Component_AI_Visualization_3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "from matplotlib import pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "matplotlib.style.use('ggplot')\n",
    "import pandas as pd\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "from matplotlib import cm as cm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Boolean functions of 3 variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bitfield(n):\n",
    "    return [int(digit) for digit in bin(n)[2:]] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "functions = []\n",
    "for i in range(0, 256):\n",
    "    part = bitfield(i)\n",
    "    temp = ([0]*(8-len(part)))\n",
    "    temp.extend(part)\n",
    "    functions.append(temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(r'all_functions_3.txt', 'w') as out:\n",
    "    for f in functions:\n",
    "        print(f, file=out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Functions with maximum component algebraic immunity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "path_vectorial = r'AIcomp2_n3.txt'\n",
    "vectorial = []\n",
    "with open(path_vectorial, 'r') as f:\n",
    "    for line in f.readlines():\n",
    "        func = ast.literal_eval(line.rstrip())\n",
    "        vectorial.append(func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 0, 1, 0, 1, 1, 0, 1],\n",
       " [0, 0, 1, 1, 1, 0, 0, 1],\n",
       " [0, 1, 0, 0, 1, 0, 1, 1],\n",
       " [0, 1, 0, 1, 1, 0, 0, 1],\n",
       " [0, 1, 1, 0, 0, 0, 1, 1],\n",
       " [0, 1, 1, 0, 0, 1, 0, 1],\n",
       " [1, 0, 0, 1, 1, 0, 1, 0],\n",
       " [1, 0, 0, 1, 1, 1, 0, 0],\n",
       " [1, 0, 1, 0, 0, 1, 1, 0],\n",
       " [1, 0, 1, 1, 0, 1, 0, 0],\n",
       " [1, 1, 0, 0, 0, 1, 1, 0],\n",
       " [1, 1, 0, 1, 0, 0, 1, 0]]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vectorial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "   0  1  2  3  4  5  6  7\n",
       "0  0  0  0  0  0  0  0  0\n",
       "1  0  0  0  0  0  0  0  1\n",
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     "execution_count": 8,
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   ],
   "source": [
    "df_all = pd.DataFrame(data=functions)\n",
    "df_all.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>1</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <th>7</th>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <th>8</th>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "      <th>9</th>\n",
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       "    0  1  2  3  4  5  6  7\n",
       "0   0  0  1  0  1  1  0  1\n",
       "1   0  0  1  1  1  0  0  1\n",
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       "3   0  1  0  1  1  0  0  1\n",
       "4   0  1  1  0  0  0  1  1\n",
       "5   0  1  1  0  0  1  0  1\n",
       "6   1  0  0  1  1  0  1  0\n",
       "7   1  0  0  1  1  1  0  0\n",
       "8   1  0  1  0  0  1  1  0\n",
       "9   1  0  1  1  0  1  0  0\n",
       "10  1  1  0  0  0  1  1  0\n",
       "11  1  1  0  1  0  0  1  0"
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     "execution_count": 9,
     "metadata": {},
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   ],
   "source": [
    "df_vectorial = pd.DataFrame(data=vectorial)\n",
    "df_vectorial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Add class labels\n",
    "\n",
    "1 - with maximum component algebraic immunity\n",
    "\n",
    "0 - else"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_all['class'] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i, row in df_vectorial.iterrows():\n",
    "    for j, row1 in df_all.iterrows():\n",
    "        ok = True\n",
    "        for k in range(0, 8):\n",
    "            if row[k] != row1[k]:\n",
    "                ok = False\n",
    "                break\n",
    "        if ok:\n",
    "            df_all.loc[j, 'class'] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "      <th>99</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>154</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>166</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <th>198</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>210</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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      "text/plain": [
       "     0  1  2  3  4  5  6  7  class\n",
       "45   0  0  1  0  1  1  0  1      1\n",
       "57   0  0  1  1  1  0  0  1      1\n",
       "75   0  1  0  0  1  0  1  1      1\n",
       "89   0  1  0  1  1  0  0  1      1\n",
       "99   0  1  1  0  0  0  1  1      1\n",
       "101  0  1  1  0  0  1  0  1      1\n",
       "154  1  0  0  1  1  0  1  0      1\n",
       "156  1  0  0  1  1  1  0  0      1\n",
       "166  1  0  1  0  0  1  1  0      1\n",
       "180  1  0  1  1  0  1  0  0      1\n",
       "198  1  1  0  0  0  1  1  0      1\n",
       "210  1  1  0  1  0  0  1  0      1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_all[df_all['class'] == 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dimensional visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_3d(func_all, func_vector):\n",
    "    fig = plt.figure(figsize=(7, 7))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "    for f in func_all:\n",
    "        if f in func_vector:\n",
    "            ax.scatter(f[0], f[1], f[2], c='r')\n",
    "        else:\n",
    "            ax.scatter(f[0], f[1], f[2], c='b')\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_2d(func_all, func_vector):\n",
    "    fig = plt.figure(figsize=(7, 7))\n",
    "    ax = fig.add_subplot(111)\n",
    "\n",
    "    for f in func_all:\n",
    "        if f in func_vector:\n",
    "            ax.scatter(f[0], f[1], c='r')\n",
    "        else:\n",
    "            ax.scatter(f[0], f[1], c='b')\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_1d(func_all, func_vector):\n",
    "    fig = plt.figure(figsize=(10, 5))\n",
    "    ax = fig.add_subplot(111)\n",
    "\n",
    "    for f in func_all:\n",
    "        if f in func_vector:\n",
    "            ax.scatter(f[0], 1, c='r')\n",
    "        else:\n",
    "            ax.scatter(f[0], 1, c='b')\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "columns_to_fit = [i for i in range(0, 8)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = PCA(n_components=3)\n",
    "model.fit(df_all[columns_to_fit])\n",
    "functions_transformed_3 = model.transform(df_all[columns_to_fit])\n",
    "vectorial_transformed_3 = model.transform(df_vectorial[columns_to_fit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_3d(functions_transformed_3, vectorial_transformed_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualization of the only first half of target functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_3d(functions_transformed_3, vectorial_transformed_3[:6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = PCA(n_components=2)\n",
    "model.fit(df_all[columns_to_fit])\n",
    "functions_transformed_2 = model.transform(df_all[columns_to_fit])\n",
    "vectorial_transformed_2 = model.transform(df_vectorial[columns_to_fit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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B789mBDcjmHqNMGE7qv+2PqhX6LlNx+JqCJEt2GGp96cQBNo/P//SOHEhCCIvA8HNEKZeo1fYTuuvzD+rR088ZaIhRLZgh5Xen844cWF5WVO1mgrLy63HEQc4ghtgWGen9Y25OW0Ui6rPzmp1cVGvuueoiYaQpWwh66z0/oSNE+caDc0sLERaDmZLAsbVy2U1zp7V6upq3EXZolpd2zRDT2KsOE4WbkVk5Y7cZG4Ads1KtgA7rNyRm8wNwEgsZAuwY61a3bQ2U4rnjtxkbgCAsemME9dnZzeNE0d9R24yNwDAWFm4IzeZGyRt3mXi8OE8i3ABJBrBDVt2mTh3bopdJiCJrbWQXAQ3sMsEQrG1FpKM4BYhC1vShGGXCYSh0YMkI7hFxMqWNGHYZSK5JtlgotGDJCO4RcTKljRhrOxJl0WjjGlNusFEowdJRnCLiJUtacL07jIxN7fBLhMRGHVMa9INJho9ycVEIIJbZKxsSdNP9x0Jzp5tENgiMOqY1qQbTGytlUxMBGohuEUk7NYlcWxJAztGHdOKosHEbZiSh4lALQS3iFjZkgZ2jDqm9Rf3ndTb9bjeqC/rDn1GP9QcDSYwEaiN7bciZGFLGtgxyu1igqCgyok3q6Er3/slvVmPPvCUXlU+OpHyIhmKxXXValvzlqxNBCJzA2IyyphWWNfT3+tavevh10+quEiAICjo8uWcJCYCkbkBMdrt7WLoekKvzkSSzY2epkqldT300MXMjZeSuQEJxBo09ArL5qWc9uxpZi6wSQQ3M1iXgmGwBg29yOY3I7gZwLoUhNnuNkSsQUMvsvnNCG4GsC4FvQa5DRFr0NCNbH6zzAQ3y91+dCegFw0eDItsfrNMzJbsnUVUq7VawVbeeNaloFcSGjxBUNDCwoxqtWkVi+uqVtdM/D1l2W5n36ZRJjI3661guhPiYzWjtz5+wjgx+rHyN5WJ4Ga9FUx3Qjwsf0Bbb/BYbzAiHpb+pjIR3Ky3giUmB8TB8gd0p8FTKjWUyzWVyzW1b5+d69V6gxHxsPQ3lYngZr0VjHgk4QN6bW1azWZOzWZOKyt5M5llEhqMiJ6lv6lMBDe6/RDG+ge0pVZwLxqM8bIyrtXL0t9UJoKbRLcftrL+AW2pFdyLBmN8LI1r9bL0N5WZ4Ab0sv4BbakVHIYGYzwsZ/SW/qYysc4N6MfyuqBR7veG9LKc0Ut2/qbI3ACjulvBe/c2+7aCrY6/YDKsZ/RWENwAwzqt4AsX6qFdf5bHXzAZg4xr0eAZU7ekc+6tkqqSpiU94r1/sOf5l0n6tKRfkfRjSRXv/Y/G8dpAlm03/mKhawjj18no+219Zn27waiMnLk556YlfVzScUlHJb3TOXe057R7JF303v+SpI9J+vCorwvA/vgLJmO7yTyWJ5xEaRzdkjdLetp7/wPv/c8lPSbptp5zbpP0qfbXj0t6s3Ou95axqUUXASaF8Rf0osHTMo7gdp2kZ7oeL7ePhZ7jvW9IuiTpmjG8tnmMiaCfcTR6LK0rgg00eFrGMeYWloE1d3GOnHP3SbpPkrz3KpVKo5cuQvl8fkuZ778/H9pFcP/91+js2UaUxRtYWD2SyHI9Tp+WKpXClnGRU6fqOnZs6/n96nLLLdKpU3Xde29ea2s5zcw09cgjDR07tnfSVdgVy+/JMCzX4+TJpo4fb25ZQnLyZDO0zJbrMopxBLdlSdd3PZ6VdL7POcvOubykvZJe6P1B3vuHJT3cfthcXV0dQ/GiUyqV1FvmixcPhp578aK2nGtFWD2SyHI97r57f2ij5+67c6ETQbary9Gj0l/+5eZjRqtt+j0ZhuV6HD0qLS5uvdfe0aP10OvCcl3CHDp0aKDzxhHcvinpRufcDZKelXS7pF/vOecJSXdK+oakd0j6ivd+S+aWRtyIFGEYF8EkWVlIHaeRx9zaY2jvkfQFSWdah/xTzrkTzrlb26c9Kuka59zTku6X9P5RXzcpBh0TYdJJtjAuAkxWrtk0m0A1z5/v7d20rV96HwRbuwi6p+72rkuRWgEwrnUpSeum6MdyPYZ9zy3XZRjUw56k1aXdLbnjbHt2KInAThvMsi4lewbdYLaT0R84UCCjB4bAxskGMP6STTuNi/Rmd5cuFTK50wSwG5nK3KyOazH+gjDWM3qrf0+AlKHgZnkxNQtx42P5A9pyRm/57wmQMhTcLLeCLd3gL0usf0Bbzugt/z0hXlYajJkJbpZbwRJ3NY6D9Q9oyxm99b8nxMNSgzEzwc1yKxjxsP4BXS7X9cADa5qe3pDU1PT0hh54YM1Ew4e/J4Sx1GDMTHCz3ApGPKx/QAdBQSdOzGh9fUpSTuvrUzpxYsZEtyl/T/Gy0vXXy1KDMTPBjXEt9LL+AW2pFdyLv6f4WOr662WpwZipdW7st4ZuO93ROG6WWsFh+HuKh+W7r1era6E778TRYMxM5maB1a6ELLM8kcdSKxh2WG70WMroM5W5xal3t4nO/bvoykE/llrBsMP6nUasZPRkbhGxPH6CePXL6LtbwXv3NhnXgiT7Y8VWENwiYrkrAfHZaXJApxV84ULdXLcp4mGp688yuiUjYr0rAfGwPDkAdlnp+rOMzC0CQVDQ5cs5SXQlYDMyemAyCG4T1ul2WlnJ68r99ZoqlRp0JWCkGZHMvgX6I7hNWFi3k5TTnj1NAlvGFYJA37p8VF/Xa/QZ3aE5/VDSYBm95YW8gAUEtwmj2wlhCkGgUqWia1ae1mv1Dd2hz+rrep1eX/r2QBk9s2/RTyEItH9+XgePHNH++XkVgiDuIsWC4DZhLMRFmJmFBeUajU3HZvWsvrjnloEyehpNCNNpNBWWlzVVq6mwvNx6nMEAR3CbMNakJNukxrWma7Whjvei0YQwYY2mXKOhmYWFmEoUH4LbhLEmJbkmOa61XiwOdbwXjaZ4nT4tk5N5Rm00pQnBLQKW9y9Ef5Mc11qrVtXMb15m2szntVatDvT9NJriEwQFHT9eMDmZZ9RGU5oQ3IA+JjmuVS+Xtbq4qPrsrDaKRdVnZ1uPy+WBfwaNpnhYnswzaqMpTdihBOhj0rvK1MtlrSwtjeVnITqWJ/N0Gk0zCwuartW0XixqrVodqtGUFgQ3oA925UcY61vp0WhqoVsS6INxLYRhMk8ykLkB22CDWvQql+s6daquu+/OmbyDO1oIbgAwpGPHRKPHuEx0S7IdDQBkS+qDG9vRAED2pD64sR0N+uGWMUB6pT64sR0NwnDLGCDdUh/crG1HQ7Zgg+VdJjq6x4rzhw/TlQ4MIfXBzdJ2NGQLdljeZULaOlY8de4cY8XAEFIf3Maxh9+4JCFbyApLt4wJy+YZK0YYen4Gl4l1bla2o7GeLWSJla21Otl8pxy12pQqlZIuXvUzhX1sMVacXf2uFXbNCZf6zM0SS9lC1lnZWqtfNr90+abQ87N46xK00PMznExkblZYyRbQYmFrrX5Z+29e9Xv6q/pNm7oms3rrErTQ8zMcMrcIWckWYEe/rH3lmsObxoo35ua2jBUz/pIt9PwMh+AWMW4wiW7b7TDfGSt+/swZNc6e3RLYmHmbLYPejYBGTwvBDYjRbrN5xl+yZ5BrhUbPFYy5AdsIgoIWFmYmemuT3Yz9Mf6STTtdK9s1euIeX44amRvQh+VWMOMvCEOj5wqCG9CH5a4/7gYdr9OnZXJci0bPFQQ3oA/LrWBm3sYnCAo6frxgMqOn0XMFY25AH8Xiumq1re0/K61gC+v0ssjyuFan0TPpceIkyFTmxh25MQxawQhjOaOXWG7UkZngxh250U+/dUF0/SEM41rJkJngxi7rCLPTjEhawehFRp8MmQlu3JEbYSzPiIRN5XJdp07VyeiNy8yEkvViUVMhgYxd1rPN+viJ1Mou778/r4sXD2Z6goAlx44p9skj2F4mMrcgKOjo5W/pNfq67tBn9EPNSWKXddgfP+l0m547N2Vu2jlgWeqDW+fD4emVa/QNvVaf1R16nb6ub5deH9sduWFDEBR0+XJOkt3xE7pNEYbNkXeW+uAW9uHwrGZ1y54vEtgyrNPoWVnJS+pcH02VSg1T4ydJ6DZFtCxvC2dJ6oMbHw4IE9bokXLas6dpJrBJ9rtNET2y+cGkPrjx4YAwSWj0JKHbFNFLwrVrQeqDG2tSEMZ6oycp3aaI3lVXbYQet3LtWpH64MYuEwhjvdGTlG5TRCsICnrhha0ZWi5n59q1IhPr3NhgFr2sbzBL1xPCLCzMaGOjt9EjlUrrZq5dKzIR3CyI4o7OGI7lRo/1OxIgHv0aN5cvp74Tbmj8RiLA1F0My3q3KeJhfazYEoJbBJi6i34GvSPB3NwGY8Wg0TMEglsEGD9BmGHuSHD2bIPABibIDYExtwgwfoIwlu/oDLssjxVbQuYWAboSEIaMHpgcglsE6EpAGCYHAJNDt2RE6EpAr2p1TZVKaVPXJBk9MB5kbkBMyOiByclc5sZialhCRg9MxkjBzTn3ckmLkl4p6UeSnPf+Ysh565K+0374d977W0d53d3qTL3udAPValOqVEq0lhGKhhCQXKN2S75f0pe99zdK+nL7cZifeu9vav+LJbBJLKZGuLCF1OwqgzCda+XAgQJ3wDZu1G7J2yS9of31pyR9TdL7RvyZE8PUa/Tql83v27fOGjRs0nutXLpUoOfHsFEzt1d475+TpPb/B/qct8c596RzLnDOvW3E19w1pl6jV79sfnXVTkMoCAo6fDi/ZYsuRIuen2TZMXNzzn1J0sGQpz4wxOv8gvf+vHPuFyV9xTn3He/990Ne6z5J90mS916lUmmIl9jZyZNNHT/e3DL1+uTJ5lheK5/Pj73McchSPV58cbjOi337FOnv5vRpqVIpbMksT52q69ixyIoxNkm+tvpdKy++mNw6Scl+T7aTazabO5/Vh3Pu/0l6g/f+OefctZK+5r3/5R2+55OS/qf3/vEdfnzz/Pnzuy5bP5OcJFAqlbS6ujqWnxWnLNVjfn6/lpe3ZkKlUkNra9NbGkJRd0H1K9/sbDJnWSb52rL2Xozrsyxp78mhQ4ekK7en72vUbsknJN3Z/vpOSZ/vPcE5t88597L21yVJr5X03RFfd9e6N6NdWlqhrzzj+m2N9tBDF02sQWOc2A5L2+gx4Wlnowa3ByW9xTn3PUlvaT+Wc+7VzrlH2ucckfSkc+7bkr4q6UHvfWzBDei23UJqCw0hxont6L5W9u5txrronvG/nY3ULTlhE+mWnKSkpff9UA87emfoSfF0j45LGt4TKf56HDlysM+dRjZ05szzQ/2suOsyrKi6JQFMUCdbmJvbYIsuvISMfmeZ234LSJpyua6zZxuJal1jsth0e2dkbgCQMGy6vTMyNwBIIDbd3h6ZW0TC9i8EAEwGwS0CrEkBgGgR3CLAmhT0Q0YPTAbBLQLsMoEwZPTA5BDcIsCalGSbVHZFRg9MDsEtApb2pMNwJpldkdEDk0NwiwBrUpJrktkVGX2yMV5qG+vcIsKalGSaZHbFLhPJ1brP3tY7uNNotYPMDdjGJLMrMvrkuvfePOOlxpG5AX0EQUGXL+ckNdW9Cfk4sysy+mRaWwvflJ7xUjvI3IAQnYkkKyt5XQlsTZVKDbIraGYm/FZhjJfaQXADQoRNJJFy2rOnSWDLuCAo6Gc/k1oZ/RWMl9pCtyQQgmn6CBN289hWRr+uhx66SMPHEDI3IATT9BGGjD45MhPcWJOCYbDwHmHI6JMjE8GNPfzQT79GD9P0EYaMPjkyEdzYww9hdmr0dKbpnznzvJaWVghsIKNPkEwEN7oSEIZGD4bVyejn5jbI6I3LxGzJYnFdtdrWOE5XQrZZb/QEQUELCzOq1aa1b5/00Y8W+BA1oFyu6+zZhlZXV+MuCraRicyNrgSEsTx+0ttleu7cFOPEwBAyEdyYHIAwlhs9dJmin0IQaP/8vA4eOaL98/MqBEHcRTIpE92SEnv4YatOo6fT9VcsrqtaXTPR6LHeZYp4FIJApUpFuUZDkjRVq6lUqWh1cVH1cjnm0tmSmeAGhLHa6GGcGGFmFhZeCmwduUZDMwsLWllaiqlUNmWiWxJIGstdpojPdK021PEsI7gBBvWOE8/NbTBODK0Xi0MdzzK6JQF3QSj9AAALFElEQVSjurtMS6WSVlcJbFm3Vq1uGnOTpGY+r7VqNcZS2UTmBgAJUS+XW5NHZme1USyqPjvLZJI+yNyAHXQvprY0oxLZVC+XmTwyADI3YBtsug0kE8EN2AaLqdEPt9GyjeAGbIPF1Ahz+rTI6I0juAHbsLz/JOJz7715MnrjCG7ANlhMjTBra7nQ42T0dhDcgG2w6TbCzMw0Q4+T0dvBUgBgB1b3n0R8HnmkoePHC5u6JsnobSFzA4AhHTsmMnrjMpO5sRAXwDiR0duWicyNhbgAkC2ZCG4sxEU/LMQF0ikTwY2FuAhDRg+kVyaCGwtxESYJGX0nszxwoEBmCQwhE8GNhbgIYz2j784sL13KkVkCQ8hEcGMhLsJYz+iTkFkieowTDyYzSwGYtote1eqaKpWS2YW41jNLRK+TzXeu2VptSpVKicZ6iExkbkAY6xm99cwS0SObH1xmMjcgjOWM3npmieiRzQ+OzA0wqjuz3Lu3aS6zRPTI5gdHcAMM62SWFy60/iewZRszvwdHcAOAhLA+TmwJY24AkCCWx4ktIXMDAKQOwQ0AkDoENwBA6hDcAACpQ3ADtsE+fkAyEdyAPrjfG5BcBDegD/bxQ5ggKOjw4TzZvHEEN6AP9vFDr042f+7cFNm8cQQ3oA/28UMvsvnkILgBfbCPH3qRzScHwQ3og3380ItsPjnYWxLYBvv4oRv32EsOMjcAGFAnm5+b2yCbN47MDQCGUC7XdfZsQ6urq3EXBdsgcwMApA7BDQCQOgQ3AEDqjDTm5pz7t5L+k6Qjkm723j/Z57y3SqpKmpb0iPf+wVFeFwCA7Yyauf2tpH8j6XS/E5xz05I+Lum4pKOS3umcOzri6wIA0NdImZv3/owkOee2O+1mSU9773/QPvcxSbdJ+u4orw0AQD9RLAW4TtIzXY+XJc2Hneicu0/SfZLkvVepVJp86cYon88nrsxhqIc9aakL9bAnTXXptmNwc859SdLBkKc+4L3//ACvkQs51gw5Ju/9w5Ie7pyTtHUkpVIpFWtfqIc9aakL9bAnaXU5dOjQQOftGNy89786YlmWJV3f9XhW0vkRfyYAAH1F0S35TUk3OudukPSspNsl/XoErwsAyKiRZks65/61c25Z0r+Q9GfOuS+0jx9yzv25JHnvG5LeI+kLks60DvmnRis2AAD95ZrN0OEvC5rnzyer9zJpfdf9UA970lIX6mFP0urSHnMLm8uxCTuUAABSh+AGbCMICpqf368jRw5qfn6/gqAQd5EADIDgBvQRBAVVKiUtLxdUq01pebn1mAAH2EdwA/pYWJjZdMdlSWo0clpYmImpRLDi9GmR0RtHcAP6qNWmhzqObAiCgo4fL5DRG0dwA/ooFteHOo5sIKNPBoIb0Ee1uqZ8fvNSmXy+qWp1LaYSwQIy+mQguAF9lMt1LS6uana2rmJxQ7Ozrcflcj3uoiFGZPTJEMX2W0Bilct1LS2txF0MGFKtrqlSKW3qmiSjt4fMDQCGUC7XdepUnYzeODI3ABjSsWMiozeOzA0AkDoENwBA6hDcAACpQ3ADAKQOwQ0AkDoENwBA6hDcAACpQ3ADAKQOwQ0AkDoENwBA6hDcAACpQ3ADAKQOwQ0AkDoENwBA6hDcAACpk2s2m3GXoR+zBQMAxCq30wmWM7dc0v455/4q7jJQj/TVI011oR72/iW0LjuyHNwAANgVghsAIHUIbuP1cNwFGBPqYU9a6kI97ElTXV5ieUIJAAC7QuYGAEidfNwFSBrn3MslLUp6paQfSXLe+4s957xR0se6Dv1jSbd77/+Hc+6Tkl4v6VL7ubu899+acLG3GKQe7fPWJX2n/fDvvPe3to/fIOkxSS+X9NeS/p33/ueTL/mW8g3yftwk6Q8kFSWtS/pd7/1i+7lPKsb3wzn3VklVSdOSHvHeP9jz/MskfVrSr0j6saSK9/5H7ed+S9I9atXpvd77L0RV7jAD1OV+SfdKakhakfQfvPfn2s+FXmdxGKAed0n6iKRn24d+33v/SPu5OyV9sH38d7z3n4qk0CEGqMfHJL2x/fAfSjrgvZ9pP2fm/dgtMrfhvV/Sl733N0r6cvvxJt77r3rvb/Le3yTpTZJ+Iukvuk75zc7zcQS2th3r0fbTrrJ2X+AflvSx9vdfVOtDNg6D1OMnkv699/6fSHqrpN9zzs10PR/L++Gcm5b0cUnHJR2V9E7n3NGe0+6RdNF7/0tqNZg+3P7eo5Jul9Sp039t/7xYDFiXv5H0au/9P5f0uKT/3PVcv+ssUgPWQ5IWu8rbCWwvl/QhSfOSbpb0IefcvoiKvskg9fDe/0bX59R/kfTfu5428X6MguA2vNskdVpjn5L0th3Of4ekU977n0y0VMMbth4vcc7l1Araj+/m+8dsx3p4789677/X/vq8pAuS9kdWwv5ulvS09/4H7az3MbXq0627fo9LenP793+bpMe895e99z+U9HT758Vlx7q0G32dv4NA0mzEZRzEIO9JP/9S0he99y+0ew++qFbDIw7D1uOdkj4XSckiQnAb3iu8989JUvv/Azucf7u2XjS/65z7v865j7W7neIwaD32OOeedM4FzrlO4LhG0pr3vtF+vCzpuskWt6+h3g/n3M2SrpL0/a7Dcb0f10l6putx2O/xpXPav+9Lav3+B/neKA1bnnsknep6HHadxWHQery9fc087py7fsjvjcLAZXHOzUm6QdJXug5beT92jTG3EM65L0k6GPLUB4b8OddK+meSusdCfkvS82p9wD4s6X2STuyupDu+/jjq8Qve+/POuV+U9BXn3Hck1ULOm9i02zG/H5+RdKf3fqN9OLL3I0TYTgu9v8d+5wzyvVEauDzOuTskvVqtsc6OLdeZ9/77Yd8/YYPU408lfc57f9k59y61Mus3Dfi9URmmLLdLetx7v951zMr7sWsEtxDe+1/t95xz7u+dc9d6759rf1he2OZHOUl/4r2vd/3s59pfXnbOnZT0H8dS6BDjqEe7G0/e+x84574m6VWS/pukGedcvp1NzEo6P/YKXCnDyPVwzhUl/ZmkD3rvg66fHdn7EWJZ0vVdj8N+j51zlp1zeUl7Jb0w4PdGaaDyOOd+Va1Gyeu995c7x/tcZ3F8mO5YD+/9j7se/pHa46Dt731Dz/d+bewlHMww18ftkt7dfcDQ+7FrdEsO7wlJd7a/vlPS57c5d0s/dvsDuDNu9TZJfzuBMg5ix3o45/Z1uumccyVJr5X0Xe99U9JX1RpP7Pv9ERmkHldJ+hNJn/be/3HPc3G+H9+UdKNz7oZ2GW9Xqz7duuv3Dklfaf/+n5B0u3PuZe2ZqzdK+j8RlTvMjnVxzr1K0kOSbvXeX+g6HnqdRVbyzQapx7VdD2+VdKb99Rck/Vq7Pvsk/Zo299pEaZBrS865X5a0T9I3uo5Zej92jeA2vAclvcU59z1Jb2k/lnPu1c65RzonOedeqVbL6X/3fP9n211735FUkvQ7URQ6xCD1OCLpSefct9UKZg967zsX+fsk3e+ce1qtMaBHIy39FYPUw0k6Juku59y32v9uaj8X2/vRznrfo9YH4JnWIf+Uc+6Ec64zQ+1RSde0f8/3qz0b1Hv/lCSv1ofO/5L07p5upUgNWJePSPpHkv64/R50Pmy3u84iNWA93uuce6pd3vdKuqv9vS9I+m21Ass3JZ1oH4vcgPWQWg3wx9oNpg4z78co2KEEAJA6ZG4AgNQhuAEAUofgBgBIHYIbACB1CG4AgNQhuAEAUofgBgBIHYIbACB1/j/bFayHWbgdEAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_2d(functions_transformed_2, vectorial_transformed_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_1 = PCA(n_components=1)\n",
    "model_1.fit(df_all[columns_to_fit])\n",
    "functions_transformed = model_1.transform(df_all[columns_to_fit])\n",
    "vectorial_transformed = model_1.transform(df_vectorial[columns_to_fit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_1d(functions_transformed, vectorial_transformed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### TSNE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.manifold import TSNE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[t-SNE] Computing 121 nearest neighbors...\n",
      "[t-SNE] Indexed 256 samples in 0.001s...\n",
      "[t-SNE] Computed neighbors for 256 samples in 0.008s...\n",
      "[t-SNE] Computed conditional probabilities for sample 256 / 256\n",
      "[t-SNE] Mean sigma: 0.747899\n",
      "[t-SNE] KL divergence after 250 iterations with early exaggeration: 115.423912\n",
      "[t-SNE] KL divergence after 300 iterations: 3.232979\n"
     ]
    }
   ],
   "source": [
    "tsne = TSNE(n_components=3, verbose=1, perplexity=40, n_iter=300)\n",
    "tsne_all_results = tsne.fit_transform(df_all[columns_to_fit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_all['tsne-3d-0'] = tsne_all_results[:, 0]\n",
    "df_all['tsne-3d-1'] = tsne_all_results[:, 1]\n",
    "df_all['tsne-3d-2'] = tsne_all_results[:, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 10))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "for i, f in df_all.iterrows():\n",
    "    c = 'r' if f['class'] else 'b'\n",
    "    ax.scatter(f['tsne-3d-0'], f['tsne-3d-1'], f['tsne-3d-2'], c=c)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[t-SNE] Computing 121 nearest neighbors...\n",
      "[t-SNE] Indexed 256 samples in 0.000s...\n",
      "[t-SNE] Computed neighbors for 256 samples in 0.008s...\n",
      "[t-SNE] Computed conditional probabilities for sample 256 / 256\n",
      "[t-SNE] Mean sigma: 0.747899\n",
      "[t-SNE] KL divergence after 250 iterations with early exaggeration: 59.116596\n",
      "[t-SNE] KL divergence after 300 iterations: 1.367476\n"
     ]
    }
   ],
   "source": [
    "tsne = TSNE(n_components=2, verbose=1, perplexity=40, n_iter=300)\n",
    "tsne_all_results = tsne.fit_transform(df_all[columns_to_fit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_all['tsne-2d-0'] = tsne_all_results[:, 0]\n",
    "df_all['tsne-2d-1'] = tsne_all_results[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(7, 7))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "for i, f in df_all.iterrows():\n",
    "    c = 'r' if f['class'] else 'b'\n",
    "    ax.scatter(f['tsne-3d-0'], f['tsne-3d-1'], c=c)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### TSNE on PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[t-SNE] Computing 121 nearest neighbors...\n",
      "[t-SNE] Indexed 256 samples in 0.000s...\n",
      "[t-SNE] Computed neighbors for 256 samples in 0.008s...\n",
      "[t-SNE] Computed conditional probabilities for sample 256 / 256\n",
      "[t-SNE] Mean sigma: 0.424384\n",
      "[t-SNE] KL divergence after 250 iterations with early exaggeration: 103.358109\n",
      "[t-SNE] KL divergence after 300 iterations: 2.366617\n"
     ]
    }
   ],
   "source": [
    "tsne = TSNE(n_components=3, verbose=1, perplexity=40, n_iter=300)\n",
    "tsne_all_results = tsne.fit_transform(functions_transformed_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%matplotlib notebook\n",
    "#from mpl_toolkits.mplot3d import axes3d  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "for i, res in enumerate(tsne_all_results):\n",
    "    if df_all.iloc[i]['class'] == 1:\n",
    "        ax.scatter(res[0], res[1], res[2], c='r')\n",
    "    else:\n",
    "        ax.scatter(res[0], res[1], res[2],  c='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[t-SNE] Computing 121 nearest neighbors...\n",
      "[t-SNE] Indexed 256 samples in 0.000s...\n",
      "[t-SNE] Computed neighbors for 256 samples in 0.008s...\n",
      "[t-SNE] Computed conditional probabilities for sample 256 / 256\n",
      "[t-SNE] Mean sigma: 0.424384\n",
      "[t-SNE] KL divergence after 250 iterations with early exaggeration: 98.457352\n",
      "[t-SNE] KL divergence after 300 iterations: 2.297149\n"
     ]
    }
   ],
   "source": [
    "tsne = TSNE(n_components=3, verbose=1, perplexity=40, n_iter=300)\n",
    "tsne_all_results = tsne.fit_transform(functions_transformed_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "for i, res in enumerate(tsne_all_results):\n",
    "    if df_all.iloc[i]['class'] == 1:\n",
    "        ax.scatter(res[0], res[1], c='r')\n",
    "    else:\n",
    "        ax.scatter(res[0], res[1],  c='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compute sum and multiplication by all subsets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def C(n, k):\n",
    "    return list(itertools.combinations(range(0, n), k))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 8\n",
    "for k in range(2, 8):\n",
    "    combs = C(n, k)\n",
    "    for comb in combs:\n",
    "        name = ''.join(str(i) for i in comb)\n",
    "        df_all[f'{name}_sum'] = df_all[list(comb)].any(axis=1).astype('int')\n",
    "        df_all[f'{name}_mult'] = df_all[list(comb)].all(axis=1).astype('int')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>class</th>\n",
       "      <th>tsne-3d-0</th>\n",
       "      <th>...</th>\n",
       "      <th>0123567_sum</th>\n",
       "      <th>0123567_mult</th>\n",
       "      <th>0124567_sum</th>\n",
       "      <th>0124567_mult</th>\n",
       "      <th>0134567_sum</th>\n",
       "      <th>0134567_mult</th>\n",
       "      <th>0234567_sum</th>\n",
       "      <th>0234567_mult</th>\n",
       "      <th>1234567_sum</th>\n",
       "      <th>1234567_mult</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.241593</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>22.263735</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>10.471485</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>20.080154</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15.872688</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 506 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6  7  class  tsne-3d-0  ...  0123567_sum  0123567_mult  \\\n",
       "0  0  0  0  0  0  0  0  0      0   8.241593  ...            0             0   \n",
       "1  0  0  0  0  0  0  0  1      0  22.263735  ...            1             0   \n",
       "2  0  0  0  0  0  0  1  0      0  10.471485  ...            1             0   \n",
       "3  0  0  0  0  0  0  1  1      0  20.080154  ...            1             0   \n",
       "4  0  0  0  0  0  1  0  0      0  15.872688  ...            1             0   \n",
       "\n",
       "   0124567_sum  0124567_mult  0134567_sum  0134567_mult  0234567_sum  \\\n",
       "0            0             0            0             0            0   \n",
       "1            1             0            1             0            1   \n",
       "2            1             0            1             0            1   \n",
       "3            1             0            1             0            1   \n",
       "4            1             0            1             0            1   \n",
       "\n",
       "   0234567_mult  1234567_sum  1234567_mult  \n",
       "0             0            0             0  \n",
       "1             0            1             0  \n",
       "2             0            1             0  \n",
       "3             0            1             0  \n",
       "4             0            1             0  \n",
       "\n",
       "[5 rows x 506 columns]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_all.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### df_all correlation with class column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "class        1.000000\n",
       "tsne-2d-1    0.080402\n",
       "07_sum       0.128037\n",
       "07_mult     -0.128037\n",
       "012_sum      0.083820\n",
       "012_mult    -0.083820\n",
       "014_sum      0.083820\n",
       "014_mult    -0.083820\n",
       "017_sum      0.083820\n",
       "017_mult    -0.083820\n",
       "024_sum      0.083820\n",
       "024_mult    -0.083820\n",
       "027_sum      0.083820\n",
       "027_mult    -0.083820\n",
       "037_sum      0.083820\n",
       "037_mult    -0.083820\n",
       "047_sum      0.083820\n",
       "047_mult    -0.083820\n",
       "057_sum      0.083820\n",
       "057_mult    -0.083820\n",
       "067_sum      0.083820\n",
       "067_mult    -0.083820\n",
       "123_sum      0.083820\n",
       "123_mult    -0.083820\n",
       "124_sum      0.083820\n",
       "124_mult    -0.083820\n",
       "135_sum      0.083820\n",
       "135_mult    -0.083820\n",
       "145_sum      0.083820\n",
       "145_mult    -0.083820\n",
       "236_sum      0.083820\n",
       "236_mult    -0.083820\n",
       "246_sum      0.083820\n",
       "246_mult    -0.083820\n",
       "356_sum      0.083820\n",
       "356_mult    -0.083820\n",
       "357_sum      0.083820\n",
       "357_mult    -0.083820\n",
       "367_sum      0.083820\n",
       "367_mult    -0.083820\n",
       "456_sum      0.083820\n",
       "456_mult    -0.083820\n",
       "567_sum      0.083820\n",
       "567_mult    -0.083820\n",
       "Name: class, dtype: float64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corr_with_target = df_all.corr()['class']\n",
    "corr_with_target[abs(corr_with_target) > 0.08] # optional threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>89</th>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "      <th>154</th>\n",
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       "      <td>0</td>\n",
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       "      <th>166</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>210</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "</div>"
      ],
      "text/plain": [
       "     0  1  2  3  4  5  6  7\n",
       "45   0  0  1  0  1  1  0  1\n",
       "57   0  0  1  1  1  0  0  1\n",
       "75   0  1  0  0  1  0  1  1\n",
       "89   0  1  0  1  1  0  0  1\n",
       "99   0  1  1  0  0  0  1  1\n",
       "101  0  1  1  0  0  1  0  1\n",
       "154  1  0  0  1  1  0  1  0\n",
       "156  1  0  0  1  1  1  0  0\n",
       "166  1  0  1  0  0  1  1  0\n",
       "180  1  0  1  1  0  1  0  0\n",
       "198  1  1  0  0  0  1  1  0\n",
       "210  1  1  0  1  0  0  1  0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_all[df_all['class'] == 1][list(range(0, 8))]"
   ]
  }
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