exploratory_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains a bit of exploratory analysis of the ionosphere dataset.\n",
    "\n",
    "Let's first load a couple of the libraries that well be needed for the exploratory analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Vendor:  Continuum Analytics, Inc.\n",
      "Package: mkl\n",
      "Message: trial mode expires in 23 days\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original data was downloaded and saved in ionosphere.txt and afterwards reshaped into a  .csv-file with the preparing_data.py script. The only difference between the original dataset and ionosphere_processed.csv is the format. I will use the latter one to explore some parts of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('ionosphere_processed.csv', index_col=0)\n",
    "n_rows, n_cols = data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pandas DataFrames come with a useful .describe() method to explore the variables assumed to be in the columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "  <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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>351.000000</td>\n",
       "      <td>351</td>\n",
       "      <td>351.000000</td>\n",
       "      <td>351.000000</td>\n",
       "      <td>351.000000</td>\n",
       "      <td>351.000000</td>\n",
       "      <td>351.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.891738</td>\n",
       "      <td>0</td>\n",
       "      <td>0.641342</td>\n",
       "      <td>0.044372</td>\n",
       "      <td>0.601068</td>\n",
       "      <td>0.115889</td>\n",
       "      <td>0.550095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.311155</td>\n",
       "      <td>0</td>\n",
       "      <td>0.497708</td>\n",
       "      <td>0.441435</td>\n",
       "      <td>0.519862</td>\n",
       "      <td>0.460810</td>\n",
       "      <td>0.492654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>0.472135</td>\n",
       "      <td>-0.064735</td>\n",
       "      <td>0.412660</td>\n",
       "      <td>-0.024795</td>\n",
       "      <td>0.211310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>0.871110</td>\n",
       "      <td>0.016310</td>\n",
       "      <td>0.809200</td>\n",
       "      <td>0.022800</td>\n",
       "      <td>0.728730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.194185</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.334655</td>\n",
       "      <td>0.969240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0    1           2           3           4           5  \\\n",
       "count  351.000000  351  351.000000  351.000000  351.000000  351.000000   \n",
       "mean     0.891738    0    0.641342    0.044372    0.601068    0.115889   \n",
       "std      0.311155    0    0.497708    0.441435    0.519862    0.460810   \n",
       "min      0.000000    0   -1.000000   -1.000000   -1.000000   -1.000000   \n",
       "25%      1.000000    0    0.472135   -0.064735    0.412660   -0.024795   \n",
       "50%      1.000000    0    0.871110    0.016310    0.809200    0.022800   \n",
       "75%      1.000000    0    1.000000    0.194185    1.000000    0.334655   \n",
       "max      1.000000    0    1.000000    1.000000    1.000000    1.000000   \n",
       "\n",
       "                6  \n",
       "count  351.000000  \n",
       "mean     0.550095  \n",
       "std      0.492654  \n",
       "min     -1.000000  \n",
       "25%      0.211310  \n",
       "50%      0.728730  \n",
       "75%      0.969240  \n",
       "max      1.000000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_descript = data.describe()\n",
    "data_descript.iloc[:, :7]             # not showing all of them for better visibility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second feature appears to be all zeros for each observation. It can safely be dropped, but before I do that, I will check if there are other features for which that is the case. For any feature not including any information, the columnwise sum of the data descriptions above should equal 351.0 (i.e., the number of observations from the 'count' row)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         1\n",
       "count  351\n",
       "mean     0\n",
       "std      0\n",
       "min      0\n",
       "25%      0\n",
       "50%      0\n",
       "75%      0\n",
       "max      0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_descript.loc[:, ~(data_descript.sum(axis=0) > 351.0)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like only the second feature is redundant. Getting rid of it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data.drop('1', axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Now I will explore (some of) the variables a bit using histograms, visualizing their distributions by target variable. (Note: There are functions within pandas to do this, but as a learning exercise I will write the various functions myself.)\n",
    "First, we need a histogram function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def heaviside(n):\n",
    "    if n >= 0:\n",
    "        return(1)\n",
    "    else:\n",
    "        return(0)\n",
    "    \n",
    "def binned_histogram(series, n_bins, min_val=None, max_val=None):\n",
    "    if min_val == None:\n",
    "        min_val = min(series)\n",
    "    if max_val == None:\n",
    "        max_val = max(series)\n",
    "    if max_val < min_val:\n",
    "        min_val, max_val = max_val, min_val\n",
    "    if min_val == max_val:\n",
    "        return({(min_val, max_val): len(series)}, max_val / n_bins)\n",
    "    \n",
    "    bin_width = (max_val - min_val) / n_bins\n",
    "    bin_counts = {(min_val + bin_width*n,\n",
    "                   min_val + bin_width*(n + 1)): 0\n",
    "                  for n in range(n_bins)}\n",
    "    bin_counts[(min_val - bin_width, min_val)] = 0\n",
    "    for partition in bin_counts.keys():\n",
    "        accum = 0\n",
    "        for sample in series:\n",
    "            accum += (heaviside(sample - partition[1]) - \n",
    "                      heaviside(sample - (partition[1] + bin_width)))\n",
    "        bin_counts[partition] = accum\n",
    "        # Explanation: the heaviside() function is equal to 1 if\n",
    "        # the input is >= 0, and 0 otherwise. partition[1] is the \n",
    "        # upper limit of the respective bin in the histogram. if \n",
    "        # the first heaviside is positive, i.e. sample - partition[1]\n",
    "        # is >= 0, and the second heaviside is 0, i.e. \n",
    "        # sample - partition[1] + bin_width (which is the upper limit \n",
    "        # of the next bin) < 0, then the count in that bin is incremented\n",
    "        # by 1. if both heavisides are 0, then the sample belongs in\n",
    "        # a different bin because it is smaller than both upper limits;\n",
    "        # likewise, if both heavisides are 1, then the sample is higher\n",
    "        # than both upper limits and also does not belong in that bin.\n",
    "    return(bin_counts, bin_width)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "counts, width = binned_histogram(series=data['3'], n_bins=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function runs without problems, but does it properly calculate a binned histogram? Let's visualize it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_histogram(bin_counts, bin_width):\n",
    "    sorted_bin_keys = sorted(bin_counts.keys())\n",
    "    x_min = sorted_bin_keys[0][0]\n",
    "    x_max = sorted_bin_keys[-1][1]\n",
    "    data_pairs = sorted([(bin[0], count) for bin, count in bin_counts.items()])\n",
    "    x, y = zip(*data_pairs)\n",
    "    plt.figure(figsize=(7, 4))\n",
    "    plt.xlim(x_min, x_max)\n",
    "    plt.bar(left=x, height=y, width=bin_width, alpha=.5)\n",
    "    plt.show()\n",
    "    plt.close('all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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45JHnWb78apYsWQXA00/v4Pbb17dsG0WmOIhygHof8J6U0g+rFtlDKUhdVrHOmcBFwMMt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\nkqQMhihJkqQM/x+/apmdq2RThgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x591d080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_histogram(counts, width)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Certainly looks like a histogram alright. A quick comparison with the pandas function confirms it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xb5674e0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6v67ys9jZm55JqLXMj/OUrenp6apL0HkrdRuT7te9e4ivq5VRj9vZ2DtUFkOU\nsrVjx46qS9B5K3UGWffrXr3EtqpePc4ktHeoLIYoZevAgQNVlyCphuwdKotropSttb7OYqVuxbLQ\n6/a3qHvhxeYuDFe/VmrB+lrvHSqPIUrK1ErdimWp113aFOCicA3OBeuqO0OUlL2VuhVL9+vO3IJk\nkLqKvIYE3vpGdeWaKGXr2LFjVZeQiZW6Fcugi7p73cZE6tdwF6zbO1QWQ5Sy1Ww2qy5BUg3ZO1QW\nP85TllqtFm9729t6NkOvkrw8gy8iV7nmL9p/7rnnmJqa4qqrruLSSy+d94zqfhf6OcFg8G1nLGd/\njx49uujj0rAYopSllVpUvdYMvohc5ZoC+lu0X93vwhSw3FqHt62/+8qJIUqZW6lF1WvNoIvIVa6F\nfl65/i70c4LBINvmsr/SBYYoZW5mwakG0/199OO8/C3088r1d2FuXYvNr0G2lfLjwnJJ0qrSaDSq\nLkFrRK2PRK3U1W7Xkl7fw8UWs67l7+1KXUV8UL3qchH5atZ7Afby5uHgC7hz1Gq1uOGGGzwpRaWo\ndYjyareDK7LweC1/b3Nd8O4C8rVoClh4Afby5mHv5y//NfIzOTnJrl27ej5e1/1Snmodoi7wareD\n67Xg0+/twnJd9OpVxNeeQX9Hc53Lg1qt+6WcrJIQ5QLEwfVa8On3dmG5fl/6Wbir1WHQuZjrXB7U\nat0v5cSF5ZIkSQWskiNRxeS6SDhfy7+acpkL0/s5wWChbfvZh34WavfzXr3qlfrTz5XBl/8aeZyg\nsLz+07vW8vrXoD2pn/daKfav5VmREBURO4G9wHrgs8DulNKnV+K9BpHrIuF8TQH9XU15IcP+vvZz\ngkGZC7BdtK/yTQGD/o4O4zVWwhQwSF2DPr9tOb+jw+pJVfYD+9fyDD1ERcRW4D3A7cBjwB7gwYj4\nxymlPx/2+w2HCxD7s5yrKVexML2f9yq6D0UWatfp6tNaHYZxgkGuV7lf6vdpqVrL7F9Fe1JO/cD+\ntZiVOBL1E8C9KaVfA4iIHwO+F9gBjK3A+w2BCxD7s5yrKVexML2f9yq6D0U+1qjT1ae1OgzjBINc\nr3K/1O/TUrWW2b+K9qSc2L8WM9SF5RHx92h/Zx+eGUsppc6/Nw/zvSRJkqo07CNRLwFeBJybM/5n\nwDULbP/V7T9+E/gMACmd5ZlnruCDH/zgrA0vuugiXnjhhVljTz75ZOdv93MhIbfH7r///nkLDOe+\nxsLP7/0O3TyhAAAGA0lEQVQaC9Ww0FgO2y73+b2/B59YYHy5Y73GV+Zn0888WHjbfvah17bLrWvQ\n5/e77Ur8HMvc1rr8HuRS16D9q5+etPz36jXWz7bL/+/r8vvXStU1vH2YyR+DifaBouGIiJcB/wfY\nnFJ6rGv8EHB9Sunb5mz/w8DstCRJkrSy3pJS+tCgLzLsI1HTwFdon5XXbT3wpwts/yDwFtqnTXx5\nyLVIkiR1+2rgKtr5Y2BDPRIFEBG/D3wqpfTOzr8vAs4Cv5hSOjTUN5MkSarISpyd917g1yLiM8Cn\ngXcBlwK/ugLvJUmSVImhh6iU0q9HxEuBu4ArgT8Absz3GlGSJEn9G/rHeZIkSWuBNyCWJEkqwBAl\nSZJUQKkhKiL+XUQ8GhGtiPhiH8+7KyKe7jzvoYjYuJJ1qhoR8XUR8cGI+OuI+GJE/EpEXLbEc94f\nES/M+bq/rJq1ciJiZ0RMRcRzEfH7EfGaJbZ/Q0Q0I+LLEfFERPxIWbWqXP3Mjc68mNsjvhIR/6DM\nmrXyIuL6iPhoRDzV+Tl//zKeM1DfKPtI1FcB9wG/tNwnRMQdwG7aNzR+HfAl2jc0vmRFKlSVPkj7\npkxvBP4FcD1w7xLPScDv0D6JYeZr2wrWqBJ03ch8P/CtwGdp/96/tMf2VwO/Dfwu8C3APcCvRMSW\ncipWWfqdG11exYUe8Q8BT3ZafdbRPpltZ+ffiy76HkbfqGRheUS8FXhfSulrl9gugKeBn08pvbcz\ndjnt28q8NaV030rXqnJExCbgj4F/mlJqdsZuoH29/penlJ7p8bz3Ay9OKb2prFq18iLiMeCxruvN\nBfAnwOGU0rwbmUfEGHBTSumbu8bGgStSSjeVVLZKUGBuvAH4GPC1KaW/LrNWVSciXgBuSSl9ZJFt\nBu4bua+Jupr21c67b2j8LPAY3tB4tdkM/NVMgOr4XeAF2kcge0nAGyLiXERMRsQvRcTXrWShWlkF\nb2S+uXv7jlOLbK8aGvAm9/+jsyzkVET8sxUsU/UxcN/IPURd2flz7g2Nz3U9ptXhSto3qj4vpfT/\ngL9k8Z/1A8C/Ar4LuAP4DuB3OlfKVz0tdiPzXnNh/QLbnwMu96P/VaXI3Hia9nKQNwM/QPuo1e9F\nxLeuVJGqjYH7xsAX24yInwP2LbHZNSml/znoe3W/Le0jFMrcMufHpqKvP+cj3T+OiMeBLwBvoH0I\nX9Ia1vlvT/d/fz4ZEd8A7AFuq6YqrRbDuGL5LwD/eYltniz42jPrYOamxfVAc/7mytBy58czwKyz\nZSLiYuDruDAPlpRSejIipoFvwBBVV/3eyBzac2TukYj1wLMppb8dbnmqUJG5sZBPA98+rKJUWwP3\njYFDVEppmvbEXgkz/3F9I/A4nF9Y/lrg6Aq9p4ZoufMjIj4JXBERI13ror6L9kfOjy33/SLiHwFf\nT38NVRlJKT0fERO0f+8/AudvZP7dwC/2eNongZvnjH0P8OhK1anyFZwbC7mO9sd8WtsG7htlXydq\nQ0RcB2wAXhQR3xIR13VfC6izOPgWOL9g8B7gzoj4voi4FvgA8BRwsszatbJSSmdor2/6TxHxmoj4\nduAIMN59Zl73/IiIyyLi5yPidRFxVUR8N/DfgCeAByvYDQ3Pe4EfjYjbOmdu/ge6bmQeET8bEb/W\ntf1/BF4ZEWMRcU1E/BvgXwLvK7twrbi+5kZEvCsiGhGxMSJeHRH30P643/8RX2U6/024rpMzoN0T\nrouIV3QeH3rfGPoNiJdwFxc+g060r+eQgO8E/ntn/BuBy2eekFI61AlZ9wJXAI/QvqHx82UVrdK8\nhXZwmjkr778A75yzTff8+ApwLe05dQXt/7N8EHh3SunvyihYK2MZNzK/EnhF1/ZTEfG9tJvfj9Ne\nPPy2lNJD5Vauldbv3KB9fcL3AC8HWrSvK/XGlNLHy6taJXkNF5ZxJNqBG+D9wA5WoG94A2JJkqQC\nPA1ckiSpAEOUJElSAYYoSZKkAgxRkiRJBRiiJEmSCjBESZIkFWCIkiRJKsAQJUmSVIAhSpIkqQBD\nlCRJUgGGKEmSpAL+P4Ggjeu5z+IUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb5f6a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.loc[:, '3'].hist(figsize=(7, 4), bins=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems correct.\n",
    "\n",
    "The histograms above show that, for that particular feature, there appears to be a concentration of sample values around -1, 0, and 1. Let's find out if there is a relationship between any of these three peaks and whether or not the target variable of the samples in question was 'good' or 'bad'. For that, I will write another function that plots two histogram on top of each other, coloring them according to their target variable values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_histograms_by_target(**kwargs):\n",
    "    data_pairs_pos = sorted([(bin[0], count) for bin, count in\n",
    "                            kwargs['positive'][0].items()])\n",
    "    data_pairs_neg = sorted([(bin[0], count) for bin, count in\n",
    "                            kwargs['negative'][0].items()])\n",
    "    x_pos, y_pos = zip(*data_pairs_pos)\n",
    "    x_neg, y_neg = zip(*data_pairs_neg)\n",
    "    plt.figure(figsize=(7, 4))\n",
    "    plt.bar(left=x_pos, height=y_pos, width=kwargs['positive'][1],\n",
    "            alpha=.5, color='blue')\n",
    "    plt.bar(left=x_neg, height=y_neg, width=kwargs['negative'][1],\n",
    "            alpha=.5, color='orange')\n",
    "    plt.xlim(kwargs['min_val'] - kwargs['positive'][1], \n",
    "             kwargs['max_val'])\n",
    "    plt.show()\n",
    "    plt.close('all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ERcTVEfH1iNgbEQsRcX2FZW6OiH0RkYuIb0XERc0rV5IkqTvU+05UP/Aj4EPF26n0zojY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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb5f62b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g_series = data.loc[data['target'] == 'g', '3']\n",
    "b_series = data.loc[data['target'] == 'b', '3']\n",
    "min_val = min(min(g_series), min(b_series))\n",
    "max_val = max(max(g_series), max(b_series))\n",
    "plot_histograms_by_target(\n",
    "    positive=binned_histogram(g_series, 100, min_val, max_val),\n",
    "    negative=binned_histogram(b_series, 100, min_val, max_val),\n",
    "    min_val=min_val, max_val=max_val\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interestingly, the overlay of the two histograms according to their target value indicates that the two concentrations around -1 and 1, in the majority of cases, correspond to 'bad' readings whereas the concentration around 0 appears to be almost equally distributed among 'good' and 'bad' target values. \n",
    "\n",
    "This type of analysis could now be used for the rest of the variables in order to identify other variables that could turn out to be good predictors (possibly after some transformations) of the target variable. Given the number of features, however, I will omit this here. Instead, I will explore the data a bit further using principal components analysis (PCA)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate a PCA, I will need the covariance matrix of the features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = data.as_matrix()[:, :-1]\n",
    "X_centred = X - np.mean(X, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cov_mat = (X_centred.T).dot(X_centred) / (X_centred.shape[0]-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The principal components are nothing else but the eigenvectors of the covariance matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cov_mat = cov_mat.astype(np.float64)\n",
    "princomps = np.linalg.eig(cov_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([ 2.90436153,  1.13708673,  0.69266341,  0.64279583,  0.45167303,\n",
      "        0.34064532,  0.27816012,  0.26632153,  0.25042157,  0.20886699,\n",
      "        0.19117632,  0.17037042,  0.16147008,  0.15246957,  0.02134866,\n",
      "        0.13388771,  0.12946504,  0.03121104,  0.0377422 ,  0.03978231,\n",
      "        0.04506265,  0.04815018,  0.05340651,  0.05760683,  0.06454805,\n",
      "        0.06699981,  0.07225005,  0.1188362 ,  0.0880885 ,  0.09342543,\n",
      "        0.10980726,  0.10096348,  0.10494425]), array([[-0.02325839, -0.00635553,  0.08183259, ..., -0.02209133,\n",
      "        -0.05125669, -0.03927536],\n",
      "       [-0.10138455, -0.07767383,  0.30494054, ..., -0.26768934,\n",
      "         0.3191141 ,  0.07597261],\n",
      "       [ 0.07201262, -0.04604199,  0.14870004, ..., -0.01811717,\n",
      "        -0.14071322, -0.24593471],\n",
      "       ..., \n",
      "       [-0.02009187, -0.173524  ,  0.13899732, ...,  0.03810156,\n",
      "         0.032129  ,  0.05001005],\n",
      "       [-0.20017617,  0.14413142,  0.21658876, ..., -0.10611353,\n",
      "        -0.18583495, -0.08591548],\n",
      "       [ 0.01747586, -0.14498102,  0.18385181, ..., -0.10526569,\n",
      "        -0.00861954, -0.22249622]]))\n"
     ]
    }
   ],
   "source": [
    "print(princomps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first array are the eigenvalues, the second array are the corresponding eigenvectors. Interpretation-wise, the magnitude of the eigenvalues as a fraction of the sum of all eigenvalues gives the overall variance along the axis of the corresponding eigenvector.\n",
    "\n",
    "Let's compare with the PCA implementation from scikit-learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, n_components=None, whiten=False)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "pca.fit(X_centred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.02325839 -0.00635553  0.08183259 ...,  0.57718291 -0.33591403\n",
      "   0.21739276]\n",
      " [-0.10138455 -0.07767383  0.30494054 ..., -0.13978823 -0.01663054\n",
      "  -0.16641603]\n",
      " [ 0.07201262 -0.04604199  0.14870004 ..., -0.02875172  0.05510034\n",
      "  -0.14428516]\n",
      " ..., \n",
      " [-0.02009187 -0.173524    0.13899732 ...,  0.02912933  0.07656747\n",
      "   0.15213392]\n",
      " [-0.20017617  0.14413142  0.21658876 ...,  0.30603865  0.25578736\n",
      "  -0.15173189]\n",
      " [ 0.01747586 -0.14498102  0.18385181 ...,  0.07506407  0.07102973\n",
      "  -0.22516923]]\n"
     ]
    }
   ],
   "source": [
    "print(pca.components_.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking good; any discrepancies are very likely due to slight differences in the numerical algorithms used. For convenience, I'll use the scikit-learn class from now on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To take a first look at the results of the PCA, let's put together a function for a scree plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def scree_plot(explained_var):\n",
    "    plt.figure(figsize=(7, 4))\n",
    "    plt.bar(left=range(len(explained_var)), height=explained_var)\n",
    "    plt.title('scree plot')\n",
    "    plt.xlabel('principal components')\n",
    "    plt.ylabel('% variance explained')\n",
    "    plt.show()\n",
    "    plt.close('all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nmyOq6sFVdZ+qem5VfWfQ80iSJM1Xg3RZ/hnw/Kp6KU0o+1OAqvplVb0N+GPg\nLaMvUZIkaXEbJJDdQjNRK8AjgPW6J6vqCmCvEdUlSZI0NgYJZG8GPpTkh8AXaGboX087CF+SJEkD\nGGTaiw8nORd4NHBVVf1s45UlSZI0PgZ6yrKqfgz8eCPVIkmSNJaGfrm4JEmSRsNAJkmS1DEDmSRJ\nUscMZJIkSR0zkEmSJHXMQCZJktQxA5kkSVLHDGSSJEkdM5BJkiR1zEAmSZLUMQOZJElSxwZ6l6Vm\nduutt7J69eqh9l22bBlLly4dcUWSJGmhMJCNyOrVq1mxYsVQ+65cuZLly5ePuCJJkrRQGMhG7nRg\nl1lueyVw4EasRZIkLQQGspHbBbC1S5IkzZ6D+iVJkjpmC9k8MexDAT4QIEnSwmcgmyeGfSjABwIk\nSVr4DGTzzmwfCvCBAEmSFgsD2bzjQwGSJI0bB/VLkiR1zEAmSZLUMQOZJElSxwxkkiRJHTOQSZIk\ndcxAJkmS1DEDmSRJUscMZJIkSR0zkEmSJHVs3geyJEcmWdf3uaLruiRJkkZlobw66ZvAs3u+39VV\nIZIkSaO2UALZr6rqpq6LkCRJ2hjmfZdla+ck1ye5OsnpSR7edUGSJEmjshAC2VeAlwPPAw4FdgDO\nT3LfTquSJEkakXnfZVlV5/R8/WaSi4DvAS8BTpl+r+OAM/qWTbSfxefWW29l9erVQ+27bNkyli5d\nOuKKJElafCYnJ5mcnFxv2dq1a0dy7HkfyPpV1dok3wZ2nHmrNwIHbKqSOrd69WpWrFgx1L4rV65k\n+fLlI65IkqTFZ2JigomJ9Rt3Vq1aNfS/g3stuEDWdlXuDJzWdS3zz+nALrPc9krgwI1YiyRJmq15\nH8iS/BNwJvB94CHAUcAdwOSG9htPuwC2dkmStNDM+0AGPJQmfN0f+BFwPrBHVf2k06okSZJGZN4H\nsqpanCPxJUmSWgth2gtJkqRFzUAmSZLUMQOZJElSxwxkkiRJHTOQSZIkdWzeP2WpjW/YVy/52iVJ\nkkbDQKahX73ka5ckSRoNA5l6zPbVS752SZKkUTKQqYevXpIkqQsO6pckSeqYgUySJKljdllqToZ9\nQhN8SlOSpCkGMs3JsE9oQvOU5rJly5xyQ5I09gxkGpHZPqEJvU9pOuWGJEkGMo3MXJ/QHHzKDbtL\nJUmLhYFM88TggW6u3aW2sEmS5gsDmRaB4bpLJUmaLwxkWgSc0FaStLAZyDS2fKm6JGm+MJBpbM3l\nCc9hp+vMNcUJAAAN30lEQVQAA50k6TcZyKQhnvD0gQJJ0igZyKQ5jUEb7oECu0slSb0MZNKcDBfm\n7C6VJPUykEmd2vTdpb6uSpLmHwOZ1KlN313q66okaf4xkEkL1sJ7XRVg65wkTcNAJo2tTf+6KsCx\nc5I0DQOZpCHM9XVVC2vs3NT5h2EYlDQbBjJJQ5hrd+nCGjsHw7XsTe3vgxSS7omBTNICs+nHzg2+\n7/r7dznNydT5h9nXMChtOgYySWNmLoFu04fBLsft+VSttOkYyCRpk9n0XbWD7z8/nqoddt+p/W3d\n00JjIJOkBWHTj9vrsnVu2H2n9vchDi00CyaQJflr4H8D2wGXAq+uqou7rUqSxsGmb52b67kX6kMc\n0G0YnJycZGJiYk7H0HAWRCBLsj9wHHAIcBHweuDcJI+tqh91WpwkLXpdPlU7Xg9xQLdh8OSTT+ax\nj33sUPvbMjg3CyKQAW8A3l9VHwJI8krg+cCfA//QZWGSpPnMMDgbU2Hwi1/84iZ/Ing+tAzOB/M+\nkCW5N83/I945tayqKslngT07K0ySpA0yDM7GKFoGF8MTwfM+kAEPAJYAa/qW3wQs2/TlSJI0341X\nGFwMFkIgG8SWzY8vDbDLNQBceeWVPcvOovkfemPu67k9t+f23J7bcy/Gc1+zCfadaf9Nr+f8W87l\nOKmquVezEbVdlrcAL6yqM3uWfwjYuqr+uGfZy4APb/oqJUnSmDugqj4y7M7zvoWsqu5IshJ4NnAm\nQJLNgGcBJ/Rtfi5wAHAtcPsmLFOSJI2nLYFH0WSQoc37FjKAJC8BPkQz7cXFwOuAFwHLnPZCkiQt\ndPO+hQygqv49yQOBo4HtgUuAfQxjkiRpMVgQLWSSJEmL2WZdFyBJkjTuDGSSJEkdW1SBLMlfJ7k2\nyW1JvpLkyV3XNF8lOTLJur7PFV3XNd8k2SvJJ5Nc316j/abZ5ugkNyS5NclnkuzURa3zxT1dsySn\nTnPvndVVvfNBkrckuTjJzUnWJPl4ksdMs533Wo/ZXDfvt/UlOTTJpUnWtp8vJ9mnbxvvsz73dN1G\ncZ8tmkDW8wLyI4AnApfSvID8gZ0WNr99k+YhianP07stZ15aSvMQyV+339cbdJnkMODVNE8A704z\nZ965SbbYlEXOMxu8Zu33s1n/3pvYZNXNT3sB76G5h54DbA58OsmvX9DnvTate7xueL/1uw44jGYq\n/hXA54EzkzwevM82YIPXjRHcZ4tmUH+Si4CLquo17ffQXMD3VJUvIO+T5Ehgv6p6Yte1LBRJ1gEv\nmJqguL3HbgD+sar+uV22Nc1rvg6uqjM6K3ae6L9m7bJTgW16J3XW+pI8gOb1cHtV1QXea7PTf93a\nZafi/bZBSX4CvAk4Fe+zWZu6blX1wVHcZ4uihaznBeSfnVpWTdL0BeQbtnPbrXR1ktOTPLzrghaY\nHYDtWP++uxm4CO+7DSlg77aLaXWSf0lyv66Lmme2bX/+tP3pvTY7/dcNvN9mlGRJkpcCWwDn4302\nK9NcNxjBfbYg5iGbBV9APrivAC8HvgU8hKar9/wkv1NV/9NpZQvH9u3P/vtuTc86/aZzgP+ieRHd\nTsDfAWcn2bOq1nVa2TyQ5k0kxwMXVNXUuE7vtXsww3UD77ffkGRX4EKaQHEb8JKq+k6Sp7abeJ9N\nY6br1q6e8322WAKZBlRV5/R8/Wbb5fs94CXAKd1UtWgEGMt/0M9GX7fH5UkuA64G9qYZlzHuTgIe\nx+zGdHqv3W3a6+b9Nq3VwBOAbYAXAx9NsvcGtvc+a0x73apq1Sjus0XRZQn8GPgVTVNrr+2AH276\nchaeqloLfBvYsetaFpAb25/T3Xc3olmpqmto/j889vdekhOBfYHfr6obelZ5r23ABq7bb/B+g6q6\ns6q+W1WXVNXf0nRJHsrd/770PpvGBq7bdNsOfJ8tikBWVXcAUy8gB9Z7AfmFXdW1kCS5L7AzBthB\nXEPzD6ne+25r4Cl4381akocB92eM7700TgT2A55ZVd/r28R7bRqzuG7T7TP299s0lgCbtSHC+2z2\nljBDjhrmPltMXZb/DHwoyde4+wXk9wE+2GlV81SSfwLOBL5PM4bsKOAOYLLLuuabJFvRBNUpj06y\nG/CTqrouyfHA4UmuAq4FjgGuBz6xyYudJzZ0zWgGWx8J/CfNuJQdgWOBq4BzN22l88pJNI/I7wfc\nkmRqvM7Pq+r2qirvtWlt8Lq19+KReL/9WpJ3AWfRzELwW8DLaKYPeUe7iffZNDZ03UZ2n1XVovnQ\nzHt0LXA7TZp/ctc1zdcPTfC6vr1W1wEfAXbouq759qHp/1/Xfn7V8/spPdscRfNfQbcBnwZ26rru\n+XrNgC1pBr+uAX5J0/JzMvDAruvu+Jr1X6upz0F923mvDXDdvN+mvWb/1l6H29vr8mngWX3beJ8N\ncN1GdZ8tmnnIJEmSFqpFMYZMkiRpITOQSZIkdcxAJkmS1DEDmSRJUscMZJIkSR0zkEmSJHXMQCZJ\nktQxA5kkSVLHDGSSZpTkUUnWJXnCCI95TZLXjOp47TGPTHLJKI8pSZvSYnqXpaTR+z6wPc17KEfl\nScCtIzyeRiDJ3sDngW2r6uaOy5HGjoFM0rSSbF5VdwI3jfK4VTXKcKfRS9cFSOPILktpDCQ5L8l7\nkpyY5OdJfpTk6L5trk1yeJLTkqwF3tffZZlk7/b7M5N8LcktSb6U5DF9x/qjJBcnua0918f6zvPa\nnu/rkrwyydlJbk1ydZIX9h3vH5J8qz3f1UmOTjLQf1AmeXySTyVZm+TmJF9M8uh2XZK8Pcl1SW5P\nckmS5/XsO3UdXpzk/LbOi5LsmGSPJCuT/CLJWUke0LPfqUk+nuSIJDe1535vks17ttkiyQlJ1rTX\n6/wkT+pZP9trvl+SVe0xrm7/niV91/kv2npuSfLtJH809ffRtI4B/Kzd9pR23YuSfKP9m3+c5DNJ\nlg5y7SXdMwOZND5eDtwBPBl4LfCGJK/o2+ZNwCXAbsAxGzjWO4DX03Q/3gWcMrUiyfOBjwGfao/z\n+8CFPftW++l1DPAfwBOADwMfTbKsZ/3Nbf27tLX/ZXv+WUnyUOCLwG1tPU8E3s/dvQSvA94AvBHY\nFTgXODPJTn2HOhI4GlgO/Ao4A/gH4FXA7wE7tet7PQt4LPAMYAL4E+CInvXHtssOao/7HeDcJL/d\nd5wNXfPfAz4EvJvmGh0CHAy8te8YRwAfbf/Gs4APt+f5PjAVgh9D00392iQPBiaBfwOWAXsD/4Wt\naNLoVZUfP34W+Qc4D/hm37J3AZf3fL8W+K++bR4FrAOe0H7fu/3++z3b/EG77N7t9y8Dp22glmuA\n1/R8Xwec1LfNhf3L+ta/Cbi45/uRwCUb2P7vaILOkhnWXw+8uW/ZRcCJfdfhz3rW798u27tn2WHA\nlT3fTwV+BGzZs+wQ4Ob2962AXwIv7Vl/L+AHwJsGuOafBQ7rq/9A4Pq+63xUz/el7bLn9p1n655t\nlrfLHtH1PezHz2L/2EImjYcCvtK37CvAzknSs83XZnm8y3p+v7H9+aD25+8Cnxuwvgun+b7L1Jck\n+7fddD9M8guaFrWHD3D83YDzq+pX/SuSbA08GPhS36ov9dbQ6v27p8bWfaNv2YNY36VVdXvP968A\n903ycGBHYPPec1fVXcBX7+Hc013zI9pu01+01+j9wPZJtpzuGFV1K03LY3+9vb5O87/lN5L8e5JX\nJNl2A9tLGpKBTBofs+lmumWWx7qz5/ep7sepf57cNuuKZpap4ybZEzidpgv0+TTh6p3AFgMc71YG\n72abbvvp/u7+Zf3/XB2me+/Xf/89nHvqXFsBb6cJZlOf3wF2pmmBm+4YM9V798qqdVX1HJoWuSuA\nVwPfasecSRohA5k0HgLs3rdsD+DbVdX/L/65ugx49oD77Nn3fQ/gyvb3pwLfq6p3VdWqqrqapgtx\n0Jp+b7oHAaqZ4uEG4Ol9q54GXD7geabzu32tVHsAv6iq64Cracb1/frc7YD/J9MEoNlaBSyrqu9O\n85nt/753tD+X9K+oqi9X1ZE0Y+/uAF4wQG2SZsFpL6Tx8Ygkx9F0ZS2nGYj+ho1wnqOAzyW5mmbQ\n+72AP6iqYzewz4uSfI2m6+4AmkDyZ+26b7e170/Tpfp8Bg8EJ9K07nw0ybtouur2AC6qqm8D/wgc\n1dZ8aXvuJ9AMwp+rewMfSPIOYAea8W4nAlTVLUneC/xjkp8C1wF/A2wJfGCAcxwNfCrJ92kG3a+j\naSV7fFW9bZbH+B5Ni9kfJTmbpqXzcTTh+lyasXC7Aw/k7rAsaUQMZNJ4KJqn8O5DM1j9LuD4qvrX\nWe67oe/rLauqLyR5MfA24M004ecL93COI4CXAv9C01r10qpa3R7vk0neTRNitqDpujyG9Z9UnO7J\nzbtXVv00yTNpgtcXaJ6QvAQ4v93kBGAb4DiaMVWXA/+rbY2b1d89w7KiGYN1Fc1TnlsAH6EJZVPe\nTNNb8X+A3wIuBp5XVWtne56q+nSSP6TptjyMpmvySpqnI2elqq5PcgTw98AHae6XY2meHn0tsDXN\ngx9vqKpzZ3tcSbOT0fdWSJpvkvw3zVOIG6NFbE6SrANeUFVndl3LqCU5Fdimqv6461okzW+OIZPG\nQ3DuKEmatwxk0njYYJeeNhqvu6RZsctSkiSpY7aQSZIkdcxAJkmS1DEDmSRJUscMZJIkSR0zkEmS\nJHXMQCZJktQxA5kkSVLHDGSSJEkdM5BJkiR17P8HLqaH7mJdV34AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbc84588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scree_plot(pca.explained_variance_ratio_ * 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a fairly typical result from a PCA; as can be seen from the plot, more than 30% of the total variance in the dataset is already captured by the first component, with the second PC still explaining about 12-13%. Afterwards, the variance explained per component drops off significantly. Assuming that in particular the later components mostly represent noise, one could use this insight when trying to predict 'good' and 'bad' target values by only using a subset of the components as features. I will explore how this impacts the prediction performance metrics in the prediction.ipynb notebook in this repository."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the last step in this notebook for now, I will project the observations into the 2-dimensional space of the first two principal components and visualize them as a scatterplot by target values.\n",
    "\n",
    "First the projection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "projections = X_centred.dot(pca.components_.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_projections(projections, target, x_axis, y_axis):\n",
    "    # this function assumes that the order of the rows has not\n",
    "    # changed throughout and that therefore the features can be\n",
    "    # correctly sliced by the indices in the target variable\n",
    "    x_g = projections[target == 'g', x_axis]\n",
    "    y_g = projections[target == 'g', y_axis]\n",
    "    x_b = projections[target == 'b', x_axis]\n",
    "    y_b = projections[target == 'b', y_axis]\n",
    "    plt.figure(figsize=(7, 4))\n",
    "    plt.scatter(x=x_g, y=y_g, c='blue')\n",
    "    plt.scatter(x=x_b, y=y_b, c='orange')\n",
    "    plt.xlabel('PC {}'.format(x_axis + 1))\n",
    "    plt.ylabel('PC {}'.format(y_axis + 1))\n",
    "    plt.show()\n",
    "    plt.close('all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Z/bcrZ5/JYu8Bto6gYhiIMRDzBasps7BmZsNyW1joU44hi6BKJHtpuXUgFhez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\nIPWpQqsT4sr03+YCwZO52Xd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rgPXasPIW0ZA31aNGbDuAP8v69/+AvlqyreZosAxKqTFj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\nkhoxiEmSJDViEJMkSWrEICZJktTI/wD4XUkXLrxErAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbbdb9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_projections(projections, np.array(data['target']), 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like there is an area in the middle with a much higher concentration of 'bad' target values than elsewhere; however, there is a significant number of 'bad' observations in other parts, too. It will remain to be seen how well the use of additional components might improve the separability and predictive performance.\n",
    "\n",
    "Let's take a quick look at the 2D-plots of additional principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MxMg2Nm/pwLFzDoxciJ43cgE4OqKwZWunWcMiogIxuvZW8iDo3wEoiExftoJFWskIDMTI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\n0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbd50cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_projections(projections, np.array(data['target']), 0, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T9Th1YmuAHpzC/VsBizFB3DoxNWmV6UiBmIiUjZqaGo49cYLde7q5WB3iYnWI3Xu6tWJy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\nTQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbd4b710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_projections(projections, np.array(data['target']), 1, 2)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}