{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3行で\n",
    "\n",
    "・井出・杉山の異常検知と変化検知で説明されてるアルゴリズムを実問題（に近いなにか）に適用したい  \n",
    "・まずはホテリングのT2法をkaggleのCredit Card Fraud Detectionをやってみたぞ  \n",
    "https://www.kaggle.com/mlg-ulb/creditcardfraud"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 理論の説明\n",
    "\n",
    "詳細は本をご購入ください。\n",
    "\n",
    "アルゴリズムをざっと説明すると  \n",
    "1. （パラメータ決定）異常度の分布であるカイ2乗分布から異常と判定する閾値を決定する  \n",
    "2. （訓練）（正常標本が圧倒的に多いデータから）標本平均、標本共分散行列を計算する\n",
    "3. （推論1）2で求めた標本共分散行列で定義される標本平均と推論対象のデータのマハラノビス距離を計算し、その推論対象の異常度とする\n",
    "4. （推論2）計算された異常度が閾値を超えたものを異常と判定する\n",
    "\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# データのロード"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.model_selection import train_test_split\n",
    "import scipy.stats\n",
    "\n",
    "df = pd.read_csv(\"creditcard.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "あとで使うモジュールもここでimportしておく"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# データ概観"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>...</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.359807</td>\n",
       "      <td>-0.072781</td>\n",
       "      <td>2.536347</td>\n",
       "      <td>1.378155</td>\n",
       "      <td>-0.338321</td>\n",
       "      <td>0.462388</td>\n",
       "      <td>0.239599</td>\n",
       "      <td>0.098698</td>\n",
       "      <td>0.363787</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.018307</td>\n",
       "      <td>0.277838</td>\n",
       "      <td>-0.110474</td>\n",
       "      <td>0.066928</td>\n",
       "      <td>0.128539</td>\n",
       "      <td>-0.189115</td>\n",
       "      <td>0.133558</td>\n",
       "      <td>-0.021053</td>\n",
       "      <td>149.62</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.191857</td>\n",
       "      <td>0.266151</td>\n",
       "      <td>0.166480</td>\n",
       "      <td>0.448154</td>\n",
       "      <td>0.060018</td>\n",
       "      <td>-0.082361</td>\n",
       "      <td>-0.078803</td>\n",
       "      <td>0.085102</td>\n",
       "      <td>-0.255425</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.225775</td>\n",
       "      <td>-0.638672</td>\n",
       "      <td>0.101288</td>\n",
       "      <td>-0.339846</td>\n",
       "      <td>0.167170</td>\n",
       "      <td>0.125895</td>\n",
       "      <td>-0.008983</td>\n",
       "      <td>0.014724</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-1.358354</td>\n",
       "      <td>-1.340163</td>\n",
       "      <td>1.773209</td>\n",
       "      <td>0.379780</td>\n",
       "      <td>-0.503198</td>\n",
       "      <td>1.800499</td>\n",
       "      <td>0.791461</td>\n",
       "      <td>0.247676</td>\n",
       "      <td>-1.514654</td>\n",
       "      <td>...</td>\n",
       "      <td>0.247998</td>\n",
       "      <td>0.771679</td>\n",
       "      <td>0.909412</td>\n",
       "      <td>-0.689281</td>\n",
       "      <td>-0.327642</td>\n",
       "      <td>-0.139097</td>\n",
       "      <td>-0.055353</td>\n",
       "      <td>-0.059752</td>\n",
       "      <td>378.66</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Time        V1        V2        V3        V4        V5        V6        V7  \\\n",
       "0   0.0 -1.359807 -0.072781  2.536347  1.378155 -0.338321  0.462388  0.239599   \n",
       "1   0.0  1.191857  0.266151  0.166480  0.448154  0.060018 -0.082361 -0.078803   \n",
       "2   1.0 -1.358354 -1.340163  1.773209  0.379780 -0.503198  1.800499  0.791461   \n",
       "\n",
       "         V8        V9  ...       V21       V22       V23       V24       V25  \\\n",
       "0  0.098698  0.363787  ... -0.018307  0.277838 -0.110474  0.066928  0.128539   \n",
       "1  0.085102 -0.255425  ... -0.225775 -0.638672  0.101288 -0.339846  0.167170   \n",
       "2  0.247676 -1.514654  ...  0.247998  0.771679  0.909412 -0.689281 -0.327642   \n",
       "\n",
       "        V26       V27       V28  Amount  Class  \n",
       "0 -0.189115  0.133558 -0.021053  149.62      0  \n",
       "1  0.125895 -0.008983  0.014724    2.69      0  \n",
       "2 -0.139097 -0.055353 -0.059752  378.66      0  \n",
       "\n",
       "[3 rows x 31 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "V1からV28はカード会社の持っているデータをPCAしたもののようです。  \n",
    "生データは機密だからみせられないよ！とのこと。  \n",
    "PCAされているので共分散行列は対角化されていると期待できる。  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\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>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>...</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>284807.000000</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>...</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>284807.000000</td>\n",
       "      <td>284807.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>94813.859575</td>\n",
       "      <td>1.165980e-15</td>\n",
       "      <td>3.416908e-16</td>\n",
       "      <td>-1.373150e-15</td>\n",
       "      <td>2.086869e-15</td>\n",
       "      <td>9.604066e-16</td>\n",
       "      <td>1.490107e-15</td>\n",
       "      <td>-5.556467e-16</td>\n",
       "      <td>1.177556e-16</td>\n",
       "      <td>-2.406455e-15</td>\n",
       "      <td>...</td>\n",
       "      <td>1.656562e-16</td>\n",
       "      <td>-3.444850e-16</td>\n",
       "      <td>2.578648e-16</td>\n",
       "      <td>4.471968e-15</td>\n",
       "      <td>5.340915e-16</td>\n",
       "      <td>1.687098e-15</td>\n",
       "      <td>-3.666453e-16</td>\n",
       "      <td>-1.220404e-16</td>\n",
       "      <td>88.349619</td>\n",
       "      <td>0.001727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>47488.145955</td>\n",
       "      <td>1.958696e+00</td>\n",
       "      <td>1.651309e+00</td>\n",
       "      <td>1.516255e+00</td>\n",
       "      <td>1.415869e+00</td>\n",
       "      <td>1.380247e+00</td>\n",
       "      <td>1.332271e+00</td>\n",
       "      <td>1.237094e+00</td>\n",
       "      <td>1.194353e+00</td>\n",
       "      <td>1.098632e+00</td>\n",
       "      <td>...</td>\n",
       "      <td>7.345240e-01</td>\n",
       "      <td>7.257016e-01</td>\n",
       "      <td>6.244603e-01</td>\n",
       "      <td>6.056471e-01</td>\n",
       "      <td>5.212781e-01</td>\n",
       "      <td>4.822270e-01</td>\n",
       "      <td>4.036325e-01</td>\n",
       "      <td>3.300833e-01</td>\n",
       "      <td>250.120109</td>\n",
       "      <td>0.041527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-5.640751e+01</td>\n",
       "      <td>-7.271573e+01</td>\n",
       "      <td>-4.832559e+01</td>\n",
       "      <td>-5.683171e+00</td>\n",
       "      <td>-1.137433e+02</td>\n",
       "      <td>-2.616051e+01</td>\n",
       "      <td>-4.355724e+01</td>\n",
       "      <td>-7.321672e+01</td>\n",
       "      <td>-1.343407e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.483038e+01</td>\n",
       "      <td>-1.093314e+01</td>\n",
       "      <td>-4.480774e+01</td>\n",
       "      <td>-2.836627e+00</td>\n",
       "      <td>-1.029540e+01</td>\n",
       "      <td>-2.604551e+00</td>\n",
       "      <td>-2.256568e+01</td>\n",
       "      <td>-1.543008e+01</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>54201.500000</td>\n",
       "      <td>-9.203734e-01</td>\n",
       "      <td>-5.985499e-01</td>\n",
       "      <td>-8.903648e-01</td>\n",
       "      <td>-8.486401e-01</td>\n",
       "      <td>-6.915971e-01</td>\n",
       "      <td>-7.682956e-01</td>\n",
       "      <td>-5.540759e-01</td>\n",
       "      <td>-2.086297e-01</td>\n",
       "      <td>-6.430976e-01</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.283949e-01</td>\n",
       "      <td>-5.423504e-01</td>\n",
       "      <td>-1.618463e-01</td>\n",
       "      <td>-3.545861e-01</td>\n",
       "      <td>-3.171451e-01</td>\n",
       "      <td>-3.269839e-01</td>\n",
       "      <td>-7.083953e-02</td>\n",
       "      <td>-5.295979e-02</td>\n",
       "      <td>5.600000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>84692.000000</td>\n",
       "      <td>1.810880e-02</td>\n",
       "      <td>6.548556e-02</td>\n",
       "      <td>1.798463e-01</td>\n",
       "      <td>-1.984653e-02</td>\n",
       "      <td>-5.433583e-02</td>\n",
       "      <td>-2.741871e-01</td>\n",
       "      <td>4.010308e-02</td>\n",
       "      <td>2.235804e-02</td>\n",
       "      <td>-5.142873e-02</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.945017e-02</td>\n",
       "      <td>6.781943e-03</td>\n",
       "      <td>-1.119293e-02</td>\n",
       "      <td>4.097606e-02</td>\n",
       "      <td>1.659350e-02</td>\n",
       "      <td>-5.213911e-02</td>\n",
       "      <td>1.342146e-03</td>\n",
       "      <td>1.124383e-02</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>139320.500000</td>\n",
       "      <td>1.315642e+00</td>\n",
       "      <td>8.037239e-01</td>\n",
       "      <td>1.027196e+00</td>\n",
       "      <td>7.433413e-01</td>\n",
       "      <td>6.119264e-01</td>\n",
       "      <td>3.985649e-01</td>\n",
       "      <td>5.704361e-01</td>\n",
       "      <td>3.273459e-01</td>\n",
       "      <td>5.971390e-01</td>\n",
       "      <td>...</td>\n",
       "      <td>1.863772e-01</td>\n",
       "      <td>5.285536e-01</td>\n",
       "      <td>1.476421e-01</td>\n",
       "      <td>4.395266e-01</td>\n",
       "      <td>3.507156e-01</td>\n",
       "      <td>2.409522e-01</td>\n",
       "      <td>9.104512e-02</td>\n",
       "      <td>7.827995e-02</td>\n",
       "      <td>77.165000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>172792.000000</td>\n",
       "      <td>2.454930e+00</td>\n",
       "      <td>2.205773e+01</td>\n",
       "      <td>9.382558e+00</td>\n",
       "      <td>1.687534e+01</td>\n",
       "      <td>3.480167e+01</td>\n",
       "      <td>7.330163e+01</td>\n",
       "      <td>1.205895e+02</td>\n",
       "      <td>2.000721e+01</td>\n",
       "      <td>1.559499e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>2.720284e+01</td>\n",
       "      <td>1.050309e+01</td>\n",
       "      <td>2.252841e+01</td>\n",
       "      <td>4.584549e+00</td>\n",
       "      <td>7.519589e+00</td>\n",
       "      <td>3.517346e+00</td>\n",
       "      <td>3.161220e+01</td>\n",
       "      <td>3.384781e+01</td>\n",
       "      <td>25691.160000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time            V1            V2            V3            V4  \\\n",
       "count  284807.000000  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean    94813.859575  1.165980e-15  3.416908e-16 -1.373150e-15  2.086869e-15   \n",
       "std     47488.145955  1.958696e+00  1.651309e+00  1.516255e+00  1.415869e+00   \n",
       "min         0.000000 -5.640751e+01 -7.271573e+01 -4.832559e+01 -5.683171e+00   \n",
       "25%     54201.500000 -9.203734e-01 -5.985499e-01 -8.903648e-01 -8.486401e-01   \n",
       "50%     84692.000000  1.810880e-02  6.548556e-02  1.798463e-01 -1.984653e-02   \n",
       "75%    139320.500000  1.315642e+00  8.037239e-01  1.027196e+00  7.433413e-01   \n",
       "max    172792.000000  2.454930e+00  2.205773e+01  9.382558e+00  1.687534e+01   \n",
       "\n",
       "                 V5            V6            V7            V8            V9  \\\n",
       "count  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean   9.604066e-16  1.490107e-15 -5.556467e-16  1.177556e-16 -2.406455e-15   \n",
       "std    1.380247e+00  1.332271e+00  1.237094e+00  1.194353e+00  1.098632e+00   \n",
       "min   -1.137433e+02 -2.616051e+01 -4.355724e+01 -7.321672e+01 -1.343407e+01   \n",
       "25%   -6.915971e-01 -7.682956e-01 -5.540759e-01 -2.086297e-01 -6.430976e-01   \n",
       "50%   -5.433583e-02 -2.741871e-01  4.010308e-02  2.235804e-02 -5.142873e-02   \n",
       "75%    6.119264e-01  3.985649e-01  5.704361e-01  3.273459e-01  5.971390e-01   \n",
       "max    3.480167e+01  7.330163e+01  1.205895e+02  2.000721e+01  1.559499e+01   \n",
       "\n",
       "       ...           V21           V22           V23           V24  \\\n",
       "count  ...  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean   ...  1.656562e-16 -3.444850e-16  2.578648e-16  4.471968e-15   \n",
       "std    ...  7.345240e-01  7.257016e-01  6.244603e-01  6.056471e-01   \n",
       "min    ... -3.483038e+01 -1.093314e+01 -4.480774e+01 -2.836627e+00   \n",
       "25%    ... -2.283949e-01 -5.423504e-01 -1.618463e-01 -3.545861e-01   \n",
       "50%    ... -2.945017e-02  6.781943e-03 -1.119293e-02  4.097606e-02   \n",
       "75%    ...  1.863772e-01  5.285536e-01  1.476421e-01  4.395266e-01   \n",
       "max    ...  2.720284e+01  1.050309e+01  2.252841e+01  4.584549e+00   \n",
       "\n",
       "                V25           V26           V27           V28         Amount  \\\n",
       "count  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05  284807.000000   \n",
       "mean   5.340915e-16  1.687098e-15 -3.666453e-16 -1.220404e-16      88.349619   \n",
       "std    5.212781e-01  4.822270e-01  4.036325e-01  3.300833e-01     250.120109   \n",
       "min   -1.029540e+01 -2.604551e+00 -2.256568e+01 -1.543008e+01       0.000000   \n",
       "25%   -3.171451e-01 -3.269839e-01 -7.083953e-02 -5.295979e-02       5.600000   \n",
       "50%    1.659350e-02 -5.213911e-02  1.342146e-03  1.124383e-02      22.000000   \n",
       "75%    3.507156e-01  2.409522e-01  9.104512e-02  7.827995e-02      77.165000   \n",
       "max    7.519589e+00  3.517346e+00  3.161220e+01  3.384781e+01   25691.160000   \n",
       "\n",
       "               Class  \n",
       "count  284807.000000  \n",
       "mean        0.001727  \n",
       "std         0.041527  \n",
       "min         0.000000  \n",
       "25%         0.000000  \n",
       "50%         0.000000  \n",
       "75%         0.000000  \n",
       "max         1.000000  \n",
       "\n",
       "[8 rows x 31 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "stdをみると、V1からV28まで降順で並んでいるのがわかる  \n",
    "V1からV28はPCAしたときの共分散行列の固有値の大きい順に並んでいるようだ。  \n",
    "また、meanを見るとほとんど0に近い値が並んでいる  \n",
    "PCAしているので平均が0になるようにシフトされている"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>...</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Time</th>\n",
       "      <td>2.255124e+09</td>\n",
       "      <td>1.091960e+04</td>\n",
       "      <td>-8.307031e+02</td>\n",
       "      <td>-3.021425e+04</td>\n",
       "      <td>-7.077378e+03</td>\n",
       "      <td>1.134407e+04</td>\n",
       "      <td>-3.986868e+03</td>\n",
       "      <td>4.976739e+03</td>\n",
       "      <td>-2.095683e+03</td>\n",
       "      <td>-4.518322e+02</td>\n",
       "      <td>...</td>\n",
       "      <td>1.560435e+03</td>\n",
       "      <td>4.964595e+03</td>\n",
       "      <td>1.516599e+03</td>\n",
       "      <td>-4.654076e+02</td>\n",
       "      <td>-5.769855e+03</td>\n",
       "      <td>-9.482254e+02</td>\n",
       "      <td>-9.841860e+01</td>\n",
       "      <td>-1.475443e+02</td>\n",
       "      <td>-125860.970747</td>\n",
       "      <td>-24.300717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V1</th>\n",
       "      <td>1.091960e+04</td>\n",
       "      <td>3.836489e+00</td>\n",
       "      <td>-3.668399e-16</td>\n",
       "      <td>-1.591003e-15</td>\n",
       "      <td>-7.327817e-16</td>\n",
       "      <td>8.378639e-16</td>\n",
       "      <td>3.333094e-16</td>\n",
       "      <td>9.924436e-17</td>\n",
       "      <td>-5.408793e-17</td>\n",
       "      <td>8.332734e-17</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.691534e-16</td>\n",
       "      <td>1.559269e-16</td>\n",
       "      <td>2.421982e-16</td>\n",
       "      <td>-5.106918e-17</td>\n",
       "      <td>-3.270723e-16</td>\n",
       "      <td>-1.284838e-16</td>\n",
       "      <td>9.270791e-17</td>\n",
       "      <td>2.291751e-16</td>\n",
       "      <td>-111.556566</td>\n",
       "      <td>-0.008244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V2</th>\n",
       "      <td>-8.307031e+02</td>\n",
       "      <td>-3.668399e-16</td>\n",
       "      <td>2.726820e+00</td>\n",
       "      <td>1.722431e-16</td>\n",
       "      <td>-5.294779e-16</td>\n",
       "      <td>1.705466e-16</td>\n",
       "      <td>8.324751e-16</td>\n",
       "      <td>-2.573168e-16</td>\n",
       "      <td>4.291109e-18</td>\n",
       "      <td>-1.894075e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>8.721928e-17</td>\n",
       "      <td>2.080689e-16</td>\n",
       "      <td>9.431707e-17</td>\n",
       "      <td>-1.081634e-16</td>\n",
       "      <td>1.314776e-16</td>\n",
       "      <td>2.006343e-16</td>\n",
       "      <td>-3.456338e-16</td>\n",
       "      <td>-1.968671e-16</td>\n",
       "      <td>-219.485433</td>\n",
       "      <td>0.006260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V3</th>\n",
       "      <td>-3.021425e+04</td>\n",
       "      <td>-1.591003e-15</td>\n",
       "      <td>1.722431e-16</td>\n",
       "      <td>2.299029e+00</td>\n",
       "      <td>-4.621923e-16</td>\n",
       "      <td>-1.297100e-15</td>\n",
       "      <td>2.939634e-15</td>\n",
       "      <td>5.082718e-16</td>\n",
       "      <td>-5.758069e-17</td>\n",
       "      <td>2.412002e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.889959e-16</td>\n",
       "      <td>-2.348384e-16</td>\n",
       "      <td>-7.394678e-17</td>\n",
       "      <td>3.089224e-17</td>\n",
       "      <td>5.925223e-17</td>\n",
       "      <td>-1.715297e-16</td>\n",
       "      <td>3.409186e-16</td>\n",
       "      <td>3.703327e-16</td>\n",
       "      <td>-79.975549</td>\n",
       "      <td>-0.012150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V4</th>\n",
       "      <td>-7.077378e+03</td>\n",
       "      <td>-7.327817e-16</td>\n",
       "      <td>-5.294779e-16</td>\n",
       "      <td>-4.621923e-16</td>\n",
       "      <td>2.004684e+00</td>\n",
       "      <td>-3.576902e-15</td>\n",
       "      <td>-7.963000e-16</td>\n",
       "      <td>-1.949710e-16</td>\n",
       "      <td>1.121726e-15</td>\n",
       "      <td>9.433454e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-5.786136e-17</td>\n",
       "      <td>2.599239e-16</td>\n",
       "      <td>1.700352e-16</td>\n",
       "      <td>1.347708e-16</td>\n",
       "      <td>4.773297e-16</td>\n",
       "      <td>-2.689739e-16</td>\n",
       "      <td>-6.540199e-17</td>\n",
       "      <td>-4.341005e-18</td>\n",
       "      <td>34.964556</td>\n",
       "      <td>0.007846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V5</th>\n",
       "      <td>1.134407e+04</td>\n",
       "      <td>8.378639e-16</td>\n",
       "      <td>1.705466e-16</td>\n",
       "      <td>-1.297100e-15</td>\n",
       "      <td>-3.576902e-15</td>\n",
       "      <td>1.905081e+00</td>\n",
       "      <td>1.156005e-15</td>\n",
       "      <td>-1.397105e-18</td>\n",
       "      <td>8.149115e-16</td>\n",
       "      <td>8.041837e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-7.223938e-17</td>\n",
       "      <td>4.573025e-17</td>\n",
       "      <td>9.701149e-17</td>\n",
       "      <td>-8.131900e-16</td>\n",
       "      <td>-6.929392e-17</td>\n",
       "      <td>2.398717e-16</td>\n",
       "      <td>2.521276e-16</td>\n",
       "      <td>-8.280967e-17</td>\n",
       "      <td>-133.380790</td>\n",
       "      <td>-0.005444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V6</th>\n",
       "      <td>-3.986868e+03</td>\n",
       "      <td>3.333094e-16</td>\n",
       "      <td>8.324751e-16</td>\n",
       "      <td>2.939634e-15</td>\n",
       "      <td>-7.963000e-16</td>\n",
       "      <td>1.156005e-15</td>\n",
       "      <td>1.774946e+00</td>\n",
       "      <td>-5.304010e-17</td>\n",
       "      <td>-5.904266e-16</td>\n",
       "      <td>-1.975345e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-9.924436e-17</td>\n",
       "      <td>-1.017080e-16</td>\n",
       "      <td>3.371062e-17</td>\n",
       "      <td>-8.535315e-16</td>\n",
       "      <td>3.820521e-16</td>\n",
       "      <td>-1.645278e-16</td>\n",
       "      <td>-6.873882e-17</td>\n",
       "      <td>1.897350e-16</td>\n",
       "      <td>71.970931</td>\n",
       "      <td>-0.002415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V7</th>\n",
       "      <td>4.976739e+03</td>\n",
       "      <td>9.924436e-17</td>\n",
       "      <td>-2.573168e-16</td>\n",
       "      <td>5.082718e-16</td>\n",
       "      <td>-1.949710e-16</td>\n",
       "      <td>-1.397105e-18</td>\n",
       "      <td>-5.304010e-17</td>\n",
       "      <td>1.530401e+00</td>\n",
       "      <td>-5.867842e-17</td>\n",
       "      <td>3.567608e-17</td>\n",
       "      <td>...</td>\n",
       "      <td>3.142395e-17</td>\n",
       "      <td>-5.758880e-16</td>\n",
       "      <td>-2.145430e-16</td>\n",
       "      <td>-3.648690e-18</td>\n",
       "      <td>2.201688e-17</td>\n",
       "      <td>-4.844150e-16</td>\n",
       "      <td>-5.993831e-17</td>\n",
       "      <td>3.056168e-17</td>\n",
       "      <td>122.936845</td>\n",
       "      <td>-0.009620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V8</th>\n",
       "      <td>-2.095683e+03</td>\n",
       "      <td>-5.408793e-17</td>\n",
       "      <td>4.291109e-18</td>\n",
       "      <td>-5.758069e-17</td>\n",
       "      <td>1.121726e-15</td>\n",
       "      <td>8.149115e-16</td>\n",
       "      <td>-5.904266e-16</td>\n",
       "      <td>-5.867842e-17</td>\n",
       "      <td>1.426479e+00</td>\n",
       "      <td>5.726634e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>3.613762e-17</td>\n",
       "      <td>1.493156e-17</td>\n",
       "      <td>1.519976e-16</td>\n",
       "      <td>-1.545859e-16</td>\n",
       "      <td>-1.134399e-16</td>\n",
       "      <td>-7.983458e-19</td>\n",
       "      <td>1.586213e-16</td>\n",
       "      <td>-2.243975e-16</td>\n",
       "      <td>-30.792991</td>\n",
       "      <td>0.000986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V9</th>\n",
       "      <td>-4.518322e+02</td>\n",
       "      <td>8.332734e-17</td>\n",
       "      <td>-1.894075e-16</td>\n",
       "      <td>2.412002e-16</td>\n",
       "      <td>9.433454e-16</td>\n",
       "      <td>8.041837e-16</td>\n",
       "      <td>-1.975345e-16</td>\n",
       "      <td>3.567608e-17</td>\n",
       "      <td>5.726634e-16</td>\n",
       "      <td>1.206992e+00</td>\n",
       "      <td>...</td>\n",
       "      <td>1.899876e-16</td>\n",
       "      <td>-1.223621e-16</td>\n",
       "      <td>-6.412962e-17</td>\n",
       "      <td>-1.877797e-16</td>\n",
       "      <td>1.144129e-16</td>\n",
       "      <td>-7.271184e-17</td>\n",
       "      <td>-7.746449e-17</td>\n",
       "      <td>2.986687e-16</td>\n",
       "      <td>-12.158248</td>\n",
       "      <td>-0.004459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V10</th>\n",
       "      <td>1.583108e+03</td>\n",
       "      <td>1.150616e-16</td>\n",
       "      <td>-2.581651e-16</td>\n",
       "      <td>3.983746e-16</td>\n",
       "      <td>-1.549290e-16</td>\n",
       "      <td>1.886092e-16</td>\n",
       "      <td>1.885094e-16</td>\n",
       "      <td>4.369446e-16</td>\n",
       "      <td>5.214196e-17</td>\n",
       "      <td>-3.406442e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>8.314273e-16</td>\n",
       "      <td>-2.321544e-16</td>\n",
       "      <td>1.570122e-16</td>\n",
       "      <td>-6.012542e-17</td>\n",
       "      <td>-1.976904e-16</td>\n",
       "      <td>-2.011457e-16</td>\n",
       "      <td>-1.489913e-16</td>\n",
       "      <td>8.499888e-17</td>\n",
       "      <td>-27.643420</td>\n",
       "      <td>-0.009807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V11</th>\n",
       "      <td>-1.200595e+04</td>\n",
       "      <td>6.134539e-16</td>\n",
       "      <td>5.897780e-16</td>\n",
       "      <td>1.855406e-16</td>\n",
       "      <td>-3.985991e-16</td>\n",
       "      <td>1.059954e-15</td>\n",
       "      <td>1.252530e-15</td>\n",
       "      <td>-4.654107e-16</td>\n",
       "      <td>1.648335e-16</td>\n",
       "      <td>3.325110e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>6.411715e-18</td>\n",
       "      <td>7.422121e-18</td>\n",
       "      <td>7.518562e-17</td>\n",
       "      <td>1.014404e-15</td>\n",
       "      <td>-3.322101e-16</td>\n",
       "      <td>-5.055229e-17</td>\n",
       "      <td>-6.875130e-17</td>\n",
       "      <td>-1.178776e-16</td>\n",
       "      <td>0.026545</td>\n",
       "      <td>0.006565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V12</th>\n",
       "      <td>5.900343e+03</td>\n",
       "      <td>2.879035e-16</td>\n",
       "      <td>-5.113904e-16</td>\n",
       "      <td>2.192457e-16</td>\n",
       "      <td>-2.237614e-16</td>\n",
       "      <td>4.985046e-16</td>\n",
       "      <td>3.857382e-16</td>\n",
       "      <td>8.852408e-16</td>\n",
       "      <td>6.361818e-17</td>\n",
       "      <td>-1.452939e-15</td>\n",
       "      <td>...</td>\n",
       "      <td>4.281192e-16</td>\n",
       "      <td>-4.191939e-17</td>\n",
       "      <td>1.751683e-16</td>\n",
       "      <td>2.662171e-16</td>\n",
       "      <td>5.036439e-18</td>\n",
       "      <td>7.535948e-17</td>\n",
       "      <td>-1.251532e-16</td>\n",
       "      <td>2.307594e-16</td>\n",
       "      <td>-2.384691</td>\n",
       "      <td>-0.010813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V13</th>\n",
       "      <td>-3.114775e+03</td>\n",
       "      <td>-1.150366e-16</td>\n",
       "      <td>-2.421233e-17</td>\n",
       "      <td>-1.552408e-17</td>\n",
       "      <td>6.985526e-18</td>\n",
       "      <td>-3.766882e-16</td>\n",
       "      <td>-2.110751e-16</td>\n",
       "      <td>-9.082431e-17</td>\n",
       "      <td>-3.522666e-16</td>\n",
       "      <td>1.031550e-15</td>\n",
       "      <td>...</td>\n",
       "      <td>1.101780e-16</td>\n",
       "      <td>-3.090471e-17</td>\n",
       "      <td>-4.245672e-16</td>\n",
       "      <td>-3.867362e-16</td>\n",
       "      <td>-3.703108e-17</td>\n",
       "      <td>-6.879807e-17</td>\n",
       "      <td>-1.954029e-16</td>\n",
       "      <td>3.569869e-16</td>\n",
       "      <td>1.317731</td>\n",
       "      <td>-0.000189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V14</th>\n",
       "      <td>-4.495601e+03</td>\n",
       "      <td>6.929642e-16</td>\n",
       "      <td>-5.958903e-16</td>\n",
       "      <td>9.764268e-16</td>\n",
       "      <td>-1.340223e-16</td>\n",
       "      <td>3.198373e-16</td>\n",
       "      <td>4.424582e-16</td>\n",
       "      <td>3.789648e-17</td>\n",
       "      <td>-2.466140e-16</td>\n",
       "      <td>1.055974e-15</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.480713e-16</td>\n",
       "      <td>4.201232e-16</td>\n",
       "      <td>1.360837e-16</td>\n",
       "      <td>5.972001e-19</td>\n",
       "      <td>-1.113942e-17</td>\n",
       "      <td>-1.394026e-17</td>\n",
       "      <td>8.638351e-18</td>\n",
       "      <td>7.615907e-16</td>\n",
       "      <td>8.092317</td>\n",
       "      <td>-0.012044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V15</th>\n",
       "      <td>-7.974101e+03</td>\n",
       "      <td>-1.809002e-16</td>\n",
       "      <td>1.848171e-16</td>\n",
       "      <td>-9.166008e-17</td>\n",
       "      <td>2.706080e-16</td>\n",
       "      <td>1.742967e-16</td>\n",
       "      <td>-1.507127e-16</td>\n",
       "      <td>-7.203823e-17</td>\n",
       "      <td>1.270056e-16</td>\n",
       "      <td>-9.079687e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>3.721040e-17</td>\n",
       "      <td>-2.108506e-16</td>\n",
       "      <td>6.455862e-17</td>\n",
       "      <td>-2.440054e-16</td>\n",
       "      <td>1.078079e-16</td>\n",
       "      <td>4.659096e-17</td>\n",
       "      <td>-4.597287e-16</td>\n",
       "      <td>-3.402512e-16</td>\n",
       "      <td>-0.683577</td>\n",
       "      <td>-0.000161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V16</th>\n",
       "      <td>4.952977e+02</td>\n",
       "      <td>5.285673e-16</td>\n",
       "      <td>3.155961e-17</td>\n",
       "      <td>7.528650e-16</td>\n",
       "      <td>-9.837117e-17</td>\n",
       "      <td>7.070849e-16</td>\n",
       "      <td>-1.168329e-16</td>\n",
       "      <td>4.634148e-16</td>\n",
       "      <td>1.289328e-16</td>\n",
       "      <td>-4.782091e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.574385e-16</td>\n",
       "      <td>1.641723e-16</td>\n",
       "      <td>3.941458e-16</td>\n",
       "      <td>-1.879231e-16</td>\n",
       "      <td>-1.675341e-16</td>\n",
       "      <td>-1.998359e-16</td>\n",
       "      <td>2.856098e-16</td>\n",
       "      <td>2.027221e-16</td>\n",
       "      <td>-0.856845</td>\n",
       "      <td>-0.007152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V17</th>\n",
       "      <td>-2.956329e+03</td>\n",
       "      <td>-9.979323e-20</td>\n",
       "      <td>-8.274355e-16</td>\n",
       "      <td>2.238861e-16</td>\n",
       "      <td>-4.450404e-16</td>\n",
       "      <td>5.438107e-16</td>\n",
       "      <td>1.515578e-16</td>\n",
       "      <td>5.852623e-16</td>\n",
       "      <td>-3.612764e-16</td>\n",
       "      <td>7.218917e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-5.982261e-16</td>\n",
       "      <td>-1.709583e-16</td>\n",
       "      <td>2.318197e-16</td>\n",
       "      <td>-8.313399e-17</td>\n",
       "      <td>5.065130e-17</td>\n",
       "      <td>1.111198e-16</td>\n",
       "      <td>2.314862e-16</td>\n",
       "      <td>-2.508123e-17</td>\n",
       "      <td>1.552706</td>\n",
       "      <td>-0.011515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V18</th>\n",
       "      <td>3.599748e+03</td>\n",
       "      <td>2.506182e-16</td>\n",
       "      <td>3.313010e-16</td>\n",
       "      <td>3.611642e-16</td>\n",
       "      <td>-1.999607e-17</td>\n",
       "      <td>4.699014e-16</td>\n",
       "      <td>2.479862e-17</td>\n",
       "      <td>1.761132e-16</td>\n",
       "      <td>-3.275299e-16</td>\n",
       "      <td>1.275108e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-7.473702e-16</td>\n",
       "      <td>-3.439810e-16</td>\n",
       "      <td>-1.539934e-16</td>\n",
       "      <td>-9.610399e-17</td>\n",
       "      <td>-1.062299e-16</td>\n",
       "      <td>1.221656e-16</td>\n",
       "      <td>7.003925e-17</td>\n",
       "      <td>2.214466e-16</td>\n",
       "      <td>7.473906</td>\n",
       "      <td>-0.003880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V19</th>\n",
       "      <td>1.120106e+03</td>\n",
       "      <td>2.628616e-16</td>\n",
       "      <td>1.322260e-17</td>\n",
       "      <td>4.161378e-16</td>\n",
       "      <td>-3.186273e-16</td>\n",
       "      <td>-1.326579e-16</td>\n",
       "      <td>4.128321e-17</td>\n",
       "      <td>-6.023769e-17</td>\n",
       "      <td>-3.161449e-16</td>\n",
       "      <td>9.824799e-17</td>\n",
       "      <td>...</td>\n",
       "      <td>3.482472e-16</td>\n",
       "      <td>-6.066227e-16</td>\n",
       "      <td>3.415922e-16</td>\n",
       "      <td>-4.382794e-17</td>\n",
       "      <td>3.477669e-16</td>\n",
       "      <td>2.153475e-16</td>\n",
       "      <td>-5.407545e-17</td>\n",
       "      <td>-3.659698e-16</td>\n",
       "      <td>-11.432744</td>\n",
       "      <td>0.001176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V20</th>\n",
       "      <td>-1.862195e+03</td>\n",
       "      <td>1.167581e-16</td>\n",
       "      <td>8.602176e-17</td>\n",
       "      <td>1.501888e-17</td>\n",
       "      <td>-2.057175e-16</td>\n",
       "      <td>-1.774199e-16</td>\n",
       "      <td>1.268996e-16</td>\n",
       "      <td>1.786174e-16</td>\n",
       "      <td>1.124420e-16</td>\n",
       "      <td>-2.917704e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-6.614669e-16</td>\n",
       "      <td>5.314426e-16</td>\n",
       "      <td>6.533961e-17</td>\n",
       "      <td>7.554659e-17</td>\n",
       "      <td>4.378428e-18</td>\n",
       "      <td>-1.297577e-16</td>\n",
       "      <td>-3.006146e-16</td>\n",
       "      <td>-6.298824e-17</td>\n",
       "      <td>65.445072</td>\n",
       "      <td>0.000643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V21</th>\n",
       "      <td>1.560435e+03</td>\n",
       "      <td>-1.691534e-16</td>\n",
       "      <td>8.721928e-17</td>\n",
       "      <td>-1.889959e-16</td>\n",
       "      <td>-5.786136e-17</td>\n",
       "      <td>-7.223938e-17</td>\n",
       "      <td>-9.924436e-17</td>\n",
       "      <td>3.142395e-17</td>\n",
       "      <td>3.613762e-17</td>\n",
       "      <td>1.899876e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>5.395255e-01</td>\n",
       "      <td>1.865772e-15</td>\n",
       "      <td>2.918952e-16</td>\n",
       "      <td>6.076160e-17</td>\n",
       "      <td>-4.707745e-17</td>\n",
       "      <td>-1.772897e-16</td>\n",
       "      <td>-4.174631e-16</td>\n",
       "      <td>3.679563e-17</td>\n",
       "      <td>19.474041</td>\n",
       "      <td>0.001233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V22</th>\n",
       "      <td>4.964595e+03</td>\n",
       "      <td>1.559269e-16</td>\n",
       "      <td>2.080689e-16</td>\n",
       "      <td>-2.348384e-16</td>\n",
       "      <td>2.599239e-16</td>\n",
       "      <td>4.573025e-17</td>\n",
       "      <td>-1.017080e-16</td>\n",
       "      <td>-5.758880e-16</td>\n",
       "      <td>1.493156e-17</td>\n",
       "      <td>-1.223621e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>1.865772e-15</td>\n",
       "      <td>5.266428e-01</td>\n",
       "      <td>1.313092e-16</td>\n",
       "      <td>1.332240e-17</td>\n",
       "      <td>-3.658763e-16</td>\n",
       "      <td>-8.804511e-18</td>\n",
       "      <td>4.925419e-17</td>\n",
       "      <td>-1.296150e-16</td>\n",
       "      <td>-11.762131</td>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V23</th>\n",
       "      <td>1.516599e+03</td>\n",
       "      <td>2.421982e-16</td>\n",
       "      <td>9.431707e-17</td>\n",
       "      <td>-7.394678e-17</td>\n",
       "      <td>1.700352e-16</td>\n",
       "      <td>9.701149e-17</td>\n",
       "      <td>3.371062e-17</td>\n",
       "      <td>-2.145430e-16</td>\n",
       "      <td>1.519976e-16</td>\n",
       "      <td>-6.412962e-17</td>\n",
       "      <td>...</td>\n",
       "      <td>2.918952e-16</td>\n",
       "      <td>1.313092e-16</td>\n",
       "      <td>3.899507e-01</td>\n",
       "      <td>2.487034e-17</td>\n",
       "      <td>-2.341586e-16</td>\n",
       "      <td>3.876437e-16</td>\n",
       "      <td>1.088027e-16</td>\n",
       "      <td>2.850687e-16</td>\n",
       "      <td>-17.592087</td>\n",
       "      <td>-0.000070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V24</th>\n",
       "      <td>-4.654076e+02</td>\n",
       "      <td>-5.106918e-17</td>\n",
       "      <td>-1.081634e-16</td>\n",
       "      <td>3.089224e-17</td>\n",
       "      <td>1.347708e-16</td>\n",
       "      <td>-8.131900e-16</td>\n",
       "      <td>-8.535315e-16</td>\n",
       "      <td>-3.648690e-18</td>\n",
       "      <td>-1.545859e-16</td>\n",
       "      <td>-1.877797e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>6.076160e-17</td>\n",
       "      <td>1.332240e-17</td>\n",
       "      <td>2.487034e-17</td>\n",
       "      <td>3.668084e-01</td>\n",
       "      <td>3.937607e-16</td>\n",
       "      <td>5.488754e-17</td>\n",
       "      <td>-7.522538e-17</td>\n",
       "      <td>-5.594736e-17</td>\n",
       "      <td>0.779572</td>\n",
       "      <td>-0.000182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V25</th>\n",
       "      <td>-5.769855e+03</td>\n",
       "      <td>-3.270723e-16</td>\n",
       "      <td>1.314776e-16</td>\n",
       "      <td>5.925223e-17</td>\n",
       "      <td>4.773297e-16</td>\n",
       "      <td>-6.929392e-17</td>\n",
       "      <td>3.820521e-16</td>\n",
       "      <td>2.201688e-17</td>\n",
       "      <td>-1.134399e-16</td>\n",
       "      <td>1.144129e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>-4.707745e-17</td>\n",
       "      <td>-3.658763e-16</td>\n",
       "      <td>-2.341586e-16</td>\n",
       "      <td>3.937607e-16</td>\n",
       "      <td>2.717308e-01</td>\n",
       "      <td>6.118510e-16</td>\n",
       "      <td>-1.328653e-16</td>\n",
       "      <td>6.097678e-17</td>\n",
       "      <td>-6.237072</td>\n",
       "      <td>0.000072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V26</th>\n",
       "      <td>-9.482254e+02</td>\n",
       "      <td>-1.284838e-16</td>\n",
       "      <td>2.006343e-16</td>\n",
       "      <td>-1.715297e-16</td>\n",
       "      <td>-2.689739e-16</td>\n",
       "      <td>2.398717e-16</td>\n",
       "      <td>-1.645278e-16</td>\n",
       "      <td>-4.844150e-16</td>\n",
       "      <td>-7.983458e-19</td>\n",
       "      <td>-7.271184e-17</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.772897e-16</td>\n",
       "      <td>-8.804511e-18</td>\n",
       "      <td>3.876437e-16</td>\n",
       "      <td>5.488754e-17</td>\n",
       "      <td>6.118510e-16</td>\n",
       "      <td>2.325429e-01</td>\n",
       "      <td>-5.454791e-17</td>\n",
       "      <td>-4.690671e-17</td>\n",
       "      <td>-0.386936</td>\n",
       "      <td>0.000089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V27</th>\n",
       "      <td>-9.841860e+01</td>\n",
       "      <td>9.270791e-17</td>\n",
       "      <td>-3.456338e-16</td>\n",
       "      <td>3.409186e-16</td>\n",
       "      <td>-6.540199e-17</td>\n",
       "      <td>2.521276e-16</td>\n",
       "      <td>-6.873882e-17</td>\n",
       "      <td>-5.993831e-17</td>\n",
       "      <td>1.586213e-16</td>\n",
       "      <td>-7.746449e-17</td>\n",
       "      <td>...</td>\n",
       "      <td>-4.174631e-16</td>\n",
       "      <td>4.925419e-17</td>\n",
       "      <td>1.088027e-16</td>\n",
       "      <td>-7.522538e-17</td>\n",
       "      <td>-1.328653e-16</td>\n",
       "      <td>-5.454791e-17</td>\n",
       "      <td>1.629192e-01</td>\n",
       "      <td>4.927291e-19</td>\n",
       "      <td>2.910121</td>\n",
       "      <td>0.000295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V28</th>\n",
       "      <td>-1.475443e+02</td>\n",
       "      <td>2.291751e-16</td>\n",
       "      <td>-1.968671e-16</td>\n",
       "      <td>3.703327e-16</td>\n",
       "      <td>-4.341005e-18</td>\n",
       "      <td>-8.280967e-17</td>\n",
       "      <td>1.897350e-16</td>\n",
       "      <td>3.056168e-17</td>\n",
       "      <td>-2.243975e-16</td>\n",
       "      <td>2.986687e-16</td>\n",
       "      <td>...</td>\n",
       "      <td>3.679563e-17</td>\n",
       "      <td>-1.296150e-16</td>\n",
       "      <td>2.850687e-16</td>\n",
       "      <td>-5.594736e-17</td>\n",
       "      <td>6.097678e-17</td>\n",
       "      <td>-4.690671e-17</td>\n",
       "      <td>4.927291e-19</td>\n",
       "      <td>1.089550e-01</td>\n",
       "      <td>0.846923</td>\n",
       "      <td>0.000131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Amount</th>\n",
       "      <td>-1.258610e+05</td>\n",
       "      <td>-1.115566e+02</td>\n",
       "      <td>-2.194854e+02</td>\n",
       "      <td>-7.997555e+01</td>\n",
       "      <td>3.496456e+01</td>\n",
       "      <td>-1.333808e+02</td>\n",
       "      <td>7.197093e+01</td>\n",
       "      <td>1.229368e+02</td>\n",
       "      <td>-3.079299e+01</td>\n",
       "      <td>-1.215825e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>1.947404e+01</td>\n",
       "      <td>-1.176213e+01</td>\n",
       "      <td>-1.759209e+01</td>\n",
       "      <td>7.795722e-01</td>\n",
       "      <td>-6.237072e+00</td>\n",
       "      <td>-3.869364e-01</td>\n",
       "      <td>2.910121e+00</td>\n",
       "      <td>8.469230e-01</td>\n",
       "      <td>62560.069046</td>\n",
       "      <td>0.058496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Class</th>\n",
       "      <td>-2.430072e+01</td>\n",
       "      <td>-8.243501e-03</td>\n",
       "      <td>6.260047e-03</td>\n",
       "      <td>-1.214993e-02</td>\n",
       "      <td>7.846318e-03</td>\n",
       "      <td>-5.443715e-03</td>\n",
       "      <td>-2.414579e-03</td>\n",
       "      <td>-9.619937e-03</td>\n",
       "      <td>9.857688e-04</td>\n",
       "      <td>-4.458868e-03</td>\n",
       "      <td>...</td>\n",
       "      <td>1.232718e-03</td>\n",
       "      <td>2.426933e-05</td>\n",
       "      <td>-6.963168e-05</td>\n",
       "      <td>-1.816117e-04</td>\n",
       "      <td>7.160261e-05</td>\n",
       "      <td>8.922171e-05</td>\n",
       "      <td>2.946665e-04</td>\n",
       "      <td>1.307146e-04</td>\n",
       "      <td>0.058496</td>\n",
       "      <td>0.001725</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>31 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time            V1            V2            V3            V4  \\\n",
       "Time    2.255124e+09  1.091960e+04 -8.307031e+02 -3.021425e+04 -7.077378e+03   \n",
       "V1      1.091960e+04  3.836489e+00 -3.668399e-16 -1.591003e-15 -7.327817e-16   \n",
       "V2     -8.307031e+02 -3.668399e-16  2.726820e+00  1.722431e-16 -5.294779e-16   \n",
       "V3     -3.021425e+04 -1.591003e-15  1.722431e-16  2.299029e+00 -4.621923e-16   \n",
       "V4     -7.077378e+03 -7.327817e-16 -5.294779e-16 -4.621923e-16  2.004684e+00   \n",
       "V5      1.134407e+04  8.378639e-16  1.705466e-16 -1.297100e-15 -3.576902e-15   \n",
       "V6     -3.986868e+03  3.333094e-16  8.324751e-16  2.939634e-15 -7.963000e-16   \n",
       "V7      4.976739e+03  9.924436e-17 -2.573168e-16  5.082718e-16 -1.949710e-16   \n",
       "V8     -2.095683e+03 -5.408793e-17  4.291109e-18 -5.758069e-17  1.121726e-15   \n",
       "V9     -4.518322e+02  8.332734e-17 -1.894075e-16  2.412002e-16  9.433454e-16   \n",
       "V10     1.583108e+03  1.150616e-16 -2.581651e-16  3.983746e-16 -1.549290e-16   \n",
       "V11    -1.200595e+04  6.134539e-16  5.897780e-16  1.855406e-16 -3.985991e-16   \n",
       "V12     5.900343e+03  2.879035e-16 -5.113904e-16  2.192457e-16 -2.237614e-16   \n",
       "V13    -3.114775e+03 -1.150366e-16 -2.421233e-17 -1.552408e-17  6.985526e-18   \n",
       "V14    -4.495601e+03  6.929642e-16 -5.958903e-16  9.764268e-16 -1.340223e-16   \n",
       "V15    -7.974101e+03 -1.809002e-16  1.848171e-16 -9.166008e-17  2.706080e-16   \n",
       "V16     4.952977e+02  5.285673e-16  3.155961e-17  7.528650e-16 -9.837117e-17   \n",
       "V17    -2.956329e+03 -9.979323e-20 -8.274355e-16  2.238861e-16 -4.450404e-16   \n",
       "V18     3.599748e+03  2.506182e-16  3.313010e-16  3.611642e-16 -1.999607e-17   \n",
       "V19     1.120106e+03  2.628616e-16  1.322260e-17  4.161378e-16 -3.186273e-16   \n",
       "V20    -1.862195e+03  1.167581e-16  8.602176e-17  1.501888e-17 -2.057175e-16   \n",
       "V21     1.560435e+03 -1.691534e-16  8.721928e-17 -1.889959e-16 -5.786136e-17   \n",
       "V22     4.964595e+03  1.559269e-16  2.080689e-16 -2.348384e-16  2.599239e-16   \n",
       "V23     1.516599e+03  2.421982e-16  9.431707e-17 -7.394678e-17  1.700352e-16   \n",
       "V24    -4.654076e+02 -5.106918e-17 -1.081634e-16  3.089224e-17  1.347708e-16   \n",
       "V25    -5.769855e+03 -3.270723e-16  1.314776e-16  5.925223e-17  4.773297e-16   \n",
       "V26    -9.482254e+02 -1.284838e-16  2.006343e-16 -1.715297e-16 -2.689739e-16   \n",
       "V27    -9.841860e+01  9.270791e-17 -3.456338e-16  3.409186e-16 -6.540199e-17   \n",
       "V28    -1.475443e+02  2.291751e-16 -1.968671e-16  3.703327e-16 -4.341005e-18   \n",
       "Amount -1.258610e+05 -1.115566e+02 -2.194854e+02 -7.997555e+01  3.496456e+01   \n",
       "Class  -2.430072e+01 -8.243501e-03  6.260047e-03 -1.214993e-02  7.846318e-03   \n",
       "\n",
       "                  V5            V6            V7            V8            V9  \\\n",
       "Time    1.134407e+04 -3.986868e+03  4.976739e+03 -2.095683e+03 -4.518322e+02   \n",
       "V1      8.378639e-16  3.333094e-16  9.924436e-17 -5.408793e-17  8.332734e-17   \n",
       "V2      1.705466e-16  8.324751e-16 -2.573168e-16  4.291109e-18 -1.894075e-16   \n",
       "V3     -1.297100e-15  2.939634e-15  5.082718e-16 -5.758069e-17  2.412002e-16   \n",
       "V4     -3.576902e-15 -7.963000e-16 -1.949710e-16  1.121726e-15  9.433454e-16   \n",
       "V5      1.905081e+00  1.156005e-15 -1.397105e-18  8.149115e-16  8.041837e-16   \n",
       "V6      1.156005e-15  1.774946e+00 -5.304010e-17 -5.904266e-16 -1.975345e-16   \n",
       "V7     -1.397105e-18 -5.304010e-17  1.530401e+00 -5.867842e-17  3.567608e-17   \n",
       "V8      8.149115e-16 -5.904266e-16 -5.867842e-17  1.426479e+00  5.726634e-16   \n",
       "V9      8.041837e-16 -1.975345e-16  3.567608e-17  5.726634e-16  1.206992e+00   \n",
       "V10     1.886092e-16  1.885094e-16  4.369446e-16  5.214196e-17 -3.406442e-16   \n",
       "V11     1.059954e-15  1.252530e-15 -4.654107e-16  1.648335e-16  3.325110e-16   \n",
       "V12     4.985046e-16  3.857382e-16  8.852408e-16  6.361818e-17 -1.452939e-15   \n",
       "V13    -3.766882e-16 -2.110751e-16 -9.082431e-17 -3.522666e-16  1.031550e-15   \n",
       "V14     3.198373e-16  4.424582e-16  3.789648e-17 -2.466140e-16  1.055974e-15   \n",
       "V15     1.742967e-16 -1.507127e-16 -7.203823e-17  1.270056e-16 -9.079687e-16   \n",
       "V16     7.070849e-16 -1.168329e-16  4.634148e-16  1.289328e-16 -4.782091e-16   \n",
       "V17     5.438107e-16  1.515578e-16  5.852623e-16 -3.612764e-16  7.218917e-16   \n",
       "V18     4.699014e-16  2.479862e-17  1.761132e-16 -3.275299e-16  1.275108e-16   \n",
       "V19    -1.326579e-16  4.128321e-17 -6.023769e-17 -3.161449e-16  9.824799e-17   \n",
       "V20    -1.774199e-16  1.268996e-16  1.786174e-16  1.124420e-16 -2.917704e-16   \n",
       "V21    -7.223938e-17 -9.924436e-17  3.142395e-17  3.613762e-17  1.899876e-16   \n",
       "V22     4.573025e-17 -1.017080e-16 -5.758880e-16  1.493156e-17 -1.223621e-16   \n",
       "V23     9.701149e-17  3.371062e-17 -2.145430e-16  1.519976e-16 -6.412962e-17   \n",
       "V24    -8.131900e-16 -8.535315e-16 -3.648690e-18 -1.545859e-16 -1.877797e-16   \n",
       "V25    -6.929392e-17  3.820521e-16  2.201688e-17 -1.134399e-16  1.144129e-16   \n",
       "V26     2.398717e-16 -1.645278e-16 -4.844150e-16 -7.983458e-19 -7.271184e-17   \n",
       "V27     2.521276e-16 -6.873882e-17 -5.993831e-17  1.586213e-16 -7.746449e-17   \n",
       "V28    -8.280967e-17  1.897350e-16  3.056168e-17 -2.243975e-16  2.986687e-16   \n",
       "Amount -1.333808e+02  7.197093e+01  1.229368e+02 -3.079299e+01 -1.215825e+01   \n",
       "Class  -5.443715e-03 -2.414579e-03 -9.619937e-03  9.857688e-04 -4.458868e-03   \n",
       "\n",
       "        ...           V21           V22           V23           V24  \\\n",
       "Time    ...  1.560435e+03  4.964595e+03  1.516599e+03 -4.654076e+02   \n",
       "V1      ... -1.691534e-16  1.559269e-16  2.421982e-16 -5.106918e-17   \n",
       "V2      ...  8.721928e-17  2.080689e-16  9.431707e-17 -1.081634e-16   \n",
       "V3      ... -1.889959e-16 -2.348384e-16 -7.394678e-17  3.089224e-17   \n",
       "V4      ... -5.786136e-17  2.599239e-16  1.700352e-16  1.347708e-16   \n",
       "V5      ... -7.223938e-17  4.573025e-17  9.701149e-17 -8.131900e-16   \n",
       "V6      ... -9.924436e-17 -1.017080e-16  3.371062e-17 -8.535315e-16   \n",
       "V7      ...  3.142395e-17 -5.758880e-16 -2.145430e-16 -3.648690e-18   \n",
       "V8      ...  3.613762e-17  1.493156e-17  1.519976e-16 -1.545859e-16   \n",
       "V9      ...  1.899876e-16 -1.223621e-16 -6.412962e-17 -1.877797e-16   \n",
       "V10     ...  8.314273e-16 -2.321544e-16  1.570122e-16 -6.012542e-17   \n",
       "V11     ...  6.411715e-18  7.422121e-18  7.518562e-17  1.014404e-15   \n",
       "V12     ...  4.281192e-16 -4.191939e-17  1.751683e-16  2.662171e-16   \n",
       "V13     ...  1.101780e-16 -3.090471e-17 -4.245672e-16 -3.867362e-16   \n",
       "V14     ... -1.480713e-16  4.201232e-16  1.360837e-16  5.972001e-19   \n",
       "V15     ...  3.721040e-17 -2.108506e-16  6.455862e-17 -2.440054e-16   \n",
       "V16     ... -2.574385e-16  1.641723e-16  3.941458e-16 -1.879231e-16   \n",
       "V17     ... -5.982261e-16 -1.709583e-16  2.318197e-16 -8.313399e-17   \n",
       "V18     ... -7.473702e-16 -3.439810e-16 -1.539934e-16 -9.610399e-17   \n",
       "V19     ...  3.482472e-16 -6.066227e-16  3.415922e-16 -4.382794e-17   \n",
       "V20     ... -6.614669e-16  5.314426e-16  6.533961e-17  7.554659e-17   \n",
       "V21     ...  5.395255e-01  1.865772e-15  2.918952e-16  6.076160e-17   \n",
       "V22     ...  1.865772e-15  5.266428e-01  1.313092e-16  1.332240e-17   \n",
       "V23     ...  2.918952e-16  1.313092e-16  3.899507e-01  2.487034e-17   \n",
       "V24     ...  6.076160e-17  1.332240e-17  2.487034e-17  3.668084e-01   \n",
       "V25     ... -4.707745e-17 -3.658763e-16 -2.341586e-16  3.937607e-16   \n",
       "V26     ... -1.772897e-16 -8.804511e-18  3.876437e-16  5.488754e-17   \n",
       "V27     ... -4.174631e-16  4.925419e-17  1.088027e-16 -7.522538e-17   \n",
       "V28     ...  3.679563e-17 -1.296150e-16  2.850687e-16 -5.594736e-17   \n",
       "Amount  ...  1.947404e+01 -1.176213e+01 -1.759209e+01  7.795722e-01   \n",
       "Class   ...  1.232718e-03  2.426933e-05 -6.963168e-05 -1.816117e-04   \n",
       "\n",
       "                 V25           V26           V27           V28         Amount  \\\n",
       "Time   -5.769855e+03 -9.482254e+02 -9.841860e+01 -1.475443e+02 -125860.970747   \n",
       "V1     -3.270723e-16 -1.284838e-16  9.270791e-17  2.291751e-16    -111.556566   \n",
       "V2      1.314776e-16  2.006343e-16 -3.456338e-16 -1.968671e-16    -219.485433   \n",
       "V3      5.925223e-17 -1.715297e-16  3.409186e-16  3.703327e-16     -79.975549   \n",
       "V4      4.773297e-16 -2.689739e-16 -6.540199e-17 -4.341005e-18      34.964556   \n",
       "V5     -6.929392e-17  2.398717e-16  2.521276e-16 -8.280967e-17    -133.380790   \n",
       "V6      3.820521e-16 -1.645278e-16 -6.873882e-17  1.897350e-16      71.970931   \n",
       "V7      2.201688e-17 -4.844150e-16 -5.993831e-17  3.056168e-17     122.936845   \n",
       "V8     -1.134399e-16 -7.983458e-19  1.586213e-16 -2.243975e-16     -30.792991   \n",
       "V9      1.144129e-16 -7.271184e-17 -7.746449e-17  2.986687e-16     -12.158248   \n",
       "V10    -1.976904e-16 -2.011457e-16 -1.489913e-16  8.499888e-17     -27.643420   \n",
       "V11    -3.322101e-16 -5.055229e-17 -6.875130e-17 -1.178776e-16       0.026545   \n",
       "V12     5.036439e-18  7.535948e-17 -1.251532e-16  2.307594e-16      -2.384691   \n",
       "V13    -3.703108e-17 -6.879807e-17 -1.954029e-16  3.569869e-16       1.317731   \n",
       "V14    -1.113942e-17 -1.394026e-17  8.638351e-18  7.615907e-16       8.092317   \n",
       "V15     1.078079e-16  4.659096e-17 -4.597287e-16 -3.402512e-16      -0.683577   \n",
       "V16    -1.675341e-16 -1.998359e-16  2.856098e-16  2.027221e-16      -0.856845   \n",
       "V17     5.065130e-17  1.111198e-16  2.314862e-16 -2.508123e-17       1.552706   \n",
       "V18    -1.062299e-16  1.221656e-16  7.003925e-17  2.214466e-16       7.473906   \n",
       "V19     3.477669e-16  2.153475e-16 -5.407545e-17 -3.659698e-16     -11.432744   \n",
       "V20     4.378428e-18 -1.297577e-16 -3.006146e-16 -6.298824e-17      65.445072   \n",
       "V21    -4.707745e-17 -1.772897e-16 -4.174631e-16  3.679563e-17      19.474041   \n",
       "V22    -3.658763e-16 -8.804511e-18  4.925419e-17 -1.296150e-16     -11.762131   \n",
       "V23    -2.341586e-16  3.876437e-16  1.088027e-16  2.850687e-16     -17.592087   \n",
       "V24     3.937607e-16  5.488754e-17 -7.522538e-17 -5.594736e-17       0.779572   \n",
       "V25     2.717308e-01  6.118510e-16 -1.328653e-16  6.097678e-17      -6.237072   \n",
       "V26     6.118510e-16  2.325429e-01 -5.454791e-17 -4.690671e-17      -0.386936   \n",
       "V27    -1.328653e-16 -5.454791e-17  1.629192e-01  4.927291e-19       2.910121   \n",
       "V28     6.097678e-17 -4.690671e-17  4.927291e-19  1.089550e-01       0.846923   \n",
       "Amount -6.237072e+00 -3.869364e-01  2.910121e+00  8.469230e-01   62560.069046   \n",
       "Class   7.160261e-05  8.922171e-05  2.946665e-04  1.307146e-04       0.058496   \n",
       "\n",
       "            Class  \n",
       "Time   -24.300717  \n",
       "V1      -0.008244  \n",
       "V2       0.006260  \n",
       "V3      -0.012150  \n",
       "V4       0.007846  \n",
       "V5      -0.005444  \n",
       "V6      -0.002415  \n",
       "V7      -0.009620  \n",
       "V8       0.000986  \n",
       "V9      -0.004459  \n",
       "V10     -0.009807  \n",
       "V11      0.006565  \n",
       "V12     -0.010813  \n",
       "V13     -0.000189  \n",
       "V14     -0.012044  \n",
       "V15     -0.000161  \n",
       "V16     -0.007152  \n",
       "V17     -0.011515  \n",
       "V18     -0.003880  \n",
       "V19      0.001176  \n",
       "V20      0.000643  \n",
       "V21      0.001233  \n",
       "V22      0.000024  \n",
       "V23     -0.000070  \n",
       "V24     -0.000182  \n",
       "V25      0.000072  \n",
       "V26      0.000089  \n",
       "V27      0.000295  \n",
       "V28      0.000131  \n",
       "Amount   0.058496  \n",
       "Class    0.001725  \n",
       "\n",
       "[31 rows x 31 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.cov()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "共分散行列の非対角成分は確かにほぼ0になっており、対角化されている。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Time      0\n",
       "V1        0\n",
       "V2        0\n",
       "V3        0\n",
       "V4        0\n",
       "V5        0\n",
       "V6        0\n",
       "V7        0\n",
       "V8        0\n",
       "V9        0\n",
       "V10       0\n",
       "V11       0\n",
       "V12       0\n",
       "V13       0\n",
       "V14       0\n",
       "V15       0\n",
       "V16       0\n",
       "V17       0\n",
       "V18       0\n",
       "V19       0\n",
       "V20       0\n",
       "V21       0\n",
       "V22       0\n",
       "V23       0\n",
       "V24       0\n",
       "V25       0\n",
       "V26       0\n",
       "V27       0\n",
       "V28       0\n",
       "Amount    0\n",
       "Class     0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "欠損はない。  \n",
    "なので今回の解析では補完しなくてよい。  \n",
    "このデータを作るときに誰かが前処理してPCAしてるはずだが、その際補完したのかもしれない。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/qm9dkqQRGeaRylQOqaqH2vAPgUPa8CLg/r75Jlptd/WJKeqSpBGa7lB5Tv9Lv4YtyZokW5Js2b59+3RsUpJmpekOlYfbqSva30da/QHgsL75Frfa7uqLp6hPqaour6rlVbV84cKFL3gnJElTm+5Q2QBM3sG1Grimr35WuwvsOOBH7TTZ9cBJSQ5sF+hPAq5v055Mcly76+usvnVJkkZk0KcU77UkfwG8FTg4yQS9u7g+Se/VxGcDPwDOaLNvBN4ObAOeAt4LUFWPJfkEsLnN9/Gqmrz4/wF6d5i9HLiufSRJIzS0UKmqVbuYdMIU8xZw7i7Wsw5YN0V9C/CGF9KjJKlbI7tQL0maeQwVSVJnDBVJUmcMFUlSZwwVSVJnDBVJUmcMFUlSZwwVSVJnDBVJUmcMFUlSZwwVTbsla68ddQuShsRQkSR1xlCRJHXGUJEkdcZQkSR1xlCRJHXGUJEkdcZQkSR1xlDRUPhbFGl2MlQkSZ0xVCRJnTFUJEmdMVQkSZ0xVCRJnTFUJEmdMVQkSZ0xVCRJnTFUJEmdMVQkSZ0ZSagkuS/J7Um+l2RLqx2UZFOSre3vga2eJJcm2ZbktiRH961ndZt/a5LVo9gXSdLzRnmkcnxVHVlVy9v4WuCGqloK3NDGAU4BlrbPGuAy6IUQcCHwZuBY4MLJIJIkjcaL6fTXSuDKNnwlcGpf/arquRGYn+RQ4GRgU1U9VlWPA5uAFdPdtCTpeaMKlQL+JsktSda02iFV9VAb/iFwSBteBNzft+xEq+2qLkkakVGFym9V1dH0Tm2dm+R3+idWVdELnk4kWZNkS5It27dv72q1egF8NL40M40kVKrqgfb3EeAb9K6JPNxOa9H+PtJmfwA4rG/xxa22q/pU27u8qpZX1fKFCxd2uSuSpD7THipJXpHklZPDwEnAHcAGYPIOrtXANW14A3BWuwvsOOBH7TTZ9cBJSQ5sF+hPajVJ0ojMHcE2DwG+kWRy+1+pqr9Oshm4OsnZwA+AM9r8G4G3A9uAp4D3AlTVY0k+AWxu8328qh6bvt2QJO1s2kOlqu4F3jhF/VHghCnqBZy7i3WtA9Z13aMkad+8mG4pliSNOUNFktQZQ0WS1BlDRZLUGUNFktQZQ0WS1BlDRZLUGUNFktQZQ0WS1BlDRZLUGUNFI+Pj76WZx1CRJHXGUJEkdcZQkSR1xlBR517otRKvtUjjy1DRSBkg0sxiqEiSOmOoSJI6Y6hIkjpjqOhFxWss0ngzVPSiZLhI48lQkSR1xlCRJHXGUNHIeapLmjkMFb1oGC7S+DNUJEmdMVT0ojDVUYpHLtL4MVTUqa6DwGCRxouhIknqzNiHSpIVSe5Jsi3J2lH3M5t5VCFprEMlyRzgc8ApwDJgVZJlo+1KXTOspPEx1qECHAtsq6p7q+oZYD2wcsQ9zUr+wy8JYO6oG3iBFgH3941PAG8eUS8z3iiDY+dt3/fJd4yoE0m7M+6hMpAka4A1bfQnSe4ZZT/NwcA/jrqJadbZPudTXaxlWvg9zx4zfb//+SAzjXuoPAAc1je+uNV+SVVdDlw+XU0NIsmWqlo+6j6mk/s8O8zGfYbZu987G/drKpuBpUkOT/JS4Exgw4h7kqRZa6yPVKpqR5IPAtcDc4B1VXXniNuSpFlrrEMFoKo2AhtH3cc+eFGdjpsm7vPsMBv3GWbvfv+SVNWoe5AkzRDjfk1FkvQiYqhMoyT/Lck/JLktyTeSzO+bdn571Mw9SU4eZZ9dmy2P0klyWJJvJ7kryZ1JPtTqByXZlGRr+3vgqHvtWpI5Sb6b5P+08cOT3NS+879sN9LMGEnmJ/lq+//z3Un+1Wz4ngdhqEyvTcAbquo3gf8LnA/QHi1zJvB6YAXw+fYImrE3yx6lswP4SFUtA44Dzm37uha4oaqWAje08ZnmQ8DdfeOfAj5TVa8FHgfOHklXw/NZ4K+r6jeAN9Lb99nwPe+RoTKNqupvqmpHG72R3u9qoPdomfVV9bOq+j6wjd4jaGaCWfMonap6qKpubcM/pvcPzSJ6+3tlm+1K4NTRdDgcSRYD7wC+2MYDvA34aptlRu1zklcDvwN8CaCqnqmqJ5jh3/OgDJXReR9wXRue6nEzi6a9o+GYyfu2S0mWAEcBNwGHVNVDbdIPgUNG1NawXAL8F+AXbXwB8ETff0DNtO/8cGA78D/aKb8vJnkFM/97Hoih0rEk30xyxxSflX3z/BG9UyVfHl2nGpYkBwBfAz5cVU/2T6ve7ZYz5pbLJO8EHqmqW0bdyzSaCxwNXFZVRwE/ZadTXTPte94bY/87lRebqvo3u5ue5D8A7wROqOfv5x7ocTNjaibv269Ish+9QPlyVX29lR9OcmhVPZTkUOCR0XXYubcA70rydmAe8Cp61xvmJ5nbjlZm2nc+AUxU1U1t/Kv0QmUmf88D80hlGiVZQe80wbuq6qm+SRuAM5O8LMnhwFLg5lH0OASz5lE67VrCl4C7q+rTfZM2AKvb8GrgmunubViq6vyqWlxVS+h9t9+qqt8Dvg2c3mabafv8Q+D+JK9rpROAu5jB3/Pe8MeP0yjJNuBlwKOtdGNV/cc27Y/oXWfZQe+0yXVTr2X8tP+KvYTnH6Vz0YhbGookvwV8B7id568vXEDvusrVwK8BPwDOqKrHRtLkECV5K/Cfq+qdSY6gd1PGQcB3gd+vqp+Nsr8uJTmS3o0JLwXuBd5L7z/SZ/z3vCeGiiSpM57+kiR1xlCRJHXGUJEkdcZQkSR1xlCRJHXGUJEkdcZQkSR1xlCRJHXm/wPCs6Kqdyj3BQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PABYCGzNzZ2Y+T3NTy0Vl2usz867yrJebO9YlSeqBMTmnEhEDwDuB7wLTM/OZMulZYHoZPhV4qmOxoVI7WH1ohLokqUdaD5WImAp8DfhEZr7YOa3zaZIt97AiIrZGxNbt27e3vTlJmrBaDZWImEwTKF/JzOEbUv6wHLqivD9X6tuA0zoWn1lqB6vPHKH+Cpl5Y2bOzcy506ZNO7oPJUkaVZtXfwVwE/BIZn62Y9JaYPgKruXAbR31i8pVYPOBF8phsg3AORFxYjlBfw6woUx7MSLml21d1LEuSVIPdHvr+yPxXuDDNM9hua/UrgCupnnm/SXAk8AFZdp64APAIPAScDFAZu6MiE8DW8p8n8rMnWX4o8CXgOOA28tLktQjrYVKZv4ffvGGlJ3OGmH+BC4bZV2rgFUj1LcCbzuKNiVJFfmLeklSNYaKJKkaQ0WSVI2hIkmqxlCRJFVjqEiaEAZWrut1CxOCoSJJqsZQkSRVY6hIkqoxVCRJ1RgqkqRqDBVJUjWGiiSpGkNFklSNoSJJqsZQkSRVY6hIkqoxVCRJ1RgqkqRqDBVJUjWGiiSpGkNFklSNoSJJqsZQkSRVY6hIkqoxVCRJ1RgqkqRqDBVJUjWGiiSpmtZCJSJWRcRzEfFgR+2kiNgYEY+V9xNLPSLi+ogYjIj7I+KMjmWWl/kfi4jlHfUzI+KBssz1ERFtfRZJUnfa3FP5ErDogNpKYFNmzgY2lXGAxcDs8loBfAGaEAKuBN4NzAOuHA6iMs+lHcsduC1J0hhrLVQy8++AnQeUlwCry/BqYGlH/eZs3AWcEBEzgIXAxszcmZnPAxuBRWXa6zPzrsxM4OaOdUnSiAZWrut1C+PeWJ9TmZ6Zz5ThZ4HpZfhU4KmO+YZK7WD1oRHqI4qIFRGxNSK2bt++/eg+gSRpVD07UV/2MHKMtnVjZs7NzLnTpk0bi01K0oQ01qHyw3LoivL+XKlvA07rmG9mqR2sPnOEuiSph8Y6VNYCw1dwLQdu66hfVK4Cmw+8UA6TbQDOiYgTywn6c4ANZdqLETG/XPV1Uce6JEk9ckxbK46I/wH8S+CUiBiiuYrrauCWiLgEeBK4oMy+HvgAMAi8BFwMkJk7I+LTwJYy36cyc/jk/0dprjA7Dri9vCRJPdRaqGTmslEmnTXCvAlcNsp6VgGrRqhvBd52ND1KkuryF/WSpGoMFUlSNYaKJKkaQ0WSVI2hIkmqxlCRJFVjqEiSqjFUJEnVGCqSpGoMFUlSNYaKJKkaQ0WSVI2hIkmqxlCRJFVjqEiSqjFUJEnVGCqSxqWBlet63cKEZKhIkqoxVCRNKO7BtMtQkSRVY6hIkqoxVCRJ1RgqkqRqDBVJE44n69tjqEiSqjFUJEnVGCqSxh0Pb/WOoSJJqqbvQyUiFkXEoxExGBEre92PpN7qdi/FvZl29HWoRMQk4HPAYmAOsCwi5vS2K0ljaWDluv0BYVD0Xl+HCjAPGMzMxzNzD7AGWNLjniSNkc4QOZJAMYTqO6bXDRylU4GnOsaHgHf3qBdJlY3FP/qjbeOJq89tfdvjUb+HSlciYgWwooz+JCIe7WU/Y+QU4B973USP+R00/B6O4DuIz7TUSe8czd/BP+t2xn4PlW3AaR3jM0vtF2TmjcCNY9XUq0FEbM3Mub3uo5f8Dhp+D34HMHbfQb+fU9kCzI6IWRHxWuBCYG2Pe5KkCauv91Qyc19EfAzYAEwCVmXmQz1uS5ImrL4OFYDMXA+s73Ufr0IT6nDfKPwOGn4PfgcwRt9BZOZYbEeSNAH0+zkVSdKriKEyDkXEf4iI70fEQxHxnzvql5fb2TwaEQt72eNYiIhPRkRGxCllPCLi+vId3B8RZ/S6x7ZExH8pfwP3R8StEXFCx7QJ83cwUW/jFBGnRcSdEfFw+Xfg46V+UkRsjIjHyvuJtbdtqIwzEbGA5q4Cb8/MtwJ/VupzaK6OeyuwCPh8uc3NuBQRpwHnAP/QUV4MzC6vFcAXetDaWNkIvC0zfxP4v8DlMLH+Dib4bZz2AZ/MzDnAfOCy8tlXApsyczawqYxXZaiMP78HXJ2ZuwEy87lSXwKsyczdmfkDYJDmNjfj1TXAHwCdJw2XADdn4y7ghIiY0ZPuWpaZf5OZ+8roXTS/4YKJ9XcwYW/jlJnPZOa9ZfjHwCM0dyBZAqwus60GltbetqEy/vwa8L6I+G5EbI6Id5X6SLe0OXXMuxsDEbEE2JaZf3/ApAnzHRzgI8DtZXgifQcT6bOOKiIGgHcC3wWmZ+YzZdKzwPTa2+v7S4onooj4JvDLI0z6I5r/TU+i2eV9F3BLRLx5DNsbE4f4Dq6gOfQ1rh3sO8jM28o8f0RzKOQrY9mbXh0iYirwNeATmfliROyflpkZEdUv/zVU+lBm/qvRpkXE7wFfz+Za8bsj4mWae/50dUubfjHadxARpwOzgL8v/weaCdwbEfOYIN/BsIj4t8BvAWflz387MK6+g0OYSJ/1FSJiMk2gfCUzv17KP4yIGZn5TDn0+9zoazgyHv4af74BLACIiF8DXktzE7m1wIURcWxEzKI5WX13z7psSWY+kJlvzMyBzBygOeRxRmY+S/MdXFSuApsPvNBxKGBciYhFNOeUPpiZL3VMmhB/B8WEvY1TNP9FdRPwSGZ+tmPSWmB5GV4O3FZ72+6pjD+rgFUR8SCwB1he/iv1oYi4BXiY5nDIZZn5sx722QvrgQ/QnJx+Cbi4t+206r8BxwIbyx7bXZn57zNzwvwdTPDbOL0X+DDwQETcV2pXAFfTHBK/BHgSuKD2hv1FvSSpGg9/SZKqMVQkSdUYKpKkagwVSVI1hookqRpDRZJUjaEiSarGUJEkVfP/AQXbyMn+T42oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for label in df.columns:\n",
    "    df.plot(kind='hist', y=label , bins=int(np.sqrt(len(df))))\n",
    "    plt.show()\n",
    "    plt.clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "標本のヒストグラムを片っ端から作ってみた。  \n",
    "見てみると多峰的だったり片方にテールを引いていたりするものもある。  \n",
    "現実は綺麗な正規分布になるとは限らないのである  \n",
    "だが、今回はあえて無視して正規分布を仮定してモデリングする。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "次に異常と判定されるべきクラスを概観する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>...</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.000000</td>\n",
       "      <td>492.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>80746.806911</td>\n",
       "      <td>-4.771948</td>\n",
       "      <td>3.623778</td>\n",
       "      <td>-7.033281</td>\n",
       "      <td>4.542029</td>\n",
       "      <td>-3.151225</td>\n",
       "      <td>-1.397737</td>\n",
       "      <td>-5.568731</td>\n",
       "      <td>0.570636</td>\n",
       "      <td>-2.581123</td>\n",
       "      <td>...</td>\n",
       "      <td>0.713588</td>\n",
       "      <td>0.014049</td>\n",
       "      <td>-0.040308</td>\n",
       "      <td>-0.105130</td>\n",
       "      <td>0.041449</td>\n",
       "      <td>0.051648</td>\n",
       "      <td>0.170575</td>\n",
       "      <td>0.075667</td>\n",
       "      <td>122.211321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>47835.365138</td>\n",
       "      <td>6.783687</td>\n",
       "      <td>4.291216</td>\n",
       "      <td>7.110937</td>\n",
       "      <td>2.873318</td>\n",
       "      <td>5.372468</td>\n",
       "      <td>1.858124</td>\n",
       "      <td>7.206773</td>\n",
       "      <td>6.797831</td>\n",
       "      <td>2.500896</td>\n",
       "      <td>...</td>\n",
       "      <td>3.869304</td>\n",
       "      <td>1.494602</td>\n",
       "      <td>1.579642</td>\n",
       "      <td>0.515577</td>\n",
       "      <td>0.797205</td>\n",
       "      <td>0.471679</td>\n",
       "      <td>1.376766</td>\n",
       "      <td>0.547291</td>\n",
       "      <td>256.683288</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>406.000000</td>\n",
       "      <td>-30.552380</td>\n",
       "      <td>-8.402154</td>\n",
       "      <td>-31.103685</td>\n",
       "      <td>-1.313275</td>\n",
       "      <td>-22.105532</td>\n",
       "      <td>-6.406267</td>\n",
       "      <td>-43.557242</td>\n",
       "      <td>-41.044261</td>\n",
       "      <td>-13.434066</td>\n",
       "      <td>...</td>\n",
       "      <td>-22.797604</td>\n",
       "      <td>-8.887017</td>\n",
       "      <td>-19.254328</td>\n",
       "      <td>-2.028024</td>\n",
       "      <td>-4.781606</td>\n",
       "      <td>-1.152671</td>\n",
       "      <td>-7.263482</td>\n",
       "      <td>-1.869290</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>41241.500000</td>\n",
       "      <td>-6.036063</td>\n",
       "      <td>1.188226</td>\n",
       "      <td>-8.643489</td>\n",
       "      <td>2.373050</td>\n",
       "      <td>-4.792835</td>\n",
       "      <td>-2.501511</td>\n",
       "      <td>-7.965295</td>\n",
       "      <td>-0.195336</td>\n",
       "      <td>-3.872383</td>\n",
       "      <td>...</td>\n",
       "      <td>0.041787</td>\n",
       "      <td>-0.533764</td>\n",
       "      <td>-0.342175</td>\n",
       "      <td>-0.436809</td>\n",
       "      <td>-0.314348</td>\n",
       "      <td>-0.259416</td>\n",
       "      <td>-0.020025</td>\n",
       "      <td>-0.108868</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>75568.500000</td>\n",
       "      <td>-2.342497</td>\n",
       "      <td>2.717869</td>\n",
       "      <td>-5.075257</td>\n",
       "      <td>4.177147</td>\n",
       "      <td>-1.522962</td>\n",
       "      <td>-1.424616</td>\n",
       "      <td>-3.034402</td>\n",
       "      <td>0.621508</td>\n",
       "      <td>-2.208768</td>\n",
       "      <td>...</td>\n",
       "      <td>0.592146</td>\n",
       "      <td>0.048434</td>\n",
       "      <td>-0.073135</td>\n",
       "      <td>-0.060795</td>\n",
       "      <td>0.088371</td>\n",
       "      <td>0.004321</td>\n",
       "      <td>0.394926</td>\n",
       "      <td>0.146344</td>\n",
       "      <td>9.250000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>128483.000000</td>\n",
       "      <td>-0.419200</td>\n",
       "      <td>4.971257</td>\n",
       "      <td>-2.276185</td>\n",
       "      <td>6.348729</td>\n",
       "      <td>0.214562</td>\n",
       "      <td>-0.413216</td>\n",
       "      <td>-0.945954</td>\n",
       "      <td>1.764879</td>\n",
       "      <td>-0.787850</td>\n",
       "      <td>...</td>\n",
       "      <td>1.244611</td>\n",
       "      <td>0.617474</td>\n",
       "      <td>0.308378</td>\n",
       "      <td>0.285328</td>\n",
       "      <td>0.456515</td>\n",
       "      <td>0.396733</td>\n",
       "      <td>0.826029</td>\n",
       "      <td>0.381152</td>\n",
       "      <td>105.890000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>170348.000000</td>\n",
       "      <td>2.132386</td>\n",
       "      <td>22.057729</td>\n",
       "      <td>2.250210</td>\n",
       "      <td>12.114672</td>\n",
       "      <td>11.095089</td>\n",
       "      <td>6.474115</td>\n",
       "      <td>5.802537</td>\n",
       "      <td>20.007208</td>\n",
       "      <td>3.353525</td>\n",
       "      <td>...</td>\n",
       "      <td>27.202839</td>\n",
       "      <td>8.361985</td>\n",
       "      <td>5.466230</td>\n",
       "      <td>1.091435</td>\n",
       "      <td>2.208209</td>\n",
       "      <td>2.745261</td>\n",
       "      <td>3.052358</td>\n",
       "      <td>1.779364</td>\n",
       "      <td>2125.870000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time          V1          V2          V3          V4  \\\n",
       "count     492.000000  492.000000  492.000000  492.000000  492.000000   \n",
       "mean    80746.806911   -4.771948    3.623778   -7.033281    4.542029   \n",
       "std     47835.365138    6.783687    4.291216    7.110937    2.873318   \n",
       "min       406.000000  -30.552380   -8.402154  -31.103685   -1.313275   \n",
       "25%     41241.500000   -6.036063    1.188226   -8.643489    2.373050   \n",
       "50%     75568.500000   -2.342497    2.717869   -5.075257    4.177147   \n",
       "75%    128483.000000   -0.419200    4.971257   -2.276185    6.348729   \n",
       "max    170348.000000    2.132386   22.057729    2.250210   12.114672   \n",
       "\n",
       "               V5          V6          V7          V8          V9  ...  \\\n",
       "count  492.000000  492.000000  492.000000  492.000000  492.000000  ...   \n",
       "mean    -3.151225   -1.397737   -5.568731    0.570636   -2.581123  ...   \n",
       "std      5.372468    1.858124    7.206773    6.797831    2.500896  ...   \n",
       "min    -22.105532   -6.406267  -43.557242  -41.044261  -13.434066  ...   \n",
       "25%     -4.792835   -2.501511   -7.965295   -0.195336   -3.872383  ...   \n",
       "50%     -1.522962   -1.424616   -3.034402    0.621508   -2.208768  ...   \n",
       "75%      0.214562   -0.413216   -0.945954    1.764879   -0.787850  ...   \n",
       "max     11.095089    6.474115    5.802537   20.007208    3.353525  ...   \n",
       "\n",
       "              V21         V22         V23         V24         V25         V26  \\\n",
       "count  492.000000  492.000000  492.000000  492.000000  492.000000  492.000000   \n",
       "mean     0.713588    0.014049   -0.040308   -0.105130    0.041449    0.051648   \n",
       "std      3.869304    1.494602    1.579642    0.515577    0.797205    0.471679   \n",
       "min    -22.797604   -8.887017  -19.254328   -2.028024   -4.781606   -1.152671   \n",
       "25%      0.041787   -0.533764   -0.342175   -0.436809   -0.314348   -0.259416   \n",
       "50%      0.592146    0.048434   -0.073135   -0.060795    0.088371    0.004321   \n",
       "75%      1.244611    0.617474    0.308378    0.285328    0.456515    0.396733   \n",
       "max     27.202839    8.361985    5.466230    1.091435    2.208209    2.745261   \n",
       "\n",
       "              V27         V28       Amount  Class  \n",
       "count  492.000000  492.000000   492.000000  492.0  \n",
       "mean     0.170575    0.075667   122.211321    1.0  \n",
       "std      1.376766    0.547291   256.683288    0.0  \n",
       "min     -7.263482   -1.869290     0.000000    1.0  \n",
       "25%     -0.020025   -0.108868     1.000000    1.0  \n",
       "50%      0.394926    0.146344     9.250000    1.0  \n",
       "75%      0.826029    0.381152   105.890000    1.0  \n",
       "max      3.052358    1.779364  2125.870000    1.0  \n",
       "\n",
       "[8 rows x 31 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "group_by_class = df.groupby(\"Class\")\n",
    "df_fraud = group_by_class.get_group(1)\n",
    "df_fraud.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "countを見ると、異常クラスの標本サイズは492個あるようだ  \n",
    "データ全体が284807個あるので、およそ0.2%が異常。  \n",
    "データ全体と比べ、meanは0に近くない。  \n",
    "ホテリングのT2法は標本平均からのズレをマハラノビス距離で評価するものだから  \n",
    "異常クラスの標本平均が標本全体の標本平均と違うことはホテリングのT2法が「全然使えないわけじゃない」ことを予感させる。  \n",
    "ただし、異常クラスのV1のminは標本全体のV1のminより大きい。\n",
    "これはV1の最小値である-5.640751e+01の値を持つ標本は正常クラスに属していることを示している。  \n",
    "V1以外の特徴量を考慮することでこの点は克服できるだろうか？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 訓練"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0.　データ分割  \n",
    "データを訓練用、交差検証用の2つに分割する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_use = df.drop(['Time','Amount'],axis=1)\n",
    "df_train, df_test= train_test_split(df_use, test_size=0.1)\n",
    "target_train = df_train['Class']\n",
    "target_test = df_test['Class']\n",
    "df_train = df_train.drop('Class',axis=1)\n",
    "df_test = df_test.drop('Class',axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 異常度の分布であるカイ2乗分布から異常と判定する閾値を決定する   \n",
    "下記の式にしたがって異常度の閾値を決定する。  \n",
    "$$\n",
    "1-\\alpha = \\int ^{a_{\\mathrm{th}}} _0 dx \\chi ^2 (x|M,1)\n",
    "$$\n",
    "$\\alpha$は誤報率。カイ2乗分布に従う確率変数に対して、どれぐらいの確率で起きそうなことが起きてしまったら異常であるとみなすか決めている。  \n",
    "$a_{\\mathrm{th}}$が異常度の閾値。\n",
    "$M$は自由度。\n",
    "理屈はこうだが、計算しやすいように少し変形する。  \n",
    "カイ二乗分布の累積分布関数は以下のように定義される。  \n",
    "$$\n",
    "X ^2 (x|k,s) =  \\int ^{x} _0 dt \\chi ^2 (t|k,s)\n",
    "$$\n",
    "scipy.stats.chi2で定義されている便利な関数にSurvival functionとその逆関数がある。  \n",
    "Survival functionは$1-X ^2 (x|k,s)$で定義される。  \n",
    "Survival functionの逆関数を$isf(x|k,s)$とすれば、求めるべき$a_{\\mathrm{th}}$は\n",
    "$$\n",
    "a_{\\mathrm{th}} = isf(\\alpha |M,1)\n",
    "$$\n",
    "となる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def a_threshold(prob,degree_of_freedom):\n",
    "    anomality = scipy.stats.chi2.isf(prob, degree_of_freedom)\n",
    "    return anomality\n",
    "\n",
    "def test_a_threshold():\n",
    "    prob = 0.05\n",
    "    a_th = a_threshold(prob,30)\n",
    "    print(a_th)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "テスト用のコードを実行すると異常度の閾値が表示されるので   \n",
    "これを分布表と照らしあわせて正しい値が出ていることを確認できる。  \n",
    "例えば上記の条件だと、異常度の閾値は43.77297182574217になるが  \n",
    "これは　https://www.biwako.shiga-u.ac.jp/sensei/mnaka/ut/chi2disttab.html　を見ても  \n",
    "正しい値が計算できている"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 訓練用データの標本平均、標本共分散行列を計算し、異常度を算出できるようにする"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`TsqDetector`というクラスを定義する。  \n",
    "このクラスはホテリングのT2法を実行するために必要なパラメータをメンバ変数にもち  \n",
    "与えられた`df`に対してホテリングのT2法を実行して異常度と判定結果を返すメソッドを持つ。  \n",
    "\n",
    "実装が正しく行われていることを確認するためのテストのための関数をつけておいた。  \n",
    "「手計算」でホテリングのT2法が実行できる小さなデータセットに対して正しく異常度を計算できるか確認できる。  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "class TsqDetector(object):\n",
    "    def __init__(self,mean,cov,prob,dof):\n",
    "        self.mean = mean\n",
    "        self.cov = cov\n",
    "        self.dof = dof\n",
    "        self.prob = prob\n",
    "        self.threshold = a_threshold(prob,dof)\n",
    "        \n",
    "        \n",
    "    def set_mean(self,df_train):\n",
    "        self.mean = df_train.mean()\n",
    "        \n",
    "    def set_cov(self,df_train):\n",
    "        self.cov = df_train.cov()\n",
    "        \n",
    "    def set_threshold(self,prob):\n",
    "        self.threshold = a_threshold(prob,self.dof)\n",
    "    \n",
    "    def calc_anomality(self,df_test):\n",
    "        #calc anomality for each test data\n",
    "        result = []\n",
    "        metric = self.cov.values\n",
    "        metric = np.linalg.inv(metric)\n",
    "        iter = 0\n",
    "        for index, row in df_test.iterrows():\n",
    "            dist = row - self.mean\n",
    "            dist = np.dot(metric, dist.values.T)\n",
    "            dist = np.dot(row-self.mean,dist)\n",
    "            iter += 1\n",
    "            result.append(dist)\n",
    "            if iter % 1000 == 999:\n",
    "                #print(iter+1,\" th iteration\")\n",
    "                pass\n",
    "        #return list of anomality\n",
    "        return result\n",
    "        \n",
    "    def examine(self,df_test):\n",
    "        #calc anomality\n",
    "        list_anomality = self.calc_anomality(df_test)\n",
    "        \n",
    "        #compare a_th\n",
    "        list_prediction = [0 if anomality < self.threshold else 1 for anomality in list_anomality]\n",
    "\n",
    "        #return result list\n",
    "        return list_anomality, list_prediction \n",
    "    \n",
    "    def re_examine(self,list_anomality,prob):\n",
    "        list_prediction = [0 if anomality < a_threshold(prob,self.dof) else 1 for anomality in list_anomality]\n",
    "        return list_prediction\n",
    "        \n",
    "\n",
    "#debug code\n",
    "def test_TsqDetector():\n",
    "    df_check=pd.DataFrame({'V1':[101,102,130,99,98],'V2':[95,105,70,103,101],'Class':[0,0,1,0,0]})\n",
    "    group_by_class = df_check.groupby(\"Class\")\n",
    "    df_neg = group_by_class.get_group(0)\n",
    "    Detector = TsqDetector(mean=df_neg.drop('Class',axis=1).mean(),cov=df_neg.drop('Class',axis=1).cov(),prob=0.005)\n",
    "    df_check['anomality'], df_check['prediction'] = Detector.examine(df_check)\n",
    "    no0_anomality = (101-100)*((10/3)**(-1))*(101-100) + (95-101)*(18.6666667**(-1))*(95-101)\n",
    "    print(no0_anomality)\n",
    "    print(df_check)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 交差検証用データで推論の妥当性を検証する"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "試しに誤報率を0.2%に設定して分類器を作ってみる。\n",
    "これは標本全体に占める異常クラスの標本数の割合と等しい。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000  th iteration\n",
      "2000  th iteration\n",
      "3000  th iteration\n",
      "4000  th iteration\n",
      "5000  th iteration\n",
      "6000  th iteration\n",
      "7000  th iteration\n"
     ]
    }
   ],
   "source": [
    "Detector = TsqDetector(mean=df_train.mean(),cov=df_train.cov(),prob=0.002,dof=len(df_train.columns))\n",
    "anomality, prediction = Detector.examine(df_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "confusion_matrix(target_test,prediction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "confusion_matrixのindexは(grand truth, prediction)  \n",
    "非対角成分が予測に失敗している標本の数になる  \n",
    "つまり、  \n",
    "左上がTN  \n",
    "右上がFP  \n",
    "左下がFN  \n",
    "右下がTP  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. ROC曲線の作成"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ROC曲線とは、以下の式で定義されるxy平面上の点の集合がなす曲線のことである  \n",
    "$$\n",
    "(x,y) = (1-r_0(\\tau), r_1(\\tau))\n",
    "$$\n",
    "なお、$r_0(\\tau)$、$r_1(\\tau)$はそれぞれ閾値$\\tau$の時の正常標本精度、異常標本精度で、以下の式で定義される  \n",
    "$$\n",
    "r_0(\\tau) = \\frac{TN(\\tau)}{TN(\\tau)+FP(\\tau)} \\\\\n",
    "r_1(\\tau) = \\frac{TP(\\tau)}{TP(\\tau)+FN(\\tau)} \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "Detector = TsqDetector(mean=df_train.mean(),cov=df_train.cov(),prob=0.002,dof=len(df_train.columns))\n",
    "list_anomality = Detector.calc_anomality(df_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "def make_ROC_curve(tau_list, list_anomality, Detector):\n",
    "    x = np.array([1])\n",
    "    y = np.array([1])\n",
    "    CMs = np.array([])\n",
    "    \n",
    "    for tau in tau_list:\n",
    "        prediction = Detector.re_examine(list_anomality, tau)\n",
    "        CM = confusion_matrix(target_test,prediction)\n",
    "        r0 = CM[0][0]/(CM[0][0]+CM[0][1])\n",
    "        r1 = CM[1][1]/(CM[1][0]+CM[1][1])\n",
    "        x=np.append(x,1-r0)\n",
    "        y=np.append(y,r1)\n",
    "        CMs=np.append(CMs,CM)\n",
    "        \n",
    "    x=np.append(x,0)\n",
    "    y=np.append(y,0)    \n",
    "    \n",
    "    plt.plot(x,y,marker='.')\n",
    "    plt.xlim(0,1)\n",
    "    plt.ylim(0,1)\n",
    "    plt.title(\"ROC curve\")\n",
    "    plt.xlabel(\"false positive rate\")\n",
    "    plt.ylabel(\"recall\")\n",
    "    plt.show()\n",
    "    \n",
    "    return x,y,CMs\n",
    "\n",
    "tau_list = [0.99,0.5,0.3,0.1,0.03,0.01,0.001,0.0001]\n",
    "x,y,CMs=make_ROC_curve(tau_list, list_anomality, Detector)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ROC曲線が得られたので、AUCを計算してみる。  \n",
    "AUCはROC曲線の下部面積で定義される。  \n",
    "ROC曲線は区分的に直線だと近似して台形公式で面積を求める。  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AUC= 0.943841317690511\n"
     ]
    }
   ],
   "source": [
    "def AUC_calc(x,y):\n",
    "    #make sure input x, y are sorted\n",
    "    curve=np.vstack([x,y])\n",
    "    curve=curve[:,np.argsort(curve[0])]\n",
    "    \n",
    "    area = 0\n",
    "    for i in range(len(x)-1):\n",
    "        area += 1/2*(curve[0][i+1]-curve[0][i])*(curve[1][i]+curve[1][i+1])\n",
    "    return area\n",
    "\n",
    "print(\"AUC=\",AUC_calc(x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "top kernelのAUCが0.95なのでかなり良く出来ているのでしょう。  \n",
    "https://www.kaggle.com/joparga3/in-depth-skewed-data-classif-93-recall-acc-now  \n",
    "でもなーFPがTPの10倍出てるわけで、この分類器使うと鬱陶しいかもしれない。\n",
    "詐欺検出なんだから、疑わしきは調査というスタンスならこういう運用もあり。  \n",
    "実用上は調査にかかるコストと検出漏れの際の損失を天秤にかけてバランスとるんでしょう。  \n",
    "つまり、1回あたりの調査コストを$f$、1回あたりの検出漏れ損失額を$g$として\n",
    "$$\n",
    "argmin_{\\tau}\\left[ \\frac{FP(\\tau)+TP(\\tau)}{TP(\\tau)+TN(\\tau)+FP(\\tau)+FN(\\tau)}f+\\frac{FN(\\tau)}{TP(\\tau)+TN(\\tau)+FP(\\tau)+FN(\\tau)}g \\right]\n",
    "$$\n",
    "を満たす$\\tau$を取ってくればいいでしょう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 異常度のヒストグラム"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "交差検証用のデータセットについて異常度が計算できたので、異常度の分布を調べてみましょう。  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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": [
    "hist_max=100\n",
    "\n",
    "df_result = pd.DataFrame({'Grand truth':target_test,\"Anomality\":list_anomality})\n",
    "df_result.plot(kind='hist', y=\"Anomality\" , bins=int(np.sqrt(len(df_result))), \n",
    "               range=(0,hist_max), density=True)\n",
    "\n",
    "chi2_x = range(0,hist_max,1)\n",
    "chi2_y = [scipy.stats.chi2.pdf(x=x,df=28) for x in chi2_x] \n",
    "plt.plot(chi2_x,chi2_y,label=\"chi2 dof=28\")\n",
    "\n",
    "chi2_x = range(0,hist_max,1)\n",
    "chi2_y = [scipy.stats.chi2.pdf(x=x,df=15) for x in chi2_x] \n",
    "plt.plot(chi2_x,chi2_y,label=\"chi2 dof=15\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "交差検証用データの異常度の分布はこんな感じ。\n",
    "カイ二乗分布に従う想定をしたので、カイ二乗分布を同時にプロットした。  \n",
    "自由度28のカイ二乗分布から想定されるヒストグラムよりかなりピークが左にずれてしまっている。  \n",
    "書籍によれば、データの有効次元が理論的に想定される値よりかなり小さくなるのはよくあることらしい。  \n",
    "実際、このデータに対して例えば自由度15のカイ二乗分布をあてはめてみると、多少マシになる（それでもぴったりは合わないが・・・）  \n",
    "最適なパラメータの計算方法は書籍7.4章を参照のこと（そのうち実装するかも）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "次に異常クラスの分布を見る。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f7558776860>"
      ]
     },
     "execution_count": 95,
     "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "df_result_groupby = df_result.groupby(\"Grand truth\")\n",
    "df_result_fraud = df_result_groupby.get_group(1)\n",
    "df_result_fraud.plot(kind='hist', y=\"Anomality\" , bins=int(np.sqrt(len(df_result_fraud))),\n",
    "                     density=True, title=\"histgram of anomalies\")\n",
    "                     \n",
    "df_result_fraud.plot(kind='hist', y=\"Anomality\" , bins=int(np.sqrt(len(df_result_fraud))),\n",
    "                     density=True, title=\"zoom up of histgram of anomalies\", range=(0,100))\n",
    "\n",
    "df_result_fraud.plot(kind='hist', y=\"Anomality\" , bins=5000, \n",
    "               cumulative=True,histtype='step',density=True, title=\"cumulative ratio\")\n",
    "\n",
    "df_result_fraud.plot(kind='hist', y=\"Anomality\" , bins=5000, \n",
    "               cumulative=True,histtype='step',density=True,range=(0,100),title=\"zoom up of cumulative ratio\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "この累積分布に対して1つ異常度の閾値を決めると、その点より右側は検出できる異常、左側は検出できない異常になります。\n",
    "大きな異常度のところにある程度集まっているのは想定通りですね。  \n",
    "  \n",
    "  \n",
    "ROC曲線の平坦な部分は累積分布の20あたりから70あたりの平坦な部分に閾値が来た時に対応していますね。  \n",
    "`a_threshold(10e-4,29)`は58ぐらいなので、精度を落とさずにもう少し閾値を上げられるように思いますが  \n",
    "安直に実行するのはこのデータセットだけに過学習する行為です。  \n",
    "もし試すなら、検証用データを何度も取り替えてこの平坦な領域が出てくるか確認すべきでしょう。  \n",
    "\n",
    "閾値を20以下にするとすべての異常を拾えますが、FPの割合が増えてしまいます。  \n",
    "これがこのモデルの実力です。  \n",
    "もしFPを増やさずに異常を拾う割合を増やしたければ、モデル自体を変更する必要があるでしょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "58.30117348979492"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_threshold(10e-4,29)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 考察"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・`df_train`からモデルを作る際、正常クラスに属するデータが圧倒的に多いことが必要だった。\n",
    "モデルを作る際は正常クラスを表すモデルを作ればいいので、正常クラスのみを使ってモデルを作ると予測精度が上がると思われる。  \n",
    "  \n",
    "・こんなシンプルなモデルでもそれなりにいい成績が出る。PCAが偉大なんだと思う。　　  \n",
    "\n",
    "・変数間の相関を無視して、各変数は統計的に独立だとすると精度がわるくなるだろうか？  \n",
    "試しに計算してみる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`TsqDetector`を継承して`SimpleTsqDetector`クラスを定義する。  \n",
    "ほとんど親クラスと同じだが、異常度の計算の実装が異なっている。  \n",
    "マハラノビス距離の計算の前に共分散行列の非対角項を落としている。  \n",
    "（ここ、多分`df.var()`で最初から分散のベクトル持ってきた方が計算速いと思う）  \n",
    "`ROC_curve_simple`も`SimpleTsqDetector`を呼び出すように別の関数を定義　　\n",
    "`ROC_curve_simple`の柔軟性、低いなあ・・・。\n",
    "\n",
    "追記：曲線のデータ作成機能と異常度の計算機能を分離できることに気づいたので、同じ`make_ROC_curve`を使えるようになりました"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AUC= 0.9395565768488205\n"
     ]
    }
   ],
   "source": [
    "a=np.array([[1,2],[3,4]])\n",
    "np.diag(np.diag(a))\n",
    "\n",
    "class SimpleTsqDetector(TsqDetector):\n",
    "    def __init__(self,mean,cov,prob,dof):\n",
    "        super().__init__(mean,cov,prob,dof)\n",
    "    \n",
    "    def calc_anomality(self,df_test):\n",
    "        #calc anomality for each test data\n",
    "        result = []\n",
    "        metric = self.cov.values\n",
    "        metric = np.diag(np.diag(metric))\n",
    "        metric = np.linalg.inv(metric)\n",
    "        iter = 0\n",
    "        for index, row in df_test.iterrows():\n",
    "            dist = row - self.mean\n",
    "            dist = np.dot(metric, dist.values)\n",
    "            dist = np.dot(row-self.mean,dist)\n",
    "            iter += 1\n",
    "            result.append(dist)\n",
    "            if iter % 1000 == 999:\n",
    "                #print(iter+1,\" th iteration\")\n",
    "                pass\n",
    "        #return list of anomality\n",
    "        return result\n",
    "\n",
    "tau_list = [0.99,0.5,0.3,0.1,0.03,0.01,0.001]\n",
    "Detector = SimpleTsqDetector(mean=df_train.mean(),cov=df_train.cov(),\n",
    "                                     prob=tau_list[0],dof=len(df_train.columns))\n",
    "list_anomality = Detector.calc_anomality(df_test)\n",
    "x,y,CMs=make_ROC_curve(tau_list,list_anomality, Detector)\n",
    "print(\"AUC=\",AUC_calc(x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "AUCはほとんど変わらず。  \n",
    "PCAは偉大である。  \n",
    "この手の異常検知タスクはまずPCAをしてホテリングのT2法できないか考えてみようと思えました。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 参考文献\n",
    "\n",
    "異常検知と変化検知（井手 剛、杉山 将　 講談社）  \n",
    "https://www.amazon.co.jp/%E7%95%B0%E5%B8%B8%E6%A4%9C%E7%9F%A5%E3%81%A8%E5%A4%89%E5%8C%96%E6%A4%9C%E7%9F%A5-%E6%A9%9F%E6%A2%B0%E5%AD%A6%E7%BF%92%E3%83%97%E3%83%AD%E3%83%95%E3%82%A7%E3%83%83%E3%82%B7%E3%83%A7%E3%83%8A%E3%83%AB%E3%82%B7%E3%83%AA%E3%83%BC%E3%82%BA-%E4%BA%95%E6%89%8B-%E5%89%9B/dp/4061529080"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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