Multiple Class Classifier - MNIST Dataset.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "id": "be9992a5",
   "metadata": {},
   "source": [
    "<a id='summary'></a>\n",
    "\n",
    "## Summary\n",
    "\n",
    "### [1. Dataset](#dataset)\n",
    "\n",
    "### [2. Multiclass classification](#multiclass_classification)\n",
    "\n",
    "### [3. Neural Network Models](#nn_models)\n",
    "\n",
    "### [4. Results](#results)\n",
    "\n",
    "### [5. Save/Load the model](#save)\n",
    "\n",
    "### [6. Read a handwritten digit image PNG and make a prediction](#read)\n",
    "\n",
    "### [7. Next steps](#next_steps)\n",
    "\n",
    "### [References](#refs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42b25498",
   "metadata": {},
   "source": [
    "# MULTIPLE CLASS CLASSIFIER"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "93430b0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import time\n",
    "import struct\n",
    "import gzip\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from joblib import dump, load\n",
    "\n",
    "from sklearn.linear_model import SGDClassifier\n",
    "from sklearn.multiclass import OneVsOneClassifier\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "init_time_global = time.time()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c3acd7e",
   "metadata": {},
   "source": [
    "<a id='dataset'></a>\n",
    "\n",
    "## [^](#summary) 1. Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f0b3b67",
   "metadata": {},
   "source": [
    "The version of the MNIST (Modified National Institute of Standards and Technology) database used here is a database of handwritten digits that has a training set of 60000 image samples and a test set of 10000."
   ]
  },
  {
   "attachments": {
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mPwy1K0B0DEQnwneZkJkFCFJOQ1hkjrSMYRCW/cMOx47DmYVQKRqiox1lPLcNMtMcF8TALrBgFKwZ61BIKrSEOfvytm/jE+Dp7FuJpnDIxbNsPwvnSkIZf+cfBoiMJO8M94D7h4H9Z4jqB039ry6ndBBExsC9I6HsAhgyL0f2mcsgwOiUfSmYm+5a27IxhkJo9pgxQkQYnD3tkI1XbegTDbOXgj0V5qyAnv1xaWWzn4ATFvhHc6fco6FCDzhvgzQXlIWzp8AQAeHZ59ILIkKuzmc9BA/2hZrTYHQNFxp2k/GIIqaAOXklaSFPd21MldhooqOjib9vOr9bLFiKMG8MPibHfQGAhwdGqxWry1PagI/JJ9eU9gBrFlaJcymnUVhkjuiNYUSEub4cGQK7MHnBKCLWjOXOCsEEV2jJsDn7nHa5Vzh+/ByX1zxBrRhH36Ojq/DoajuW9NQbZiiaBw8PPABPTw88neuNh9GG1QqQxeGVL9O3ZSJx0dFER8fS9OVtZGVZsFxXNnbOHjvOlTMLebBSdt9iqPvcNkpkpnHefj3ZuIjBn0B/A+lpF/MZ//lx1xsLmFB+Ob0SAgmqOpCNjXrRsqQv/n4GF9JdRKn88MJ99F/fhjlLxlOntKPvR2eP4rXMEbzZp1zhF6/Lu3ivW2dmx73H12+0JjBf1VkHP+PBe17DY8LXzOgSWaQLodE/nPDs9cngT1iYN+fOnMUOGGN7MKDhDuYuOIAtYyNzv7jMvQM6XFV/QdhPHuVE1iE+eCDeeV6jiWs3lYNeGVxIcyqZY+cwvV0K7/atR2RgWWp3eYW1p/NPSJGelo7BLxD/YrSlyVeU82KlwlYDQwEqhhVe7Q3b68KGJDh0CJJm4pKEXMYDxv3kaJsEe16heMyvBaufhtdOwqzNkHwIkndAK29HGgYIC4XTJ/hzlbGfhtPZP4wQWQYqDocDyZDs/BxLgU0TnG30hLZjYflmSDkKY4Ng+AS4kKsZd7wFVmffMjdAjItn2RgCwRZIzWX6ev48eWa4zsLYYVDpcch6G97cWXiZHgbY+XOOMlaiI6TanbK/Ar1zq+Ee4GHP2QHSZbiUb/zYT0NKdgY7nEyBkDDnOPKAXv3gxzmwfSl8Z4Y+tfIebzA4lJ/849IYAWV84d1fcuSefBjOnIQupsL7CBASDkpx7C4BYIVTZ/NlSocXukPKEHi/0803CTYYnFOy8DlpzN8u2wGmDxrIisgJrP71EMnJyRz4cojLw+rGYiAoLBTj6RM5oref5tTpolzGPSnXdiwfLd/MgZSjrB8bxNLhE1hyAaAUZcoEE9FrNknJySQ7P0dOnWH/lFZ4527J9Za7YkYInZ7PY71mYnh4ETsPJpOcfJC142vhKcd6U7hsjARHlsGn4nCWH8jpW/KxFE5vmkBNz+vJxkUMviTWiuX4nr1cyCcfQ3BjnvhsM4dTL5J2dCsf1r5AUqla1In3dCn9+kI6x4aJ99BreQNmrpxEm9Ds64iVfZt+4tC3jxLvacBg8OaONw9w+ZshRJTuxhfZ2tClHUzpci/Tw99k1YwuROWr1nJgNv07TODK2OXMG1y5aDsugD3tFKeyl1ulkZJiITgsxLE0GMrQaUAbfv/sM376dg5LPLswoKXPVWUUNO6M4WWJKNGA5384mHNe/zjO6ZQVDI1yTFyDXw36vr6AtbuOcmrvp7RJfoXH39uZ7745i6Rf91M6sWaxvqVjvOpnWAjs3wlFeq/WDukXIaoahHoDFpj3Tzh3U19I+eukXwC/WIgPdPz+5Z+wPvvO1ABtOkPaQvjsAMgCi6fBwVx7se0HwcVZMPUHyBRkpcP2r2FNsiP9zCZYuhUu2cDoDSU9oaRP8bwC6VkD7isHC75wXNyth2DO2lwZbDBnMHzTCGa9CbPHw5Q+8P15R/KJlfDGAth3DNLPwYb3YeoWaNTENWXMMx5ijsFPxxy/930O2/O952Q/CVM/houCo8vh0wNwf/uc0RfVDZrshIGvQWI/qJhPMAY/CPWCnbvzKkGeifBgdXhtPCRdAOxwZj/MXwLpuTNaYFxdqDEKcm84mO+GWvvgnRWOHbB9M+Hrc7kbDgsGw5xYmP80XD3nHVh38HqbilQZsIAzxT3kDX6EhXpxcOfuvF26HrrEhXQjEVWqU7aUAWwnWTVjUREeIdxIDAS06UyrtIVM+ewAV2Th8OJpfH7Q9cbpzCa+XLqVo845VbqkJ4aSPpT2APCmyYP9CfzyRV7+JplLdrBdPsXub2ezIrd/F2Mo4UHH2bXrzM3Zbchue2Y66dZgEhLNmIyg1B+ZMXe70y3K9WXj134QXS7O4tmpP3AiUygrnaPbv2bemmRs15WNq3hS7b6ORG1ezbp8G4n2kzv4z84jnEtP5cjmWQx/fC6+g4bRzuRaOnYrmZkZZGTZkGxkZWSQkZnlOAf206wZ14Eey+vxwZcv0dTXQkZGBplZNsCbNtOPY3PY2iFZ2DgmntLtPuTk5c/pUgJ0YQuT7u/I9NBXWDL1HsKtGWRkZGJxbodl7P0nve6cwKURi5nZNwYyMsjIzMRalAFw6Vven/IT521WzmyYzEebYrn33qrO5dJA0N0D6Hj2E4Y8tZSgnv1oUCLf8dcYd8ZynRjUNompT/+LHWezQBZSD21i8cIfOGUHsLF/9Ty+TzpHpsCzlA/eRiOlfUrl3Ui27uLbf2fS9v5m11yy/hJXWTGcWSO1qyCFREhlY6Wl+d+G6Kq8lkxO/vhSal1ZqtZQatFaGjdOKhcpfeM0KMp+WyEqRDKWkMqaJXOc9O5+FWhY+cNoKahvwXXlJ/tNC7NZ8veSfMIc36s87rC6X9ZPaj5FslmkkfHS8zsl6x6pXrT0faZ0ZY/00B1ShRpS8xZSn5ektr7Ss9ucFVilFeOl+CApqLzUe6LUwCR9eDKnDXvnS/ckSgEmyS9EqtNR+uKgI+3EEqllFSnQT/ILlBI7SsvzG+tdC4s0rrajP2EmycvP8T22sfST00AmfbvUr4FUpa7UqI3Ut0XO2xA7X5fCEqV1TmNN2aTPukpR3aUjNillldSxnhTuL3l5SeGVpaEfSuddtdSzS6uelGLKSfWaS/0nSk18Cn4bonyA422Ixz93vg2Ri0W9JKNJ+viECmTLO1K1MlJ4pBTTJcdA03ZKequfFBfqeJMlsrLUZ7Lymn5nSAOCJFPPq8fTb/OlJlGOc9Z4qNS3ktRzsTPxvNSxpFTKXwoOdn5CpIe/zlvGjTRwlHRxyzt6oFoZhYRHqmxMF83MZZzqeBuiqxZeNU/sSlnzgjpWi1Pl+k3VouW9emxCP1UxZRuUWbRuXG3FmB0W/R5efoowm2WObaznf8pStoGjqcsCZa8Alh9GKy6or77KkJT1iya1jpXZbFYZfy8ZfcJkNpsVXeVxrcpUAYaZVu17rb5MHT7Wabvj97EV49UuPkh+QeVVp/dEDW1gUtsPT7pk4Gg7sUSjWlZR2UA/+fkFKjKxo55ZfiSXPbRFfyx/Xl3rRSnI1yTf4PJKbDtIM3flNiqzaN+s/qpTLkShkWVlbv2GdrtkEFa47DKW9VNY8yn6w2bRhpHxqvX8TmVZ9+gf9aI17PtMyZ6mzVN6qHZ8RdVp3EIt73pILw5tKJ9mU/SHzTXZXNo7X2PuSVTZAJNMfiGKqdNRT3xxUDaXZOMitmRNb1dOHWflNTq1/vq+HqgcLh/vEvIrV0udnvtaf1hcT89cOVAhRgS5PiWdYzh1tu4tmS8N5P2nbPKeh/wGjgWWjaeqPrtNWcrS5qcqyjNf2RgjNPib/AtSwTjehnggz9sQA2bszPfWQYbWj4iVh3d9vbavIKlfe9zZU7fqo0faqFK4n0wmf4VXaKQuL6zWKaeB4/YpD6hubKj8fP0UEBqnJgM/1PYLeWfMpe+HK77KWG0skkXr9TFIN3MT7n8E2y6o2wzGH4GuLmx3u7k+m56EjoccOxPBt8JKECALhseDPoFpLW9RG/6fYtvFi3WbsXv8ET53z6m83ELZZGybSLOHM5n6w2s0LHX9/G4AbPz2RhPqrujFzjWPEX0zH/3ZD/F+h7v4cch6Pu0USnGupDkbzYZbtUD/F6As+H4V1GjvuJCtmwlHG0Pj0m65/V0kyDoMb82B+2c65HszZbrjGyjdACr4wdElsMIOU2o70q7XDree/TewkvT9Kiw12lM92MCZdTP54mhjRjYufasbdhtw+8imZJ0X2Lz9plf7X43t9Gre/Og3Wj3XHfPNthEyxjBs9V6G3YCic5QF98JXCBZY+yr0HgRGDwiqDZ984Hj90C23v8fS/tBjEdQZDFPaOf67aTIVfDUCRvQDixG8IuCRuXCP/01ux/9H7Jxa+yoDew/istEDz6Da9P3kA/pH3hYWmLcYt2z+O8liwxPV6PDBeSp0n8zCHmHFemd/q3E/hnDjxo0bN27cFIpbVXXjxo0bN27cFIpbWXDjxo0bN27cFIpbWXDjxo0bN27cFMrNVxbS5oBvfdhXjN5hLKuhagyUD4aSbeB4Ec0wLs0H39qw+y+2afMLEBcNYT5Q68Xii2eRn1WDIH40FBDbPQ/fDoHox6+f72bwd2Xr5oZjWTWIiPjR/PCXxouVLU9XJqjvV0VzJ/zfjM4wr28C0dGRBJTwofuiIvbcfpipzX1p++FJ/orBmHXzCzSJi8Yc5kOJWi+y6wZOrYxtE6lf+yk2FclJ3+2L5dshlI1+nHW3w9pYIBZ2vtSQGqPWcfFWNyUf+ZQFK7xQE7p+fuNqLFUP3hoLVwW/+Bt43wm/HoKNL8DV8UJuPPUnwu/J8G6HG1tPld4wsVPxeH78E8G616F1LfD3hlKd4VJxll8M2I9Ba1+YdvRWt+TmYz/G+619aTXt6A3zMuhZpTevTOz0F13DGjHf+yyT+lUvHu/rN5PML+jmm8jEnUUMLWUIoefs/SQfWMHjCcU6GV3Cs/5E/vN7Mnvf7ZDHdXWxY/+DT8bPJHLESBr86WMhk92fPs599eMJ9ytJqcAYGvV+g3UpOaNTF7bzwaCmxIX4YvILIa7pID7cnv6nYpSRNI+R7SoT7mfCNzCKej0nsT6Xq+/C07PY/n4/7qwXT3BJIyWaT+XwzXS/CTd4TnqTOHws1RaPZ3px3lAXAzd/Z8G7IgzuCgH/Sy+V3CSiWkHfJsV/1kpHwcBX4I3O7gdT/w8xRrViYN8mlPlL595IWKPePNQ2pnh1WDe3HOvPH/HezuYM6BSR6xXALE6e8qD5U7NZn3SCo1vep8Whf/DAoE85bgewsvXV3ozcUJm3d5zh4tndTK+9mZHdn+dHC2A7wPuDHmKh7xg2nEwn9eBCOh5+mW5jljlC5VwvHQMlytSn13Mf8/7ACv+TY84QeBcDOhzlw+k/3Fa7dc7lQfBZH4iOh8l7YeVwZxS/ivB1rv2nbc+A7wMw7wmokQBRkdDqTUdMgjPfQaeGEBEIvoFQ4z5Y9kfOsdZd0CYOzKFQIv9jCOeORptR0Lct1IqFuLbw79x++v8ONpj1ECRGgZ8vhMbDwOmQli9+wOxBUD4AAmPgsQV54wgkLYC7qoG/CcIrw1PLihD1MgNmPwIVwiAgEMpVgxfWud78ozOhQjSE+0JcAY8h0rdDv3rg7wtxrWDFiZy0tPVQIxLeS3L81gV4sia0fddZjgHq9YTeHSDGz/U2ZZP5BfgmQvbdmc7AXb7welKuTNeS7QXoHwnD1uQuEEZXgC7zHHE4HqsCsQ1h42WY2MgxLhN6wAnnubOfhrf7QkwQmAKhQX/YmuZ6+3//HJpFO8bsHQ9Dn0rQc7Ez0QovNoKIiJxPaY9c6dnZdvJG+6okDvqcs8X2IrKFVY9VISa2Ic9tvMyPExsRGx1NdEIP/nUipxLrtmeo6vsAb8x7gjtrJBAXFUl0qzf5xQpXNk+hZ7MqlA3yxeQfQeV2jzN3b858th+dSdcK0USH++Idl/8xhJVfXqiJqc0oXu7blia1YomMa8vEf5/78w7x4pLBVIyOJjKgBAH5H0M4774aDnmehzs0o25COcx3PM6SY9n3YjZOrHqWDhWD8fUvS62ezzK4QVG25jPYO/sRmlcIIyAgkJBy1Wj7Qu6t2yyOrHieznXKE2jyJTiuBY/O2euxbDgWAAAgAElEQVQIeZP1E8/fEUt0xWGsuJzE1LscUf7i73ybPcVyM2djz6yHaJMYRYifL36h8TQbOJ2tedYbcXHbVLomlsHfN4SKHZ5l1fGcyq8kLWDMXdUo42/CL7wyHZ5axuEirDeFy8YVrOxeuowjDe6kWR6nkSbajH2H0Z0aUbFMIMHx7Rk9qBEZ2zez1+o47tjhE/g17USHciXAK4KWnVoSdmwvSekC+wkOH4O6D3QhobQBj8C6dGofz4V9SZy0cf10PKn6wHD6d2xMhWCvv+bHwHaEr0a3IDbYF/9yDRjw0U7nZuoFvuofSfSwNblCI2Xyn9EVCOkyj7NyYU7aT7Ph7b7cEROEyRRIVIP+TNualjOmrX+w9Mn2VC0TSEBgMJEVmzFqaf4xX4pG7e7g/PKlbLudHpfk9f5cQIyG3GwdL3mZpP6zpIt2SRZpT5Jkl3RilTRtpXTqkmS/KP2rh+TfPseHfzapsyVTPWlvbp/ZznoD2kr7MiRlSq81khpOUpEcmh9+VzK1lo7l9y6fJc2ZJP2YLGXapZT1UgNfadQGR/LFeVJJo9RxmpRuk44skSr6S28nOdu8WooNlMYsly7ZpJNrpHqh0uT9eauZ31mq+cLVbT47R/JPkFamSLJL55Kk9UlF6JiTlQOluFGOmA9/kiE9UVGq+5R0OktKWSvVLSVFPZaTb9ebUmR9aXO69NVAKbrn1edFkr4ZLJXuJF0sQpsyFkqm6tIOp899+2mpgylvbIjCZPv9o1KZ/tIFZ3mXv5WiykhfXcipw3ZUamWS3ssfT8MqTWkhRXeWtp6RbOnSjM5SzJCc8grDuk9q7CcN/ELKsEm/TJFCjFKPRQXn3/e+FFlR+vpU3v9vZGyIq2Is5CVr63hV8TKpUv9Z2uuck6f2JOm0Xbq4YYbeXLxdx9KzZM84rGWPVJFP3Vf0a77xmblyoMLjRuk/ecaVIzaEV0BbTXXOyb2vNZKp4SQlWfPm2/xUJQX2WZo37IbtqKa1KqGS9Z7TlnTH74/vDlKFMT/KIsl27BPdG1JWD3y0RxdtV/T7nJ6K8iihNh+ccCk2hP3sHN3vn6BHVqYoS3ZZziXp3+uTlO0OP2Pzs6rhX1WD5u1RmtWqc5tfV+vwRD2zJVcMgIyF6mqqrud2ZBVYx3XJ+lkTqvmq2xf5A3Nk6ec5k/TZj8lKzbTLkrJezzTwVeyoDY4paftDU5p5yzOmn+YfvCL7pf2a2aWcQu7/VCfskj11tYbGBqrBmOU6eMkmy8k1erJeqJpP3p9nabk0v7NMNV/QL/nO5/Vk4xL2c/rkHh9VemqzCpdOmlY+HKWgez/RCbsk2ZW2/lk1qjNICw9eku3KES1/tJoiOnykgzZJytDOd9qpRpcP9OsFqywpGzShUZga/ONn53J1vfQcGW97tqpKFxgz4tpkfjNYER5+avrijzprzVLKuqdU16+qnv7JMS6ufP+oYsr0z1l+Ln+roVFl1D/felTwnLQqaUoLBUZ31vStZ2SxpWvPjM6Kihmi1c7DM1Y9pIjIbppzOFOSVRcObdS/fzl31Zi37npJtXxa6/2rrmW3jqJvPHpWgfF9cQS594LKCY7wwRF3wrD2EFYaDD7QYwCU2gu/FUFVb9QDEkoA3nBHfTi4t5iMBT2h91hoaAZvA4Q2hh41YNevOVEMjREwYhCYjFDuHugXD0tXO8JSr5oBmd3gpbugtBHCW8KQOrB4JS49tDJ4gDEd9uyB81YITICmCcXRMbDugGVHYcgoCPGE0GbwSIu8eaqNhElR0KslDNsCs6Y7vE/eLAqTbZP+ELgCVjh3kdbMBY/O0Na30CIBx27VPzfDqLegTjAYTdB/NHgsg02W6x+fvBx+ToCx90MJI1R/GDoGF5w3dS10exFGLYC7w/KmeTVk0n4rGasHE34rnq55VmHA+L5Ucs7JsMoJhBjAp8lDPPFALSJNnhhKlKf9wPuI+u0X9hXhEb13ox70dM7JuDvqE3pwbxEiV3qS2LkXtUyAMYKGd8RwIuk3LiHS1izme79uPDGgMj7GksR2H0GPuCJsKhs88DCmc3TPHv44b8UrMIEWTROc4YYt/GfmTJJbP8Mb3Svj5+FBYL3hPN7uBEuW7HZ9Q/Av40nN3mPp2dCMv7cBr9DGPNSjBim7fs218+RJpT6j6BxTEkPpCvQZ0QXf75ewNh0urJrBvMxuvPTSXcSUNuIV3pKxQ+qwffFKjrq43lxbNi6iNFLThMnPVMjdu41jix7jseXVeOWNXkQYAAz4Vr2HXpV+YlC8L14+UXRbU4c33+3vDI/uTUzr3jQ6/AyJAd6UDG/Dv0In8OHImk5zs+ulFwM+bRk2oiFBHp6ENh3FkEbJLFv2K1agZJP+9AhcwewVjh20i2vm8pVHZwa4uB7N+edmqo96i8F1gvEymqjcfzRdPJaxKHs98vDA48pJkn49wOkMI77RjWhRPfAqGRt8fTEpjdS0m22QcW2KfsXwiILyBUzqtO0woiNUjIGYGEgYAGczHaF/XcXHxJ9S8/AAqzVXSGIbvN7A4a/fYIAq44vwGCALVr4MLROdj1di4eVtkGXJpSyEQmh2v4wQEQZnT4PdDseOw5mFUCnaeXwMPLcNMtNcUxYCu8CCUbBmLFQIhgotYc6+vHk2PgGezr6VaAqHXBwk9rNwriSUcbooxgCRkeQdfR5w/zCw/wxR/aCpfwEFFULmMggwOmVfCuamX/+Y3FxTtoBXbegTDbOXgj0V5qyAnv1xaWWzn4ATFvhHc+d5iYYKPeC8DdJcUBbOngJDBIRnTwMviAi5Op/1EDzYF2pOg9E1XGjYTcYjipgC5uSVpIU83bUxVWKjHdvs903nd4sFSxGulgYfk+O+AMDDA6PVitXlKW3Ax+STa0p7gDULq8S5lNMoLDJH9MYwIsJcX44MgV2YvGAUEWvGcmeFYIIrtGTYnH3ORyFXOH78HJfXPEGtGEffo6Or8OhqO5b01JsQjjqLwytfpm/LROKio4mOjqXpy9vIyrLkWg6NhEWE/rkAG0MjCLWd40yalbPHjnPlzEIerJTd9hjqPreNEplpnHeh8YXLxkUM/gT6G0hPu3iNx0J2Tq4cyd2jjjDwy3kMTnBeynWaBUM78tyRLiw7comsKyf5btApxrQewtKzgsvfM67jMDY1+hcHLmSReXYLE0u/TbvuM/nDzvXTiwGjfzjh2euLwZ+wMG/OnTnrGBdetenbJ5o1s5eSYk9l1ZwVBPbsT2MX16NjJyxs/0dzx+OJ6GiiK/Tgs/M2LjnXoxKtXuLzl2uw68VOVAsLxNyoH9O2pV8lY6VfIN3gT4D/7WNElq8lzotVoR6gDQWoGFZ4tTdsrwsbkuDQIUiaCYHFeZvlAeN+crRNgj2vcJX5tYcHYANbvvafng+9ZsLDi+BgMiQfhPG18vbTfhpSsm+Z7HAyBULCwGiEyDJQcTgcSIZk5+dYCmyakLcNVyk42XhC27GwfDOkHIWxQTB8Ak6LHQd3vAVWZ98yN+BUw6+PMQSCLZCakfPf+fN526CzMHYYVHocst6GN3e6VnY2JTpCqt0p+yvQO7eW7QEe9pwdIF2GS/kEcE3ZOo/v1Q9+nAPbl8J3ZuhTK+/xBoND+ck/Lo0RUMYX3v0l57wkH4YzJ6GLC9H5QsJBKfCnJbcVTp3NlykdXugOKUPg/U433wDUYHBOycLnpDF/u2wHmD5oICsiJ7D610MkJydz4MshLg+rG4uBoLBQjKdP5IjefppTp4tyNfCkXNuxfLR8MwdSjrJ+bBBLh09gyQWAUpQpE0xEr9kkJSeT7PwcOXWG/VNa5XmD4LrLXaHdMOLhIazWvFstOj2fx3rNxPDwInYeTCY5+SBrx9fCM09FdlJOppDT/ZOc9gwhNMCT4Mgy+FQczvIDOW1PPpbC6U0TqJlrvTF6eGCwWq9a7gqXjat98yWxVizH9+zlwlXl2zj+9WO0H7qHHl8s4an6fjn3Jtbf2LL9IrW6P0STyJIYvcNoOKQPDVJWsnxbFrYjW9mWEs/9A+8k2seIZ2B1+gxojb5fxg+XuG56cWBPO8Wp7OVSaaSkWAgOC3FObQ8q9upHjR/nsHD7UuZ8Z6Z3n1p5dzWuNSeNEZQt40uHd3/JOW/Jhzlx5iRzstcjYyh3DJvKlxv3cfLkz7xd9SfGjfkXR/IN/cv7fuWPiBokht4+LwIYr/oZFgL7d0KR3qu1Q/pFiKoGod6ABeb9E87d5LATwQkQuA/WHs/7f2Y6WIMh0ezoceqPMDdfKDX7SZj6MVwUHF0Onx6A+9s78rcfBBdnwdQfIFOQlQ7bv4Y1yXnLiK8ER/8Dv+fT4c9sgqVb4ZINjN5Q0hNK+hTPK5CeNeC+crDgC8dOi/UQzFmbK4MN5gyGbxrBrDdh9niY0ge+P5+r71bIzIAsG8gGGRmQ6aJljWc8xByDn445fu/7HLbnO7Yw2QJEdYMmO2Hga5DYDyrmE4zBD0K9YOfuvEqQZyI8WB1eGw9JFwA7nNkP85dAej7j1XF1ocaovEar5ruh1j54Z4VjB2zfTPg6t1GtHRYMhjmxMP9p8LmGDKw7eL1NRaoMWMCZ4h7yBj/CQr04uHN33i5dD13iQrqRiCrVKVvKALaTrJqxqAiPEG4kBgLadKZV2kKmfHaAK7JwePE0Pj/oeuN0ZhNfLt3KUeecKl3SE0NJH0p7AHjT5MH+BH75Ii9/k8wlO9gun2L3t7NZkduw2hhKeNBxdu0689d2G4zlqVTBm53fr+NsrgKUmU66NZiERDMmIyj1R2bM3Z7PLtnKvrmTWZycga78xpwpX3Cx9QO0MIFf+0F0uTiLZ6f+wIlMoax0jm7/mnlrkvM8lfWMr0T00f+wNt96U7hsXMWTavd1JGrzatbl2Ui0cnjRENoO/ZUuc+czItGbzIwMMjKzHDL0jKdW9VLsWPQpW85awX6B3XMXstmYQJVYTzzK1aRG8AGWzVnLCQvo8kGWzl/LBXMVEkpx3XQAWS1kZmRgsQrJSmZGBplZRRjYl77l/Sk/cd5m5cyGyXy0KZZ77636532fMaobA5rs5N2Br7E+sR+9CliPCpyTnon0erA6618bz6KkC9iwk3FmP+vmL2G7M+Olncv4/IdDpGUJg1cpSnkZ8PTxoUQeneAyG7/5gaC776PurXAFcC2usmI4s0ZqV0EKiZDKxkpLL+ekbR0vmbpK+e15JOmPL6XWlaVqDaUWraVx46RykdI3ToOiLx+WzGYpKkQylpDKmiVznPTufhVoWPnDaCmob8F1XROr9MUwKdIklfaVHv3W8bc9TZrSQ4qvKDVuId31kDS0odRsimSTwwjPVFV6sr9UPkAKiJYe/1zKZQulvfOlexKlAJPkFyLV6Sh9cTBv9fYU6ZnWkl8pySdYmu+0ajmxRGpZRQr0k/wCpcSO0vL8xnrXwiKNq+2QXZhJ8vJzfI9tLP3kND1K3y71ayBVqSs1aiP1bSGZnQaOO1+XwhKldWnO8mzSZ12lqO7SEad5zsqBkvHPPRvHp+Q1zvNV2KVVT0ox5aR6zaX+E6UmPnkNHK8nW0la1EsymqSPTxRczZZ3pGplpPBIKaZLjoGm7ZT0Vj8pLlQy+UqRlaU+k6X03AdnSAOCJFPPq/v023ypSZTjnDYeKvWtJPVc7Ew8L3UsKZXyl4KDnZ8Q6eGv85ZxIw0cJV3c8o4eqFZGIeGRKhvTRTNzGadmbR2vKqauWnjVubIrZc0L6lgtTpXrN1WLlvfqsQn9VMXUSfMuSpJF68bVVozZLHOYSR5efoowm2WObaznf8pStoGjqcsCZa8Alh9GKy6or77KkJT1iya1jpXZbFYZfy8ZfcJkNpsVXeVxrcpUAUZgVu17rb5MHT7Wabvj97EV49UuPkh+QeVVp/dEDW1gUtsPT7pk4Gg7sUSjWlZR2UA/+fkFKjKxo55ZfiSXAaBFfyx/Xl3rRSnI1yTf4PJKbDtIM3flNtezaN+s/qpTLkShkWVlbv2GdhfFoFpSxp6P1ScxVD6lfORfe6K2ZUmyp2nzlB6qHV9RdRq3UMu7HtKLQxvKJ9sYz/aHpjTzUcPB49UlMUJ+pmAltH9Gq47nnNdLe+drzD2JKhtgkskvRDF1OuqJLw7mNaizp+jbZ1or2q+USvsEq7tzvbm+bFzElqzp7cqp46xcRqe23/VWY2/hUNtzPiWzx5VkO/6dXu5WT1GBJvmYAhRZo6OeWnzAOeXtOrfpXQ1oEqdgk498/MJVue1w/WtXtlX19dKztPmpivLMV793q2k66oKhY+Y3gxVZ7gGNHt5cMUEm+ZWtrwEzdupSvnypi3opxGjSXR8XbHB7zTlpO6V1b/VTk7hQ+Zl8FRhZWc37TNaPzvUofe0LurOGWcF+vvILCFelNiM0Lynv5LWf/Vw9yt+hSXuLfMZuKO6ok25uDzY9CR0POXYmgm/V1lsWDI8HfQLTWt6iNvw/xbaLF+s2Y/f4I3ze1YVHSG5uChnbJtLs4Uym/vAaDUtdP///CpZNT5LY8RDP7/ucHjd1PbKw48Wm9Ds/iY3vNOd2mgk5yoLh9nk24ub/ERJkHYZeDSFgJsxof3PH4o5voHQDqOAHRxdCs9EwZTd09L9+O9x69t/AStL3q7DUaE/1YANnvh9Dq+6/MXLnVwy8mW/quHGTn6zDzO7VkGcCZrJnRvvb6oJ9K8kxl3EvfG5uBUv7Q49FUGcwTGnn+O+mjUXBVyNgRD+wGMErAh6ZC/f43+R2/H/Ezqm1rzKw9yAuGz3wDKpN308+oL9bUXBzC8lc2p+yPRZRos5gPpzSzq0o5ML9GMKNGzdu3LhxUyhuNd6NGzdu3LhxUyhuZcGNGzdu3LhxUyhuZcGNGzdu3LhxUyg3T1nI/BL842Hj3wyjtWoQxBcQefF/gbQ54Js/ImcBfDsEoh+/PWRwaT741obdt4W3Hzf/30ibw32+9XntenPmvxSlfcuj1ZvzZlECevwvc2k+nX1r8/JtvN5cXDuCxDte4RcXPM7/N5FPWXCGiu76+dU5bftheEeoFAYeXjBhe/4MsPo5qBoOpf2hfl/YWhT/oi5SpTdM7FQ83g9vN0rVg7fGQkQx6nD2P2BYcygfCF7eULYGjFvEbRUo3X4MWvvCtKO3uiW3H85Qz62mHb0xMQ0yv6CbbyITd96Ki5EjDLZv18+L5jA2N6XqMfitsbQrzjlz22Bl19TxrKz/JIMr5fYrn8X29/txZ714gksaKdF8KofzDY6MpM8Zc08ikb4lKeVfjpoPfnZVHrBzfF5Xynh4U+cfe3K8Q9pPs35ST+pHBWIy+RFWqS0j5yfxp4fkC9v5YFBT4kJ8MfmFENd0EB9ud8Y3sG5lfBUvDAZDno+xRFPeOWTHfmgyTUsYrkr3qjyerTdrCN7gOWVqNoZH/abz7NxjNyEOyc2jCDPMExIfgPc/gXoF+KA8Mgt6zYLR6+HCIbjrIHQdB0WMOXRdolpB3yb/mw9QvCvC4K4QUIx+Bgx+0P0lWLcXzp2FNS/CqgfhrV+Lrw43bm4V3hW5e3BXahfnnLlduPw90/6Zyn0PtsUvT4KBEmXq0+u5j3l/YIWr7puUuoqRdw1lbczTfL3vJCd+W8uHAxMx5RORTi5kzBvHiInJW8Kl1U/T44XfaDl7P6npKWx+PoKlg/oxea8NsLL11d6M3FCZt3ec4eLZ3UyvvZmR3Z/nRwvgWZvnt6WSnp7u/KSy6ZlETI26cr/ZiDF6ON+eS89JT9vLOy38qNSla564F//VGMvRtX8Dfpw2i7237wZI0XE4crRLc3s73AgHeEs+oY7v5gRp2eW8Ph9tf0jNSkvPbsv9pzS1uVTpaf0Z/PzCF1JQiLTU6UgzY7HkFyf9YHHk/2aMVL6+9M1J13xNHvlYijc7XB7HjlKe4ObL+klxjaXq4VLMfdLTnaUgf+neD+TwcWqVZg6SqpeXfE1SSJz04PtSarYjT6u08hkpIUjyi5R6PCPVN0kf5HI9vG++1KGq5OcjhVWSxn2V01fZpc3vSg3Mkn+AFGKW7pus6wSCzyHrF6l1rMMVtnc9Kb+bzwvbpL51JT+TFNtSGtkxx52z/aQ0IE7qPs/hulp2aemDUlS3HHfOuTm/VbqjlNR3qWtty1gomapLO5ydsZ+WOpgKdudczt/hznn4fKc7Z7v0z7uk6s/llcWSPlLUEOlSpjS8smQuJ5U0SsHlHOOuQnfpePa5sUjLJ0q1y0k+Jim2uTR7j2ttl6SLO6T+9RznPa619MR9ObJTlvRCQyk8POdTyij1WJS3jKwdmnRnFVUfuEBnblp4+UytHF5Z0eZyCi5pVMngcjKbzTJX6K5Pcsnm8PKJ6lS7nAJ8TAqKba5hs/f86Z5ZWclaMvZOVYkIkH9AkMokNNXIJU73tZZNmtgoRmZzqHyM3gqINMtsNiuu3Vv61UUvs/ZTa/TSAzVVNtBfAYFhim0wQJ/8lnOwPXWbPhrSUhVCTPLxK6Manf+hf5+ySbIrZW5vVTCbFRngLaNPqKNv5gQNzb/eXItsd9NRISrtXU+v5p4z1iS93jBENVs2U3RQqOoOfU6P3lFGfsG19cS352WXdPmnyerRtLIiA03y8QtXpbaPac6eXHVf3KGP+tdTpK9JwXGtNfqJ+xRhfkxrs9cdW4rWv9VHjaID5eMToPL1++m9Lal/uga+nmxcIeO7oSoXMVArrlxTCNr2bFWVznYj7ahZJ2feLf/qz2qb5VrHSbKf1MLeNdR51vd6tUFp1X75V6c7aLtOfdROpSs+pc3Zc/bKInU3BajfVxmSrujLXv4KHbjyT4/tlrWPKapUB80saHJcWacRcUG6f/apAt0mW3e/rDq+TfT2ARd8NUvSxXnqZKqqPk/2V71y/jIFRKvZ8Pn6zbneHP/nXQqo/px+zrXepC3po/CoIfrmUjHMKV3Rnk+Hqll8qPz9AxRctqraPL82r3d5SfbjH6iNqb5e23d7uWz+O+SLDVFAjIb8FKgsZEpDIqT75kgHv5RGvSOd3CXVLp1zUflTWbgkLRosmVtJG88XvcUrB0pxBSgL5qFS2nGpvY/U5TPp/FKpXANpn9XRrzmTpB+TpUy7lLJeauArjdrgOP7YJ1JIWemjPZLtijSnp+RRIkdZSF0txQZKY5ZLl2zSyTVSvVBp8n6nTH53xEOYsNlxwc5Ikb7dqCI7Y0+dLZnyKwsZ0hMVpbpPSaezpJS1Ut1SUtRjOTK48B+pVlnpvSTp4EypfFXpu3O5yrBJ77aXwoMlL4MU1EBal+pam1xRFkoapY7TpHSbdGSJVNFfejvJkX7ucyk0QdroXFrsZ6UuIdKYjbmad1RqZZLeKyBexuZnJf+q0rw9ktUqbX5dCk+UtuQPLlFg46VxVaTaY6WTFunsRqmRKa/scrPvfSmyovT1qbz/3+DYD4VyVYyFHDI2P6sa/lU1aN4epVmtOrf5dbUOT9QzTtlkrHpIEZHdNOdwpiSrLhzaqH//ci7vop2xUF1N1fXcDlc122yytOXpygpoO1n7Ltsl6yUd3bpGW05k+8g/prldyii8zT+07niGbFcOadFDlRTReW4uGV4df6LIpM7WvaYClIUGJjWfmqz0/4xWQskamrD9ova93lChfZfqiqSLG2bozcXbdSw9S/aMw1r2SBX51H3FqShlaNO4KvKtPVZrTlpkPbtRzzUyyTMqW1mwKmlKCwVGd9b0rWdksaVrz4zOiooZotUXXJCNS9j02xuN5NP4Lf1+zcMKUhYytWZYeUV0fUGvdquhMn4mBcc21UMzduS6oNl1alFfVWs/XQczk/R6HmVBsp/8So/UaqIx3x1Xpu2i9n/aUzHmvlqcYpdkV9r6Z9WoziAtPHhJtitHtPzRaoro8JEOXtVOu84v6qXwyAf19YWC2n9F60bEKbDjJ67Pq4vz1KmkUeEdp2l3uk2ZR5ZocEV/NXk7SVZJ9nOfq3togsbkWm/mdQlRwpiNOeFo/sacsp+do/v9E/TIyhRlyS7LuST9e32SrtLnLGv1WJSfui3MH3Xiv5di2swXXLwMPqVh/2r4dAEcLwGlBem544paYHZ/6L8FPv8KGgUUT/UA5RPAFALxYVCpIvjGQvgZZ/hhT+g9FhqawdsAoY2hRw3Y9avDS9+axeDXDQZUBmNJ/q+9M4+Lqmof+HcWQGDYhGEXBkQRF8wtt3Lfywy3TBMyXDLLsjQrK9d6820zy/yZpa9CuW+5kmFaaa4kuUIuWKhsLoAiy8w8vz9mjGERoddsee/387mfD8M963PPPee55zznPDzyLNS1mZrbthCKBsPMPuCkBp/OMKYFrN2KZVFKbbGhOHsE0vPAQQ/d2t4ZuwrjYdiYDmMmgJcW9B1gbKeyYVzaQ/wk+FcU9HsVxsZBVw+bAGp44nNIOgCr34HoodDQhTuG2heejQWdGgIfhOgw2JBgkY1HH+hXAHHfWcJmfQmJgRB9bzUSLoZFi6DrFHgkwuICvNXT0OMirD96++jGZFh/DsZOBB87qN0GnuxUedirO2HwDJiwAh7wLnvPrg3/TjVSmDAan7/MbHcx3y9aRFrXKbz9SASuGg0erZ5mfI+LrF9/FCOARoPmRgYpx06RXajGxdCWTk08uFNV0Gg0lGSf4mhKBgUqJwJadKGl1XbAfH4tC7fUZtTsF+ng54C6loF+E2MISlxN4h9gylQBlSth9fxwDq1HHfu6NKzvTHDdYIyZmeQKON83kheimuGv06JyqEOvJ/oR9PNPnDQCxmTWrT9Hu7ET6exjh6Z2G559shMON9M2HiH+0/00mfAuo1t4YqfWERHzPAM1G1mzt/i2sqkeZnKv5CI61wrLB1Uj5OfmcnnTMk48tIKUS1kkzb2H/c8NZvoPFkMlyf6SF6ec4/H3RhJSSR+l8mrBgAG1Wdc3EEc7VxqMT6XfvNk8pFcBKlwaPcjQBnCKA1gAACAASURBVPuIDXPBzjmIwYkteOfDmIruz83nWbFgE66PjqRbJd2NXN3CguXX6TsyqmbvldqXqGdjaaRTYx/4IM9Fh/HjhgTOm0Hl0YeYfgWsivuOG4BkfcnniYEMi763jGvyyqnGO6XSoFHnk378OOeuGLHzqE+n++tTq4IQXXDVGcm9eo1/yqmHd0hZUIHOCa4XQM/5kPMDRJZAAaCz8etrTodvbkBYGizbX9bdMCaY3dpyHr9KBQ1fsbhcri4aa6vXakCrBTSgNlnTKIGts6BzJBgMYAiFWYegpNiiLGRlg7d/qTTU3uB984cZzl+AnFXQwGCNHwKvH4KiXMuAqDbAwjhQLYMOBvBuCC9tpIw/2T0vgNZaN4f74Ww1TV/Ml+ByLfCzHkGMCvz9qdDjRzwG92XDLy1gxD0V03GqDf4h8NBzELACxiwrlb/kQJ9aVtlrYFRC9cp2E7Ue9Dd7HTX4esOlbKsi5Qwxg2BDHOSbYW08NIqGRtXRpG7AhcuQ+AKEGKyybwgJZsi/evvo5hy4VE523j4VZWc8CyOGwz3z4Pmm1aryn88NLly4TEHiCzQLMWAwGDAYGjIuwUxx/lXMgEOXmayc1ZQjM/rT2NuD4LbRzDuUf4c6Ly33TIpnfo8sPhzeCn+PAJoPfJOd2ZbUzRnpXCw5y/9FhVnLZqBuj7mcsSskL/cumH2pNJYuQaNFq9Kg1YJKo0FtMmICbqSs4uVB7WkYailbWL/5nC4uptgImHPIulQLPz83a1NRofP2KR20zRc5f7GYpDc6Emqtm6HeEL64YuJ6bvFtZVM91Lh5uKHKz+NajR6YCkcnRwgfyqQh4bhoHQnq/SzRkens2HEak1xh68uTOT5kDk9HVGYkYObM/MfoPw+e+z6LwpJrnFvdk30x3XjpuwKQbFY82ZfXfx3Ixl+vU3Ijg69jM5nYdQwbLpUtqOnEEj75vh4xI1qXKlo2+ZxfuYBNuiGM7Ola4W6VqPX42vQ3emt/c9na33SJGYT9hji+zjeTvjae7xtFM6ya/c3t3imVx0DmrJiAb+IketbzxLNeZ56KP1nRXlzyyb2mxc1dd8eU8z+bcsqCdTCr8QnQWmgUDinHSgf4ghOQ5gwN69jkFgQL1sKy6RA/AtZl2KShgcn7Sp0kH3/T1nPFf4FA9nIYughGrYEzaZB2Bl5pZq2nCrz1kH2R30xXzdmQffOHGvz9IPxpOJUGadbrfBbsfa20jPWiYOl2SMuCzdHwyVjYabN3pt27YLTWreg7Kqrht0DtBZ7FcLWw9H9XrpRTtMyw/Ck42AX6/gxjFletaGlUkPxjaRiVF2wptMreBAt72gYGjblU8ZECuF6ufZizIetmADNkZIGXd2nrahMNXltg0yH44jDEPFK25alUlgG8QrtzBD9PGBpXKve0NMjMgQ+6VFFBK2o9eBZC5s1PWYHsrHKyy4fpj0DWGPi4/1/PcFalsr6SFWXj5+eJ79A4UtLSSLNev2bmkPpBF8tXlFpPu6fmsm7PSTIyfuS9RvuYPHEJv5orZPG73GCoXJsyfPYKdh5JJ/PEUrqlvcn4j5IxAmqfAHwdWjNt95nfypZ27gLZWVt4MuimkC2W8Ijcva8vEcR4ivmxT7DF/zUSjp0lLS2NU+vGlL6Saj3enoVkZuZZyyVcz84qbfZqXwL8XOj94U+ldUv7hYs5GcQP1N1WNtVDTVCzpnicPsrJGu1c0lK3QV20apXNIKVCpbbUA9M59u47zYFpzamlUqHShjN5XwFJrzbCqevHnDeXcGz/j5juG05sc0/s1I4Edh7J4IizbEk4idH4MweSrtHskZHc518Ltb03bcY8RuusrWw+ZLuXu5DdCxfxc7tYoiMqGahNJ1iy4HtCo5+gXUVNomrM2Vy06W+yrf2Np/X5ObSJ5lGvLcRtOsTKLw7TNuYRQsv1N7/7nUJLYPdJfLJ5P6ey0vl2Um02PP0a68vNlkn2cU5cCqdZk5pW7q+LusJPby9ITabSvUwlRVBYZOlZjMWWv41iiddvGGTFwdJUMF6G994D1wHQ2ckmAS3YqaDBOHi/BYyNhdN3Yb9MUT4YPSEy2FLjqz/A5ze3fqqg2wDIXQVfnAIphrXz4IzNtECvWLi2GObuhiKBknxI2gSJaZb75l9g1TbIvAFowNEBVE7gdAd0Sm1T6BcIK1ZbBnfjWYjfWTbMsTnwfAos/gQWLIWMV+Ata/0uboW3V8DJ85B/Gb77GOYegLb3VU8Z04ZByHnYd97y++RKSCp3wIM5A+Z+BtcE0jfD0lPwcK/S1qVtAtH1YGYspHSB/n5l46tcQW8HyUfLDeT2MCIG1s2Ar9IsylxBJmyPK3cWRTFMbglNJ4Dt3mZtU4gKhgVz4JIJcg/CJ7tsCw4rRkN8KCx/GWwmwcpgPMzsbuE0fHwFOXd7TlHlirfejjPJR8kvJ5v7RsTgsW4Gs75K47oZTAWZHN0exxarbK4nb2Tl7rPklggqO0cc7VRonZ1xsG2Waj0+tS9w5EhODbd5mUhNWMaOlMsUCWgdnbFXq3FydkQFqAP7E9s9hbkvL+HwpRKQYq6e3cvaVbvJ/C0jNZ7eXkhqMsd+997J34FcJy9fjW/DJgQ4qsCUwbaFazh9s0lpmxIVFcyeBXPYfcmEOfcgH32yq/TrURvJ0BFN+PatV1iTkocJM4U5qexavp6kfLmtbKqLfZuH6W3/LV8drLhhX4zFFBUWUmwURIwUFRZSVGIC1BgeGkTL0/F88OUvFEoJmTvnE58cSJfOYWi09zDjSAlisVdDjCnMbu1E81nHKEh8igC1lohmjVHtWUb8sXzMGLm0/wvWH3UkPCIQjTaMZk0cObxmKQcuGcGcx9HPV7FfXZ+GoTZ+Ca9uYcGyXHqNHExgJQp44e6FLEq9l9iYRjVfrTVnsH7uZxy7JhSnb2bO0lO0fLgX/jb9zfDoenw9M5b/S+lCTH+/snL/L94pydnLug0HSb9uArU9TrW0qGo541SmEsLlb7ZzOPwh+ob9g/b4V7BiyEkU6VFPxMtXJCBUZIPV9Mh0WqS9/c3vfuulFZmWbI1oFNn6qkiEl4ijq0jLYSIHckvTLbMbQkTMWSKxoSLt3pDbWzcVi0xubrGU99aJ2Lla/g5tL7KvxGLg2PEDEVOxyHNhljIZj4u0MojsKBIx54p8MEQkLFykfSeRPiNFnmwj0uED6w4Co8iWV0TCaovUriMybKpIa53IApudGieWizwYKeKuE3H1EmnRV2T1GWvVU0VGtBPxdRdxdRMJaiXy72+lUvPfylg3ylKfIC8RtYNIQLBIcF2RD60GlPlJItGtRRq2FGnbTWR4p1KL/txdIk31Im8ll6Z3Yq6ITwORhByRrG0ifVuJ+LiJ2NmJ+ESIPLlA5Ep1C2cW2faiSEigSKuOIjFTLcacle2GqONu2Q0xfqVIefvD9AUizmqR6FvswjjwvkhjPxEff5GQgSLnb5oeFYtsnibSKsiyo8Gzjkj3WJEjtgZ5hSKP1xbRPSpSWC7da4dFoltankv97iKTo0QM460GjldE+tYScXQT8fS0Xl4iozaVTePPNHAUkWsH3peoxn7i5eMvASEDZZGNbM5tniaDWgVJbReduHjWkcjusbLIKpv8ndOlZ9Ng8XR1EVd3H2nQ7VlZllJeQMVycnGMtAj0Er1/gAR3fVuOVsswt0SSPoiSlqF6cXVxFXd9XbnviQWSlFcqIPPVg/LJ2G7SwMdVdDo38anXVgZOT5BMGxmacxLl9R71xMfLVwICQmXUhuqZOuavGyX1g4MtuyHUDuIRECzBwXXlgQ9TxWhMkdlt68jor4rEnLlQeroNklWFIoXrhopnl3mSbjJLVuJ06du4rkTce7906vyQPPNatDTU9Zdl124K/bAsiG4pfq5u4lO/u7w4OUp8DeNl12+7ITJl17vRcl9dvbjqXMTDP0I6PjZHfsivnmyqR4kkz2wphhEbJbfc//e/FC5ai2r922XfZZ6km0REiuXs+held0MfcXV2Fg9De4ktY+Bog7GigaMUnZZ1kx+USD83cXbWSe3gVjJ41na5YA1guvC1zBrcSoI8dOKscxf/pn3lpbWnbF55k/y6oIe4Bo6WhGsVchQxX5E1Q72ldv/PJbumIrHdDVHHXXTuBuk4fqWcLtffmNIXSA9ntXhHb5DKbCt/7ztlurheJnRuKAEeruLq6iH+kX1lyuZfy9qym87JvG4B0nfx+QoGlH9nFK+TlWE6Ai07wCu/wiDFSekd4domCB8HS05CN8c/rxyrh8CsCDg49Q4tcyn8L3B99RDqzIpg58GpRN7FdiO52xnXfiahq3cwsYHSYKvNtU2MCB9HrSUnmX+X+5trO56h7RRfPt81hcjbW1X+bShtfap/ihnG70BKYMc2aNoLPFWwaxGkt4f21iWU/2XZ/LeIADdg4fvgPgw6Ot5deWbsg599oX0QFKbCkl3Qfbyl5d+uHIoe/T+LOXM/X/3sS4f2QTgVphK3ZBc+3ccTfpfHa5Vbdz4+2v3uZvq35wbHF77Pl+7D2Nbx7n+Y6Lp8yJEf7nq2fzg2i0z/yx1jMez8FwyLBbUGajeH//wfvy2C/U/L5r8k41No8Ax4dIAlk8COuyvPs0tg3ADINIOmFvSYCq+3tdxTnqvCrSg4wefjBhCTaUajqUVIj6l8/nrbSqz6Ff5KSMan9G3wDN96dGDSkkm0rOSwYYXfh7IMoaCgoKCgoFAlf7WNYgoKCgoKCgp/MRRlQUFBQUFBQaFKFGVBQUFBQUFBoUrunrJQtA7cwmBPye3DlkdyYHh9MPiDgzOsqdGRZpZDkzq6wIKM24etjP3Toa4BvJ2h2YyyxzjfSXLjweXecgcOVcL2MWAYD79DlHec68vBpTkc/Sf5YlX4a2Pi548eJMxgwNfVnqBndtbwVTCS9Fpj3B5dW/GY3uogOSwbXh+DwR93B2ceqWl/VJOscrczrklH3jl5Fw6vuyP8l7K9C0j2KoZFPMAnaXfh2PF/EOWUBSNMvwcGrawY0pQKT/eFBt6gsYPXksoHgITXoZEPOLnBvcPh4B3yGKPygrhUOLUF6v8JJ2LdOxVOp8GHvf/YfBxbwbuToEYOZ26HwK7Z0LUZuNmD4wC4fvtYdxXzeejqAvPS/+yS/PUwn+fjri50mZdewxMWq0nRaga7RDI1+c8YjIz8NP0eXAatrPTA2Fujod7TmziVlkr8MO+7f/a+yotH41JJO7WF8X9of2TkyNxX2Hrvi4y+xRkLxtQP6equplbPT8i0mqobk6cSaWc5SttyqdFVOnibubBsEH4ae1q8cdz6DSTk7p3H6F7NCdE74+DkRf1Oo1lwKPeuOkQq/mYcQXWeYkfFwyv/a1T6KF4elsW/pm8hVzHvrzY1GJW0EBkFH/8HWlWyH+XXxTB0MTz/LeSdhT5nYNBkyL9jZf3nYx8OoweB+x3u/pyC4Ik34e0BysKTgsLfhYIdzPv0Kv1GdKdSV0umU3zy7H+4Ee5b8bWuFUVcTj75+ZYr8z/9Kmz7lIxVTHz7PCFlXE8K1y5eona/mazee5bMc7uY1eAHJjz0HJtz72Tl/ky0NBw+nOANH7L8gjK7UF1uHiQAXzwGhjCYcwK2Pm318BcOm6w6vyYURj8BnRpT9nB5ADOsjwfv4RATDtra8MLzkLcavimoJFszbJ8EQa1he+YdqIYJFo+EyCBwdQF9GDwxn7Jqo8ChuRDpBy5e0PtVuGAzdZ6yAvo0Bjcd+ERYvEZW+2NL4MBH0MYA7h6gN8DDH1Q/vvEIdKsLwXpwqGQZIj8JoluBmwvU7QJbLtpknQkjwmDIcqsjLIEvn4DgRyDdDKig1aMwrDeE1NC7G0DRanCJhJtfnpIDfVxgdopNoGKIi4U67uARAs+ssPpoEPjsAYicWlYWG4ZD8JNQUAzPNITQNrCnAKa2tbS7+kPg4s1nVwJbpkGLOqBzgbqdIP5E9ct/PRkev9fSLsK6wcSHbZZwjDCjLfj6ll5OGnh0bdk0jMm83asRkbEruXTXvkSK2fZMQ0JC2/D6ngJ+mNrW4uGw/hCW2Mjm1y3TGNCiDh46FzzrdmJc/InSr3TjOTa82ItGfh64e3jiH96BCRsyLF+IJfuY1i4UQ/hTbClIYW4fi3fIsJ7vcbyaK0qStYNZ/ZsRWNsdj9o+1G0zgiWnSiNLbhILn+xCfb0LOjd/7hn4JjuzzICQ/cVj1DeE0XvOCQq2Pk2EwYDBEM7YTXfGSYTkfM2M/m2o7+uBi4sHgU37MWXjuTLLFZKzkxl9GuDt6opv04G8vfty6dezOZvv3htOu5Da6HQeBLWOYd7B6n9d30421aHoh3VsKe5Aj5aVHQNo4szC8SwMmsqr9ztXMruipZZOh06nQ6dzxtmh3AyIZLJm4r8oHv8GD3nZqhpqAqJe562xD9Cirjfu+kYMeG4oja4c4kBa9WefbiVb08nZtHbrwkfnSgdpufgpvd2b8FqSEVPqhzwQZqD+o3FczIhnaH0DBkMo907Z/duzu5Gygol9GuPnpsPVJ4LeL23kl9+KJuQd+IjhbQx4uXtQW2+g2cMf8GO5oqsDu9DNsJcNCTn/GBfSfzhlT38uEZnWVGTgilsfEG06J9LBSeTVQzb/LBIZ4yvSL17kzDqRCe+LZBwRae5U6kPgN98Q10XWjBYJ7iKy50rNDqcu+VGksYvI6vLn25eIxP9b5Ic0kSKzSNa3Iq1dRCZ8Z1Nme5GQaJEzN0Sup4oMDBR5eKnFf8PVBJFQD5GJm0Wum0QyEkVa6UXmpJbNZvkAkXumi5Q/O9902uIv4bX9Fl8ThVki2/dUDHc7rsaJ6FqJnLCNWCjyQrhIy5dEsktEsnaKtHQUCbL6hhARyftepFmAyEcpImcWidRpJPL15YrpfzVaxKm/SGXntd+KwlUiuiYih62+GMzZIr11ZX1D1FKL9J0nkm8S+XW9SLibyHsplvuXV4ro64vssR7ebr4kMtBLZOKe0jxM6SJddCIf/Vox//2virg1Ell2XMRoFNk/W8QnUuRAeecTlRZeZHJDkeaTRDKKRS7tEWmrKys7W05+LOIfLrIps+z//0zfEKZ0mddFJ50/+rXCOfOF+1+Vpm6NJHbZcck1GuXy/tnS1SdSplhlU7htpPj6D5b4X4pExCh5Z/fINz9dLuuypHCVDNI1kdcPl0jNKJEDL0eIe/c5crLALGK8LukHE+XARWspTefl84F+4tPtDdl1oVBMN87KmpENxHfA5zYyLJHkaU1FN3DF7d3DVEqRbH8yQIKe/qbC4zRd3Cbz5m2Vo5nXxWi+JilLhkiQWy9ZeN4kIiVy6NVGonWIlOcSLkqxKVeS3u4mXnVGytY8ERGjpHzQSTwMA2T+wRwpNuXL8YUDJChkjCTYOhoo+VFea+wigyvpj6qUTbUwyc9vtxXn9u/K6UqiGc8skD6NhsmqzCLZMzFMnGzaZsnh16WJvacE168j/nUaSNtBU2RNqq2EzZK5Zrg07jVfzhRV4huiDGbJiHtYPAOekM2VOVmowG1kazon87q6SevZJ635mSRtbidxbT1bTtoUoGjHU1IncKwklnvNzVcT5MlQD2k9cbOcuW6S4oxEebGVXjrOSbWkZzot79/nLC1f2y9XTSLmwiw5sn2PpFWoXIGsGeIqgeN2VNoVKFTkDk1KC1wrAGcnSE2ApSvgggM4CeTbLpAXQ1wMxByAlV9CW/c7kz1aGDYJ2gSDvQr07WFIUzhyzMaLoRYemwAhtcCpHjw7EHastyyTbFsIRYNhZh9wUoNPZxjTAtZupXoLxWrQAGePQHoeOOihW1tq7k6tEoyHYWM6jJkAXlrQd4CxncqGcWkP8ZPgX1HQ71UYGwddPe5A5tVE7QvPxoJODYEPQnQYbEiwyM6jD/QrgLjvLGGzvoTEQIi+txoJF8OiRdB1CjwSARoNtHoaelyE9UdvH92YDOvPwdiJ4GMHtdvAk50qD3t1JwyeARNWwAPeZe/ZteHfqUYKE0bj85c5+buY7xctIq3rFN5+JAJXjQaPVk8zvsdF1q8/apnI0WjQ3Mgg5dgpsgvVuBja0qmJxx1b49doNJRkn+JoSgYFKicCWnShpdXexnx+LQu31GbU7Bfp4OeAupaBfhNjCEpcTeIdMmWqCrVvT556qheNvJ3QqJypP+Rxejie4KefS7/u7duO4vluvtipXWk2dhw9r29m/b5iMB4h/tP9NJnwLqNbeGKn1hER8zwDNRtZs7d6i+hVyaZ6mMm9kovoXNFVmMhNY/H4d7Gf9Bb9vSs+TbVvb2as2sDGTTv5Zs2/eOBGHMN6T+Jr65KwZH/Ji1PO8fh7Iwm5TR9VnLqQUS//RO85M+nlUv3S31K26joMiunEqc+/4KgRMJ1ixRc/0irmUepVo7/M27aQZUWDmTmzDyFOaux8OjNpTAuS1m61TKSiRqOBq2ePcDI9D5ODnsbd2hJcIW0NOhdH8q/m/TG2QP9A7pCyoAKdE1wvgJ7zIecHiCyBAkBn4/fXnA7f3ICwNFi2v5w7YhPMbm05r1+lgoav1GAZoAS2zoLOkdblk1CYdQhKim3yUIOvvjSK3hdMlyHXCOcvQM4qaGCwxg+B1w9BUW71lAW1ARbGgWoZdDCAd0PLMobtrOOeF0BrrZvD/XC2mk3UfAku1wI/N+s/VODvT4UeP+IxuC8bfmkBI+6pXto3kRzoU8sqew2MSqhZfLUe9DffRjX4esOlbKvsnCFmEGyIg3wzrI2HRtHQqDqa1A24cBkSX4AQg/XZNIQEM+RfvX10cw5cKic7b5+KsjOehRHD4Z558HzTalX5z+cGFy5cpiDxBZqFGDAYDBgMDRmXYKY4/ypmwKHLTFbOasqRGf1p7O1BcNto5h3Kv0PTrlrumRTP/B5ZfDi8Ff4eATQf+CY7sy2pmzPSuVhylv+LCrOWzUDdHnM5Y1dIXu4f3z1LbhKfPduXe8NDMISEYKj/OCsuFVFcXFp7td4H/c0e0N4bH/c8ci4ZwXyR8xeLSXqjo2Xpx2DAUG8IX1wxcT23OspC1bKpHmrcPNxQ5edxrUw0M+lxE3ir6FneeSyw0g5c7dOGhx9qT5N6odRv9TCvfPYaHS+sYdXeYpArbH15MseHzOHpiKodXZSc+YIRD76F5rVNLBzoX6PB4payRYW+3+P0zlpB/IFijMeXs+znzjw+sPK6lMXMpfMXuJGzihENbrb5EFq+fgiHolyumAG1gVEL4ximWsaTHQzU9m5In5c28muFFSAT+Xk3cHF3Vcy4qkm51mIdzGp8ArQWGoXDrmOWAV4LFJyANGdoWKc0mDoIFqwFnwVw/wi4fy/097Xe1MDkfTC5imxUatAIGMs9+ezlMHQRzEuAIfVAbYb37ocNtvUwQ0YWEGCNkwFaL3DXgr8fhHeDQ9Or9kSo0YDRSKW9bb0oWBoFGOHAO9BzLHTvCV2t643t3gXju1UkfgvUXuBZDFcL4aaJ0pUrIE5l67b8KTjYBfomw5jFsOaJ6ntVVHnBlsJb3NSAxlyq+EgBXC8nAHM2ZJmwZGiVs5d3qSraJhq8esCmQ/DFYYhZWlZNVaksA3iFducIfp4wdAl83LWalbFBrQfPQsjMA/SAQHYWiMEmUD5MfwSyxkB8/7+eAahKZX0lK8rGz88T36FLSPm4a+U+C9R62j01l3VPgRScZe34XsRMXELfxKcJsqnn73rlAZVrU4bPXsHw2VB0IZHXHurH+I/6kDT9HtQ+Afg6tOaZ3V8zLvBWQrVY6yPyOxUYFRqNGpPRWC6+kYP/GsYLSUPY/N0a2nvbQ9FWYoNiy4QzZ2WQbYY6aqAki8xcd/ReWlD7EuDnQu9Xf2Ll4CrsfFRqNBrBWL4/omrZVO+1VBPUrCke7xzlZBGE/uYPycjJvfs4u309YdpxNuHH4Ov0NauurmRg+cagtcdOZcJkAkzn2LvvNAc+a06taTZh9jXCacc8zmx/igA1FJ+K4/EHplE4aTPLRkVQq1plLuWWsgVw7cnjURMYGf8NfV1XkNnnTR7Sl9XgVSoVKjGXe65qPP39cA7vxuZD02l6C0HWqhfFtKVRTMPIpQPvMLjnWN7s3pP5XW1sP0ynOJYCTbo3VJzPVhN1hZ/eXpCaTKV7mUqKoLDI0rMYiy1/G8USr98wyIqDpalgvAzvvQeuA6Cz7aCmBTsVNBgH77eAsbFwugZbttR1oJ497NhV9ou/KB+MnhAZbKnR1R/g8/JbO43w+RxIK4QbP8MHq6FrFOiAXrFwbTHM3Q1FAiX5kLQJEtPKJhHWANK/h9PlNiGZf4FV2yDzBqABRwdQOYHTHZjw1TaFfoGwYrVFETOehfidZcMcmwPPp8DiT2DBUsh4Bd6yqb/ZCEWFUGICMUFhIRRVc2e6NgxCzsO+85bfJ1dCUrm45gyY+xlcE0jfDEtPwcO9SluXtglE14OZsZDSBfr7lY2vcgW9HSQfLaeI2cOIGFg3A75KszzzgkzYHlfOCLQYJreEphOshpU2sosKhgVz4JIJcg/CJ7tsCw4rRkN8KCx/GWwmwcpgPMzsbuE0fHwFOXfbGkrlirfejjPJR8kvJ5v7RsTgsW4Gs75K47oZTAWZHN0exxarbK4nb2Tl7rPklggqO0cc7VRonZ3L2ier9fjUvsCRIzk1nI41kZqwjB0plykS0Do6Y69W4+TsiApQB/YntnsKc19ewuFLJSDFXD27l7WrdpP5W0ZqPL29kNRkjv0uu0YNdRvUJW/fNxy+VvbDID//Go5BjYnQ2wPFnFn2KVsvl314xXs/5b2vMygx53F4/jwSdA8Q1doetJEMHdGEb996hTUpeZgwU5iTyq7l60myfQjqOjSoZ0/yjl1cKiO8qmVTXezbPExv+2/56qBto7an2/wLmEQQEUSK2TMxDKceC8goWMlABxNnEpaw7odUkIUsxQAABWJJREFULlzJ5+ov+/jPC2+xo/aDPNzaDrT3MONIiTWuIMYUZrd2ovmsYxQkWhSFwhOfMrTna1x/di2LhodAYSGFRUUYa9BAbilbABzp8PgjOK5+gXGfF/BwTI8Kuz3UXj545h7np1/K9jWuvWIZeG0xr87dzcUiQUrySU/axLLENMv3jPkXdq7axpHMG5jR4ODogFrlhK5cX2z+JZGvz7WmX0/93d96+3elghVDTqJIj3oiXr4iAaEiG6yGMabTIu3tRSyqgvXSikxLtkY0imx9VSTCS8TRVaTlMJEDuaXp/mbgaDUnMWeJxIaKtHtDamTddPwzkUi9iKOzSPOpIiUiYs4V+WCISFi4SPtOIn1GijzZRqTDBxaDQ9M5kQ7OIqNfEYn0FdF5ivSaInLBxnLoxHKRByNF3HUirl4iLfqKrD5TNm9zlsiUriKujiLOniLLrRY/xlSREe1EfN1FXN1EglqJ/Ptbkeoaw60bJRIcLBLkJaJ2EAkIFgmuK/Kh1cAyP0kkurVIw5YibbuJDO8kEmw10svdJdJUL/JWcml6J+aK+DQQScix/N76hIiass+u1iCR8nZZlWIW2faiSEigSKuOIjFTLcactgaOukYiL8aI1HEXcTeIjF8pUt7+MH2BiLNaJHpD5dkceF+ksZ+Ij79IyECR8zefTbHI5mkirYJEXHQinnVEuseKHLE1yCsUeby2iO7RinW6dlgkuqXludTvLjI5SsQw3mrgeEWkby0RRzcRT0/r5SUyalPZNP5MA0cRuXbgfYlq7CdePv4SEDJQFtnI5tzmaTKoVZDUdtGJi2cdieweK4usssnfOV16Ng0WT1cXcXX3kQbdnpVlKeUFVCwnF8dIi0Av0fsHSHDXt+VotQxzSyTpgyhpGaoXVxdXcdfXlfueWCBJeaUCMl89KJ+M7SYNfFxFp3MTn3ptZeD0BMm0kaE5J1Fe71FPfLx8JSAgVEZtqKGpY94+eeeh+uLh6CjOHt3kozSLbIzn1snzXSMkrHEb6dCpqwyaPFn6B/rL6K+K5KYRnku3Z+SV3uGid3ER7yYD5e3dNsafpkzZ9W603FdXL646F/Hwj5COj82RH/LLZl94/DN5LFIvzo7O4tZ8qhwqqZ5sqkeJJM9sKYYRGyX3lmGKyxk4GuXYxwMkso6HOGrVYufsK416PiP/Sc6rvDsyljdwLJH9L4WL1qK2l15qX6vsbl/m28pWRMR4VGY1txNN2Auyu7JkTb/K2vH3iUGvF7+AOtL8pe9+M0S8fmK5THwwUgLcdaJz9ZKQFn3lhdVnLAbAxlRZMqKd1Pd1FxdXN/EMaiVD/v2t5JTJvESSpzeX4BEb5eqf8D7/XVG8TircHa5tgvBxsOQkdLv7PuZ/Y/UQmBUBB6dWf5lGQeFPQnK3M679TEJX72DiLQ5m+lsimfznoQa812wHSTOa3dVXUbJXMez+xXTatonRhr/auuNfl1JlQaVMxij8AYgAN+D9B+HT1nD4TcuOlbtFxj742RfaB0FhKgzuCA3WwNvtbt/mFT1aQeEPQMjb+yqde33LYwd3MiHsTziVV6HGlCp0Sseo8EeQ8Sk0eAY8OsCSSWDH3W1rZ5fAuAGQaQZNLegxFV5va7mntHkFhbuL6Rhv3d+WGScD6DNrGWMUReFvg7IMoaCgoKCgoFAlyoKNgoKCgoKCQpUoyoKCgoKCgoJClSjKgoKCgoKCgkKVKMqCgoKCgoKCQpUoyoKCgoKCgoJClSjKgoKCgoKCgkKVKMqCgoKCgoKCQpUoyoKCgoKCgoJClSjKgoKCgoKCgkKVKMqCgoKCgoKCQpUoyoKCgoKCgoJClfw/rudvVrCmazYAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "3c21415c",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)\n",
    "\n",
    "\n",
    "**Dowload**: http://yann.lecun.com/exdb/mnist/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c8773fea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['train-images-idx3-ubyte.gz',\n",
       " 't10k-images-idx3-ubyte.gz',\n",
       " 't10k-labels-idx1-ubyte.gz',\n",
       " 'train-labels-idx1-ubyte.gz']"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# after download\n",
    "os.listdir(r'./datasets/mnist_784/compressed/')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20476d3f",
   "metadata": {},
   "source": [
    "### Auxiliary functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5cf7d086",
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_dataset(path_dataset):\n",
    "    with gzip.open(path_dataset,'rb') as f:\n",
    "        magic, size = struct.unpack('>II', f.read(8))\n",
    "        nrows, ncols = struct.unpack('>II', f.read(8))\n",
    "        data = np.frombuffer(f.read(), dtype=np.dtype(np.uint8).newbyteorder('>'))\n",
    "        data = data.reshape((size, nrows, ncols))\n",
    "        return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "39a60e58",
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_label(path_label):\n",
    "     with gzip.open(path_label,'rb') as f:\n",
    "        magic, size = struct.unpack('>II', f.read(8))\n",
    "        data = np.frombuffer(f.read(), dtype=np.dtype(np.uint8).newbyteorder('>'))        \n",
    "        return data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aea9eb59",
   "metadata": {},
   "source": [
    "### Load datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "02a7308b",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = load_dataset(r'./datasets/mnist_784/compressed/train-images-idx3-ubyte.gz')\n",
    "y_train = load_label(r'./datasets/mnist_784/compressed/train-labels-idx1-ubyte.gz')\n",
    "\n",
    "X_test = load_dataset(r'./datasets/mnist_784/compressed/t10k-images-idx3-ubyte.gz')\n",
    "y_test = load_label(r'./datasets/mnist_784/compressed/t10k-labels-idx1-ubyte.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2ea7067f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimensions:\n",
      "\n",
      "X_train.shape = (60000, 28, 28)\n",
      "y_train.shape = (60000,)\n",
      "\n",
      "X_test.shape = (10000, 28, 28)\n",
      "y_test.shape = (10000,)\n"
     ]
    }
   ],
   "source": [
    "print('Dimensions:')\n",
    "\n",
    "print(f'\\nX_train.shape = {X_train.shape}')\n",
    "print(f'y_train.shape = {y_train.shape}')\n",
    "\n",
    "print(f'\\nX_test.shape = {X_test.shape}')\n",
    "print(f'y_test.shape = {y_test.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea6a4b39",
   "metadata": {},
   "source": [
    "## Histogram of labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2d080c82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1050x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(figsize=(15, 5), dpi=70)\n",
    "x_ticks = np.arange(min(y_train), max(y_train)+2, 1)\n",
    "bins = x_ticks - 0.5\n",
    "plt.hist(y_train, edgecolor='k', rwidth=0.8, bins=bins, color='#AA99AA')\n",
    "plt.title('Histogram of y_train', size=16)\n",
    "plt.xlabel('Label', size=14)\n",
    "plt.ylabel('Frequency', size=14)\n",
    "plt.xticks(x_ticks)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f7cd879",
   "metadata": {},
   "source": [
    "## Looking at some samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ed93cc5",
   "metadata": {},
   "source": [
    "### One sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f6e4a523",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0,   0,   0,  85, 243, 252, 252, 144,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0,   0,  88, 189, 252, 252, 252,  14,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,  91, 212, 247, 252, 252, 252, 204,   9,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,  32, 125, 193, 193,\n",
       "        193, 253, 252, 252, 252, 238, 102,  28,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,  45, 222, 252, 252, 252,\n",
       "        252, 253, 252, 252, 252, 177,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0]], dtype=uint8)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train[7,:,:][10:15]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9f73c79b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 100x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(figsize=(2, 2), dpi=50)\n",
    "plt.imshow(X_train[7,:,:], cmap='binary')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a09750d",
   "metadata": {},
   "source": [
    "### Matrix of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "265620ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1050x350 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows=5, ncols=5, figsize=(15, 5), dpi=70)\n",
    "for idx, ax in enumerate(axs.ravel()):    \n",
    "    ax.imshow(X_train[np.random.randint(0,len(X_train))].reshape(28, 28), cmap='binary')\n",
    "    ax.axis('off')\n",
    "    fig.suptitle('5x5 digits of the Training Dataset', fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "323968b7",
   "metadata": {},
   "source": [
    "### A random sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2fb6d593",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "idx_random = 36781\n"
     ]
    }
   ],
   "source": [
    "idx_random = np.random.randint(0,len(X_train))\n",
    "print(f'idx_random = {idx_random}')\n",
    "\n",
    "some_digit = X_train[idx_random]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7d30d91a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 29x29 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_dpi = 30\n",
    "\n",
    "fig, axs = plt.subplots(figsize=(29/my_dpi, 29/my_dpi), dpi=my_dpi)\n",
    "plt.imshow(some_digit, cmap='binary')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ab8c3478",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(28, 28)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  11,\n",
       "        112,  34,   0,   0,   0, 249, 157,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0,   0,   0,  72, 252, 106,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   2,  60,\n",
       "         60,  46,   0,   0, 140, 253, 106,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0]], dtype=uint8)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(some_digit.shape)\n",
    "\n",
    "some_digit[10:13]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ec73215",
   "metadata": {},
   "source": [
    "**Note:** shape = 28x28 => 724 pixels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62318157",
   "metadata": {},
   "source": [
    "<a id='multiclass_classification'></a>\n",
    "\n",
    "\n",
    "## [^](#summary) 2. Multiclass classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "865cb08a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b9e4bebe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000,)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "739b00f7",
   "metadata": {},
   "source": [
    "### Model SGDClassifier\n",
    "\n",
    "`Stochastic Gradient Descent (SGD) Classifier` is a simple but very efficient approach to fitting linear classifiers under convex loss functions (e.g., Logistic Regression). It has a good performance for large-scale learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a54dff32",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import make_pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6b0a2b7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_sgd_classifier = make_pipeline(StandardScaler(),\n",
    "                                     SGDClassifier(random_state=42))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "531b2015",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 229.40 s\n"
     ]
    }
   ],
   "source": [
    "init_time = time.time()\n",
    "\n",
    "model_sgd_classifier.fit((X_train).reshape(len(X_train), 28*28), y_train)\n",
    "\n",
    "print(f'Elapsed time: {time.time() - init_time:.2f} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "10b32e45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2], dtype=uint8)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_sgd_classifier.predict([(some_digit).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fcb2eef",
   "metadata": {},
   "source": [
    "**Question:** Is the predicted value equal to or different from the randomly chosen value?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "003d4f4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8933"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_sgd_classifier.score((X_test).reshape(len(X_test), 28*28), y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "819493f6",
   "metadata": {},
   "source": [
    "### Model SGDClassifier (with probability estimation)\n",
    "\n",
    "**Note**: For predicting probability we can use `loss='log_loss'` or `loss='modified_huber'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3e4605d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# to add probablities\n",
    "model_sgd_prob_classifier = SGDClassifier(random_state=42, loss='log_loss', \n",
    "                                           alpha=1e-3, class_weight='balanced')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "91ffc096",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 8.89 s\n"
     ]
    }
   ],
   "source": [
    "init_time = time.time()\n",
    "\n",
    "model_sgd_prob_classifier.fit((X_train/255).reshape(len(X_train), 28*28), y_train)\n",
    "\n",
    "print(f'Elapsed time: {time.time() - init_time:.2f} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "39e2a5ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2], dtype=uint8)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_sgd_prob_classifier.predict([(some_digit).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4f2d90a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.24951769e-92, 0.00000000e+00, 5.00000000e-01, 5.00000000e-01,\n",
       "        0.00000000e+00, 0.00000000e+00, 5.54565586e-46, 0.00000000e+00,\n",
       "        8.59815555e-98, 0.00000000e+00]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_sgd_prob_classifier.predict_proba([(some_digit).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "83a5f5ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9132"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_sgd_prob_classifier.score((X_test/255).reshape(len(X_test), 28*28), y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "386f0357",
   "metadata": {},
   "source": [
    "### Model Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "382c7bba",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "05c0289a",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_rf = RandomForestClassifier(max_depth=16, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "64c1d432",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 20.21 s\n"
     ]
    }
   ],
   "source": [
    "init_time = time.time()\n",
    "\n",
    "model_rf.fit((X_train/255).reshape(len(X_train), 28*28), y_train)\n",
    "\n",
    "print(f'Elapsed time: {time.time() - init_time:.2f} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a6c3a76d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2], dtype=uint8)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_rf.predict([(some_digit).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "91abb0b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9676"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_rf.score((X_test/255).reshape(len(X_test), 28*28), y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d578a0e",
   "metadata": {},
   "source": [
    "### OneVsOneClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "63dd8371",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_ovo_classifier = OneVsOneClassifier(SGDClassifier(random_state=42, n_jobs=-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "e9339103",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 16.457059860229492 s\n"
     ]
    }
   ],
   "source": [
    "init_time = time.time()\n",
    "\n",
    "model_ovo_classifier.fit((X_train/255).reshape(len(X_train), 28*28), y_train)\n",
    "\n",
    "print(f'Elapsed time: {time.time() - init_time} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f2307b16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2], dtype=uint8)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ovo_classifier.predict([(some_digit/255).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "953c1baa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9315"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ovo_classifier.score((X_test/255).reshape(len(X_test), 28*28), y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "033950c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# %whos"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98dc2697",
   "metadata": {},
   "source": [
    "<a id='nn_models'></a>\n",
    "\n",
    "\n",
    "## [^](#summary) 3. Neural Network Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ad33457",
   "metadata": {},
   "source": [
    "### Model MLP Classifier\n",
    "\n",
    "`MLPClassifier` implements a multi-layer perceptron (MLP) algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "5aafa1e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neural_network import MLPClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "c653b898",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_mlp = MLPClassifier(random_state=42, max_iter=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "032ea874",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time: 42.81110858917236 s\n"
     ]
    }
   ],
   "source": [
    "init_time = time.time()\n",
    "\n",
    "model_mlp.fit((X_train/255).reshape(len(X_train), 28*28), y_train)\n",
    "\n",
    "print(f'Elapsed time: {time.time() - init_time} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "64b7e1eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2], dtype=uint8)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_mlp.predict([(some_digit).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "53772f7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9782"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_mlp.score((X_test/255).reshape(len(X_test), 28*28), y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec456ba7",
   "metadata": {},
   "source": [
    "<a id='results'></a>\n",
    "\n",
    "\n",
    "## [^](#summary) 4. Results\n",
    "\n",
    "\n",
    "|     Model                         | Score (X_test)     |  ~Time (s)        | Variable                   |\n",
    "|-----------------------------------|:------------------:|------------------:|:--------------------------:|\n",
    "|SGD Classifier                     |   0.8933           |   229.41          | model_sgd_classifier       |\n",
    "|SGD Classifier (loss='log_loss')   |   0.9132           |   8.83            | model_sgd_prob_classifier  |\n",
    "|Random Forest Classifier           |   0.9676           |   20.16           | model_rf                   |\n",
    "|One Vs One Classifier              |   0.9315           |   16.44           | model_ovo_classifier       |\n",
    "|Multilayer Perceptron Classifier   |   0.9782           |   40.98           |  model_mlp                 |\n",
    "|[EnsNet](https://paperswithcode.com/paper/ensemble-learning-in-cnn-augmented-with-fully#code)|0.9984| ? | [see paper](https://arxiv.org/pdf/2003.08562v3.pdf)|\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3747c61b",
   "metadata": {},
   "source": [
    "### Make a cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46c52bb0",
   "metadata": {},
   "source": [
    "#### 1st model: Multilayer Perceptron"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "098808af",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9732  0.9717  0.97185]\n",
      "Elapsed time: 38.134296894073486 s\n"
     ]
    }
   ],
   "source": [
    "init_time = time.time()\n",
    "\n",
    "print(cross_val_score(model_mlp, (X_train/255).reshape(len(X_train), 28*28), y_train, \n",
    "                      cv=3, scoring='accuracy', n_jobs=-1))\n",
    "\n",
    "print(f'Elapsed time: {time.time() - init_time} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28106618",
   "metadata": {},
   "source": [
    "#### 2nd model: Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "bcf7e0e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9628  0.9609  0.96355]\n",
      "Elapsed time: 54.98952555656433 s\n"
     ]
    }
   ],
   "source": [
    "# init_time = time.time()\n",
    "\n",
    "print(cross_val_score(model_rf, (X_train/255).reshape(len(X_train), 28*28), y_train,\n",
    "                      cv=3, scoring='accuracy', n_jobs=-1))\n",
    "\n",
    "print(f'Elapsed time: {time.time() - init_time} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daff7a98",
   "metadata": {},
   "source": [
    "<a id='save'></a>\n",
    "\n",
    "\n",
    "## [^](#summary) 5. Save/Load the model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9a82787",
   "metadata": {},
   "source": [
    "### Using Pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "ff6deb14",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "\n",
    "output = open('model_classifier_mnist.pkl', 'wb')\n",
    "\n",
    "pickle.dump(model_mlp, output, -1)\n",
    "\n",
    "output.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "b4235907",
   "metadata": {},
   "outputs": [],
   "source": [
    "pickle_file = open('model_classifier_mnist.pkl', 'rb')\n",
    "\n",
    "model_test = pickle.load(pickle_file)\n",
    "\n",
    "pickle_file.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ec15c9e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>MLPClassifier(max_iter=300, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">MLPClassifier</label><div class=\"sk-toggleable__content\"><pre>MLPClassifier(max_iter=300, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "MLPClassifier(max_iter=300, random_state=42)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "0884e611",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2], dtype=uint8)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_test.predict([(some_digit/255).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba0a4b13",
   "metadata": {},
   "source": [
    "### Using Joblib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "9ec0e39e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['model_classifier_mnist.joblib']"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dump(model_rf, 'model_classifier_mnist.joblib')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "4cb3979f",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_test_joblib = load('model_classifier_mnist.joblib')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "58cb2c8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RandomForestClassifier(max_depth=16, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RandomForestClassifier</label><div class=\"sk-toggleable__content\"><pre>RandomForestClassifier(max_depth=16, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "RandomForestClassifier(max_depth=16, random_state=42)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_test_joblib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "b388659f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on method predict in module sklearn.ensemble._forest:\n",
      "\n",
      "predict(X) method of sklearn.ensemble._forest.RandomForestClassifier instance\n",
      "    Predict class for X.\n",
      "    \n",
      "    The predicted class of an input sample is a vote by the trees in\n",
      "    the forest, weighted by their probability estimates. That is,\n",
      "    the predicted class is the one with highest mean probability\n",
      "    estimate across the trees.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    X : {array-like, sparse matrix} of shape (n_samples, n_features)\n",
      "        The input samples. Internally, its dtype will be converted to\n",
      "        ``dtype=np.float32``. If a sparse matrix is provided, it will be\n",
      "        converted into a sparse ``csr_matrix``.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    y : ndarray of shape (n_samples,) or (n_samples, n_outputs)\n",
      "        The predicted classes.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(model_test_joblib.predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16e999f8",
   "metadata": {},
   "source": [
    "#### Make a test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "2564f85f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "idx_random = 30014\n"
     ]
    }
   ],
   "source": [
    "idx_random = np.random.randint(0,len(X_train))\n",
    "print(f'idx_random = {idx_random}')\n",
    "\n",
    "some_digit = X_train[idx_random]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "2e8e13ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 29x29 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_dpi = 30\n",
    "\n",
    "fig, axs = plt.subplots(figsize=(29/my_dpi, 29/my_dpi), dpi=my_dpi)\n",
    "plt.imshow(some_digit, cmap='binary')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "856c086e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>MLPClassifier(max_iter=300, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">MLPClassifier</label><div class=\"sk-toggleable__content\"><pre>MLPClassifier(max_iter=300, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "MLPClassifier(max_iter=300, random_state=42)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "d05b216f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2], dtype=uint8)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_test.predict([some_digit.reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "67c953b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-4 {color: black;background-color: white;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RandomForestClassifier(max_depth=16, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RandomForestClassifier</label><div class=\"sk-toggleable__content\"><pre>RandomForestClassifier(max_depth=16, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "RandomForestClassifier(max_depth=16, random_state=42)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_test_joblib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "ba7264b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2], dtype=uint8)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_test_joblib.predict([some_digit.reshape(28*28)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0396ec41",
   "metadata": {},
   "source": [
    "<a id='read'> </a>\n",
    "\n",
    "## [^](#summary) 6. Read a handwritten digit image PNG and make a prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "1c7ce19f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from PIL import Image\n",
    "\n",
    "import cv2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "80025a08",
   "metadata": {},
   "outputs": [],
   "source": [
    "PATH_IMG = r'./imgs'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "51817e63",
   "metadata": {},
   "outputs": [],
   "source": [
    "l = 1\n",
    "file_name = os.path.join(PATH_IMG, f'digit_{l}.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e3448a1",
   "metadata": {},
   "source": [
    "**Note:**\n",
    "\n",
    "- 1, 2, 4, 5, 8, 9 => ok\n",
    "\n",
    "- 3, 6 => ok?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "ec7fad34",
   "metadata": {},
   "outputs": [],
   "source": [
    "img = cv2.imread(file_name, cv2.IMREAD_GRAYSCALE)\n",
    "# img = cv2.imread(file_name, cv2.IMREAD_UNCHANGED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "a1da9a3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "724e00f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[255, 255, 255, 255, 255, 255, 255, 255, 255, 255,   0, 255, 255,\n",
       "        255,   0, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,\n",
       "        255, 255],\n",
       "       [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,\n",
       "        255,   0, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,\n",
       "        255, 255]], dtype=uint8)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img[10:12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "2602c7f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   0,   0,   0,   0,   0,   0,   0,   0,   0, 255,   0,   0,\n",
       "          0, 255,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0, 255,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0]], dtype=uint8)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img = cv2.bitwise_not(img)\n",
    "img[10:12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "2cedd7a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "blur_image = cv2.GaussianBlur(img, (3, 3), 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "8036b65b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 150x150 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(figsize=(3, 3), dpi=50)\n",
    "plt.imshow(blur_image, cmap='binary')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "8f7e3713",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1], dtype=uint8)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_mlp.predict([(blur_image/255).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "0eb20e7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1], dtype=uint8)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_sgd_prob_classifier.predict([(blur_image/255).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "353a131c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.74161359e-05, 6.43333817e-01, 2.43334704e-02, 4.57142610e-03,\n",
       "        1.82776712e-03, 1.63575371e-01, 4.16589805e-03, 1.14029596e-01,\n",
       "        4.89274472e-04, 4.36459634e-02]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_sgd_prob_classifier.predict_proba([(blur_image/255).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "bd43bd69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1], dtype=uint8)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_rf.predict([(blur_image/255).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "16165bf8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.0028373 , 0.35321106, 0.07411634, 0.04624998, 0.06242589,\n",
       "        0.07556958, 0.03322564, 0.17098307, 0.13025777, 0.05112338]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_rf.predict_proba([(blur_image/255).reshape(28*28)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "4fc5d327",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.62925107932416"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(model_mlp.predict_proba([(blur_image/255).reshape(28*28)]))[0][-1]*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "e5e217cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {color: black;background-color: white;}#sk-container-id-5 pre{padding: 0;}#sk-container-id-5 div.sk-toggleable {background-color: white;}#sk-container-id-5 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-5 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-5 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-5 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-5 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-5 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-5 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-5 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-5 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-5 div.sk-item {position: relative;z-index: 1;}#sk-container-id-5 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-5 div.sk-item::before, #sk-container-id-5 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-5 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-5 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-5 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-5 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-5 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-5 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-5 div.sk-label-container {text-align: center;}#sk-container-id-5 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-5 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-5\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>MLPClassifier(max_iter=300, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" checked><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">MLPClassifier</label><div class=\"sk-toggleable__content\"><pre>MLPClassifier(max_iter=300, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "MLPClassifier(max_iter=300, random_state=42)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_mlp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "af11607f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABUAAAAVCAYAAACpF6WWAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAAAnAAAAJwEqCZFPAAAAo0lEQVR4nN2UMQrFIBBEN59fWnuE9FaewM67pbfLWSxzAnsbK8FU2ZDMv0HYD4KQqYfHzs6yEwBQZ316A/+G7vveF8rM5JzrCw0h0HVdMjMEWpYFSikYYyR2PELP88S6rpjnGTFGWGtF0O9TilortdYopUTMLN2ULD4AHMchnnT8nb4PKi7Ke4+cc9+iSimktRZ5x8bftg33fYu8E/DGJz0U+gN7f7E1WviokAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 28x28 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(figsize=(28, 28), dpi=1)\n",
    "plt.imshow(img, cmap='binary')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "28620814",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 112x112 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(figsize=(28, 28), dpi=4) # dpi=1)\n",
    "plt.imshow(img, cmap='binary')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bb9bcdb",
   "metadata": {},
   "source": [
    "<a id='next_steps'></a>\n",
    "\n",
    "## [^](#summary) 7. Next steps\n",
    "\n",
    "\n",
    "- https://paperswithcode.com/sota/image-classification-on-mnist"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b3ea482",
   "metadata": {},
   "source": [
    "<a id='refs'></a>\n",
    "\n",
    "## [^](#summary) References\n",
    "\n",
    "http://yann.lecun.com/exdb/mnist/\n",
    "    \n",
    "https://stackoverflow.com/questions/39969045/parsing-yann-lecuns-mnist-idx-file-format\n",
    "\n",
    "https://stackoverflow.com/questions/50280640/open-load-image-as-numpy-ndarray-directly\n",
    "\n",
    "https://stackoverflow.com/questions/13714454/specifying-and-saving-a-figure-with-exact-size-in-pixels\n",
    "\n",
    "https://paperswithcode.com/sota/image-classification-on-mnist\n",
    "\n",
    "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDClassifier.html\n",
    "\n",
    "https://stackoverflow.com/questions/7624765/converting-an-opencv-image-to-black-and-white"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "472bc16f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# print(f'>>> Elapsed time: {time.time() - init_time_global}')"
   ]
  }
 ],
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   "language": "python",
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    "name": "ipython",
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   "file_extension": ".py",
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