "1          0.2750                  0.08902  2.387802  -3.768172 -0.529293   \n",
       "2          0.3613                  0.08758  5.733896  -1.075174 -0.551748   \n",
       "3          0.6638                  0.17300  7.122953  10.275589 -3.232790   \n",
       "4          0.2364                  0.07678  3.935302  -1.948072  1.389767   \n",
       "\n",
       "       label k2 k3  \n",
       "0  malignant  1  1  \n",
       "1  malignant  1  1  \n",
       "2  malignant  1  1  \n",
       "3  malignant  1  2  \n",
       "4  malignant  1  1  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "do_kmeans(combined_df, feats_use = ['0', '1'], k = 3, col_name = 'k3')\n",
    "\n",
    "combined_df.iloc[:,28:combined_df.shape[1]].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca_plots(combined_df, 'k3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have 3 groups of samples that looks close to one another. Also notice that again, separation only happens in PC 0 and PC 1, the variables that were input to kmeans clustering\n",
    "\n",
    "### Side Notes on Kmeans\n",
    "\n",
    "Kmeans starts with randomly assigned clusters, and tries to improve cluster assignment in an iterative process. We set a seed for a random number generator which ensures that, given a particular random seed, we get the same clustering result every time. Different start points can result in different solutions. If you really want to be rigorous about checking if the solutions that come out don't vary too much given different start points, you can run kmeans 100-1000 times with different seeds and calculate the similarity of solutions with the [adjusted rand index](https://en.wikipedia.org/wiki/Rand_index#Adjusted_Rand_index).\n",
    "\n",
    "Kmeans works best if data is distributed roughly spherically, i.e. the density of points emanating from the center of a given group doesn't change that much depending on the direction outward from the center of the cluster. Kmeans also doesn't work well when groups of samples have a curved distribution. Examples of how violations of this assumption can lead to bad clustering are given [here](https://scikit-learn.org/stable/modules/clustering.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Choosing the number of clusters\n",
    "\n",
    "The question then arises: How many clusters is the best number? If we choose too few, we might not be capturing all of the cool structure in the data. \n",
    "\n",
    "We can use the silhouette score, which compares the the distance between samples in the same cluster to samples in the nearest cluster (more on the silhouette score [here](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html).  Ideally, we want to maximize this score across all clusters, so we'll take the average silhouette score across all samples and make this the function we want to maximize.\n",
    "\n",
    "Let's see both the clusters that come out and the resulting scores\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'silhouette score')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "\n",
    "def silhouette_analysis(df, feats_use = ['0', '1'], k_use = np.arange(2,9)):\n",
    "    # copy dataframe and do not modify input\n",
    "    df_copy = df.copy()\n",
    "    mean_silhouette_scores = []\n",
    "    for k in k_use:\n",
    "        col_name = 'k' + str(k)\n",
    "        do_kmeans(df_copy, feats_use = feats_use, k = k, col_name = col_name)\n",
    "        input_data = df_copy[feats_use].to_numpy().astype('float64')\n",
    "        clust_labs = df_copy[col_name]\n",
    "        dist_mat = metrics.pairwise.euclidean_distances(input_data)\n",
    "        s_mean = metrics.silhouette_score(dist_mat, clust_labs)\n",
    "        mean_silhouette_scores.append(s_mean)\n",
    "    return(mean_silhouette_scores)\n",
    "\n",
    "s_scores = silhouette_analysis(combined_df)\n",
    "plt.plot(np.arange(2,9), s_scores)\n",
    "plt.xlabel('number of clusters')\n",
    "plt.ylabel('silhouette score')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, and perhaps unsurprisingly, 2 clusters gives the best separation of datapoints into clusters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary:\n",
    "\n",
    "We did an initial data exploration of a breast cancer dataset with PCA, and learned how clustering can automatically group similar samples together. Now it's your turn to apply what you've learned to your own data and see if you can find any cool insights!"
   ]
  },
  {
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