JNotebooks/tutorial04_fully_connected_neural_network_2D_synthetic_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fully Connected Neural Networks \n",
    "\n",
    "This tutorial demonstrates the usage of fully connected neural-networks to classify 2-dimensional synthetic data. We implement the network using Keras and TensorFlow. Keras and TensorFlow are powerful frameworks that allow you to build many  deep-learning-based applications.\n",
    "\n",
    "The goals of this tutorial are:\n",
    "  - Introduce Keras and TensorFlow to implement fully connected neural network.\n",
    "  - Illustrate the non-linear decision rules that multi-layer neural networks can achieve.\n",
    "  \n",
    "      \n",
    "## Importing Python Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import tensorflow as tf\n",
    "\n",
    "physical_devices = tf.config.experimental.list_physical_devices('GPU')\n",
    "tf.config.experimental.set_memory_growth(physical_devices[0], True)\n",
    "\n",
    "from tensorflow.keras.utils import to_categorical # Function to convert labels to one-hot encoding\n",
    "from tensorflow.keras.models import Model \n",
    "from tensorflow.keras.layers import Dense, Activation,Input \n",
    "from tensorflow.keras.optimizers import SGD\n",
    "\n",
    "import sys\n",
    "## Adding dataset_utils to the system path so we can import it\n",
    "MY_UTILS_PATH = '../Modules/'\n",
    "if not MY_UTILS_PATH in sys.path:\n",
    "    sys.path.append(MY_UTILS_PATH)\n",
    "import dataset_utils "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading and Displaying a Synthetic 2D Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lFY3eL1AZ4Js3Z8QhIhWLhCcAEXGIyBwRmZzoWJKdCSwD3zRqLwkZAHsrVL4XeafQRowd+1Wf2j/5K/xN7gmWkpHS8EYqLhKeAICbgCWJDkIBgflEbO835eGJ3yIKhhOESmoDRh0QdeWv+njTPJx1w0lxiEjFIqEJQES6AacC/0lkHKqKoxNItI9EtC+3wRi9iZfsPCkebnnuejwp7pg6ju124hXjGPeLI+IXmKqXGNP4rN1sJxd5C/g7kAHcaoypM5xURMYD4wHy8vJGTJw4sWWDrEdpaSnp6emJDiNmMcUbXA4EiF7g703CPYUaOXAsFm3p/W1LsUL84g34AqxdVEAs5YrL66LXoO4xHbctvb+tMdZx48bNNsbk7/14wtYDEJHTgK3GmNkiMjbadsaYCcAEgPz8fDN2bNRNW9zUqVNpTfE0JJZ47WA32PErsGMdoelFOn6PWM2fANrS+9uWYoX4xnvS6RcRCkbu+1/TVX+7JOYY2tL725ZiTWQT0BjgDBFZA0wEjhGRVxIYT9IzJgi7bgN7V+w7ZdwZl8JftV0HH9k/pu1Wzlsd50hUQxKWAIwxdxljuhljegEXAV8aY36ZqHgU4JsKodWAL7btvedjpV0cz4hUG3T941eSmpkSdQK43WZ+NCempiIVP7ok5D4JYSo/BUkH92GIRH87jTEQmAPBJeDoCe7Dkb1uuBp7B1RODd+I9YxF9ppj39jFmJJHoPJDIASSC9jg7Adp48E/HcpfBVMG7pFI5h8a1UffBOaGe/zEKvPPsW+rkkbvwT34z8LHePeJj1g682cWfrc0Yg8hX1klHz/3JadcnZipRHZu2cXkZ6awcu4aDhjRh1Gnj+Dbt2dSsHQDg47ozwmXjyUtM1y7Xb1wHS/88X/89Pl8/JUBUtK8nHXjyVx+/4VYVmvoTNk0Cb0J3Fj5+flm1qxZjdrH+GZgyl+F4EoIbQMqwdEVMv+M5RkdLph9X2Eq3gTjQ1LOBO+p9RbmAHbpBL75PshRBz8bfkC8SM4LiKs/xthQ+RGm7CUIrQwXyFhVPwJUtY+6RiGZtyCuwdjlb0Lx/SCOqvuvIch6ECvllPDrMCFM4RkQXEP4Ju3edh+/xiLcko7kfgRWHgR+5Otpqzlq6Ffh98A1EEn9JeLogrF3gu87jH8GVHxA7XEAkQh4xmHlPN3AdvumLbWltqVYoeXi9fsCXDP4d2xcGfmeUs9B3Zgw7xGA6oLUtm3WL9/IGw++z4JvF9OhWy5H35iPtzSD7I5ZjDj+EBzO2KYf2bm1iJIdpXTpm4ezxoyka5cU8NvRd+Mr94XvV1iEr6XcToL+ICJgDOT16sDIk4bxyfNfEPRHvq9x8JED+M0TV9J3SC9gz3sbDAR5/98f89F/viAUCHHMJUdy/q1nJGT9YxFpXTeBW4JdOgHKngSz1wjF0GrYeTm26/CqEa/b2V1wGv9sqJgEOc/WuULfzfh/hNIngWuqCnfAlGF2XoXJ/RqKfle1RGLNgjREdcG/W+A7TOFsTNbfwoU/vtqdb4ruwLgPRRy54PsGQhuIXPhDeEH3vVZkMpWYsufDyc//I9jjwf9l+Dn/TEz5a5iUS6H8RRBn1bljmZ3RgG8+dtHfwXs84h6MiC7qrep69Oqn2FpQGPX5Tau2cor3YowxDDtmMJ375vHZS1/jr/DX2qb/6T1554+v4XK7SEnz8PBXf6b7QV2jHrd0Vxl/u+Rx5n65EKfLgcPp4Df/upLjLjkKgMevnUB5zTmIqr46QX9VOVD1PdyyZhuTn/6s3te44Nsl/O7Ie5gw/xE69epYtb/hT2c9xLyvF+ErD7+W1x98j+nv/8iTP/wj5gQWb2237tIAY++E0ifqFv41BaaDvZlaV81UQGA2+L+LfuzyiUQsKE05VLweofCvTyWU/J06hTcAAr6qD19wGZgY2+arBaHiS/DPihBPKBxv+TOEE08ZUNaIY2+Hihdg58WYLfnYpU9pe66qpbiwhG/e/p6gLxh1G3+ln1AwhB2ymT1lPpOfnlKr8K8p6AtSUVLBzi1F3HvmQ3U+b7Zt88PHc3jhnoncOOoufvp8PgFfgIrSSkp3lfHPXz8Tbo4yhoXTljbraw34Arz92J7JDJb9uIJ5Xy+uLvzDrzXAxhWbmT6pca0Y8bT/1gD8c0DcYCJ/mOplyjHFf8U4uoDnGCT1XERqDFe3i4ncT15ibELZi72dyKNnQnsKfUcPEO+eGkeszE6g8XO0NI4fSp/CWHlI6jlxPpdqrfyVfgo37aR95xyCgRCv/uXt6ivqqJpwzWCMYfuGQtYt3UDPAd2qz33bsfexesE6KqKsMeCv8PPmw5MY9M5tjT9pA4KBED//tKr676UzV0RcI7mitJKF05Zw5DmHNXsMTbH/JgAriyZ9unYLrQr/+Gdhyl+D9m9Vd3cU78kY/w919zF+CM5rwskM4XV4905WQYxzcDg1eI8L1xRMBZFrC1FYmWCXNCGmxqqEsqdBE0DSMcbw4r0TefuxD6vazg1ur4vy0somTQ8RC7GkVk3hnX9+yPLZq+pNOMZAwfKNLJq+LC611dyu7at/b98lB5fbQcBXt8n2wwmfk9EunV/cdTYOR2KbgvbbJiBcw0AyadS49IgqIVSAqXhjz0Mpp4GrP3vePgvwgvNAGlU41xJl4Myum7GLHgD/95DzctU5Yn1NLki9DGjsZFtN/FjY25u2n2rT3nxkEm8/9iG+ch+VZT585X5KdpQRinLTtDk4XU76HNITCDf9vPa3dxqubRBu03/urlfjElNx4Z4LrVGnj8Dljbyinq/cx8R/vMf/u/mF6sfWL9vAmw9P4r1/fUzhpp2EQiF+/GQOHzz9Gctnr4xLvLAf1wBELGj3Imbn1RDaTrhZpqlZvxIqP4W0K6qO7YZ2L4PjY/CcCFY2knohpvgv9ZzDFV5s3f89EGtXSwNmG1S8HO6lRCjcrBXr60i/FUm7FOP/LnwTOCaO8JKQvm+ofW8kBq4hjdte7RfeeOh9fOWNvT/VSFXXPE63A4fTyR3/vZGAP8gzt/6Xj/7zea229oaOs3LumqhP3/jkVaycu4aPnv2i0SFuXLG5+ve5Xy4kUBlALIncBbbcxyfPfckV91/EW498wFuPTcYOhrAcFhNuf5nUDC9+XwA7aCOWMGhMfx6YdAcud901l/fFfpsAAMTZG3I/h+BCsEswkhqe68Z5YLjXTXBlVbdLPzh6Vc14GeUK3sqqfWxxg2Rh5fyr+jHjHgOBRdQdSOVGOn6HWFnYO8aDf2qEEzRUqFe1a5povYD2loJ4jgh3Z815FgKzwFoDOIha28CCzAcRVx+MbwaNSwAOJKP521ZV62aMoWj7vjcxiiUgYEI1vgcCl/3pAk655jimz/iO4y47mg5d23Hy1cfSuXcevx97L8t+WIG/MtbvBPjK/bTrnB3xPoE3zcNJVx6L2+Ni67pCZn06t1GvwZseXjQpGAhx33mPNJgUnW4nMyfP5u1/Tt7TnFW1fGbRXk1HC75dwpsPT+LiP5zbqJgasv82AVUREcR1MOI5HMs9FCv1gvC/ue8g7SciWY8gHb5EMm4EonVldCGplzZ8rrRLqxJFzSydAum/RqoSiKSeS+QmGRcxL8IeExscHcLnFEHcI8HqAO5oN59cSM5zWKlnIK7B4B5B7dfREAkPSFNJRUTI6ZTd8IYNcHlc/PF/v6PvkJ6k56RxyNEDefy7v3LpvefTvnMOGe3SuePFG7jyrxfTuXcey2ev5OfZqxpV+IfP4+TYS47Ck1r7u+ZJ9XDu70/D7Ql/5guWbWz0a9i2vpBQKERJYUnEG8B7C/qDLP5+Of6Khl+Dv8LfpFpJQ/brGkBDxDUAXAMAMNY4sNLBrqDO1XjatYhnTMPHs7IhdxKm9FnwfQlWOyTtCsR74p6NPCeA90uo/BgIgrgAgazHoOSBqsFq+1qd9oL3xDojiQEk4w+YHRdW9S4KEq4RuCDnOcQzcs92OU9jSidA2RMxntOEa1LSnElMtQUHHzlgn1f1skM2Q8cN5qjzRse0/ZqF65u0AI031cNlf76Ag48cwNO/f5FNq7aQlp3GhbefxQW3nVG9XW73dmxe07h1LgK+IKU7ywgGQxFv/tbkSXVz/KVHh6fLEGJq1Q3EcI+jsZI6AdQUbtefiCm6DQLzAANWV8j+Pyz3sNiPY7VDMu8A7ohyHkGyH8QELg9P3SBZVYV1JsY9ElP+ejh5BOYSfdBXfdyQchaS+cfI53cdCO0nhQeIBeaD6wAk7eo6U0aIuJGMG7BNBZS/TINdW50HIVbrmgJXtYxjLzmS7yfPjtp/PxbZHTLJaBf756fbgZ2jlpm7R/PWedzl5MlZD+JN9TD69HxGn55PqKrdfe9k8os7z+H+2VGacaIU2A6Xg7SsVNIyU0lJ99ZpZhIRjDGkZady1g0nc+m957Ns1ko+evaLmJqLjjpvVL3bNIUmgBrE2Q1p/z+MXQyEECsnfudyDQTXwNqPWelI+lWQfhXGPwez8yrCV9a7RxEL4Sv2Cup+Cr2QdhmSfiMi0RZwrzqPszuS9afY4sz4PUacUP5S1f2HNMLdVW3CScEN4kKy/hrT8dT+57BTh9NrUHfWLFxX3STjTnGTku6ldGcpINi2jYhEbBrxpLq5/vErG3VFP2DUgXQ/qAtrFqyrdWXsSfXw2yevxuly8M/rJuwpdDNT+cvku+jcO6/WcaKNyD305GFc99jlPHv7K4RCNqFAiIOPGsBBI/uyfcMOvn59eq3mJ0+qh3NuPhWny0lqZgoDRh3IounLqgt2b5qHo88fzS3PXV/rdQ4cdSBnXH8ik578hGAgiGVZGMCyBCTc1dWb7qVdXjaX/un8mN+fWGkCiECszESHgLiHQYdp4dqAKQH34WC1h8rJmOB6cPaH0BbwTwHJQtIuQzzNv7KSiAPJ+B0m/cbwyGHJAFOCKX8rXEtx9kNSL0QceQ0fTO2XHA4Hj0y9j3f+OZnPX/kWh9Pi5KuO5YzrTyTgDxL0BykrKufNhyexdObP5HZrT9AfpGD5Rjr37cQld5/LwUcOaNQ5RYSHptzLv254jm/emkEoGGLwmP7c9PT46sFhR5w7iiXfL8eT4ubA/L6NnrTt1GuO54TLx7Jl7XaycjPIyNlTQxl+7MFMuP0VSgpLcHvdnPO707j03vOqn//rh3fx+cvfMOXlr3G6nZxy1bEcdf7oiElu/EOXcvylRzF90izcXjdHnz8Kd4qbz176mo0rNjFoTH+OPn807ijdSveJMabN/IwYMcK0Jl999VWiQ2gUjTd+2lKsxuxf8YZCIRMMBlsumCq2bZvSorI6526N7y0wy0QoU7UGoJRq0xI1HbOIVE8X3Vbt991AlVJKRaYJQCmlkpQmAKWUSlKaAJRSKklpAlBKqSSlCUAppZJUwhKAiHQXka9EZLGILBKRmxIVi1JKJaNEjgMIArcYY34SkQxgtohMMcYsTmBMSimVNBJWAzDGbDLG/FT1ewmwBOiaqHiUUirZiInD2piNDkKkF/ANMNgYU7zXc+OB8QB5eXkjJk6c2OLxRVNaWkp6etuZAVPjjZ+2FCtovPHUGmMdN27cbGNMfp0nIs0P0ZI/QDowGzinoW11LqB9o/HGT1uK1RiNN55aY6xEmQsoob2ARMQFvA28aox5J5GxKKVUsklkLyABngOWGGMeTVQcSimVrBJZAxgDXAocIyJzq35OSWA8SimVVBLWDdQYM43wslZKKaUSQEcCK6VUktIEoJRSSUoTgFJKJSlNAEoplaQ0ASilVJLSBKCUUklKE4BSSiUpTQBKKZWkNAEopVSS0gSglFJJShOAUkolKU0ASimVpDQBKKVUktIEoJRSSUoTgFJKJSlNAEoplaQ0ASilVJLSBKCUUklKE4BSSiWpehOAiGSKSN8Ijx/SHCcXkZNEZJmIrBCRO5vjmEoppWITNQGIyAXAUuBtEVkkIiNrPP3ivp5YRBzAk8DJwEDgFyIycF+Pq5RSKjb11QD+AIwwxgwFfgW8LCJnVz0nzXDuQ4EVxphVxhg/MBE4sxmOq5RSKgZijIn8hMgCY8zBNf7uDEwGXgKuMMYM36cTi5wHnGSMubrq70uBw4wxN+y13XhgPBAlstsAACAASURBVEBeXt6IiRMn7stpm1VpaSnp6emJDiNmGm/8tKVYQeONp9YY67hx42YbY/L3ftxZzz4lItLXGLMSwBizSUTGAu8Bg+ITZl3GmAnABID8/HwzduzYljp1g6ZOnUpriqchGm/8tKVYQeONp7YUa31NQNcBVs12eWNMCXAScHUznHsD0L3G392qHlNKKdUCoiYAY8w8Y8zPwBsicoeEpQCPAtc3w7l/BA4Qkd4i4gYuAiY1w3GVUkrFIJZxAIcRvlKfTrjQ3giM2dcTG2OCwA3Ap8AS4A1jzKJ9Pa5SSqnY1HcPYLcAUAGkAF5gtTHGbo6TG2M+Aj5qjmMppZRqnFhqAD8STgAjgSMJ99d/M65RKaWUirtYagBXGWNmVf2+CTizqsumUkqpNqzBGkCNwr/mYy/HJxyllFItRSeDU0qpJKUJQCmlkpQmAKWUSlKaAJRSKklpAlBKqSSlCUAppZKUJgCllEpSmgCUUipJaQJQSqkkpQlAKaWSlCYApZRKUpoAlFIqSWkCUEqpJKUJQCmlkpQmAKWUSlKaAJRSKkklJAGIyP+JyFIRmS8i74pIdiLiUEqpZJaoGsAUYLAx5hBgOXBXguJQSqmklZAEYIz5zBgTrPrze6BbIuJQSqlk1hruAVwJfJzoIJRSKtmIMSY+Bxb5HOgU4am7jTHvV21zN5APnGOiBCIi44HxAHl5eSMmTpwYl3iborS0lPT09ESHETONN37aUqyg8cZTa4x13Lhxs40x+XWeMMYk5Ae4ApgBpMa6z4gRI0xr8tVXXyU6hEbReOOnLcVqjMYbT60xVmCWiVCmOls0DVURkZOA24GjjTHliYhBKaWSXaLuAfwbyACmiMhcEXk6QXEopVTSSkgNwBjTLxHnVUoptUdr6AWklFIqATQBKKVUktIEoJRSSUoTgFJKJSlNAEoplaQS0gso2a3aVMhrX85h7ZadjDiwGxcePYScjNREh6VUswqEgszftZYlxRvplJLNUR0H4LbCRY4vFGBR0Xo8losBWV2xxGKXv5xJBbNYWbqZgZndOLXbcNKd3iadu9BXwqKiAtq70xmY1Q0RadJxjDGsLduGy3LSNbVdxOcXFq1nWfFGuqTkcFjuAU06T6JoAmhmJRU+flpegNfjYsQB3XA6aleyvl+ylt8/PYlAMETINixYvYk3v57Ha3+4hLycjHqPvbxgG5NmLKK8MsCxw/oxemAvLKtpH+zGWrZ+Ky9+Nos1m3dwSJ/OXH5CPl3aZ7XIuVXbMnP7zzy0eBLrywsBEMBruUhxevjPqF+zrGgjDyx8GxHBGEOq08OIdr2ZsmkBADaGr7Ys4oVVU3lp9PXkpUSeLb4yFOCtdd/zyca5uCwH53Q/jFO6DOX//TyF19dOx2U5sI2hozeLf4+8kjxv+PMaMjYWEjUprCrdwobynfhCfv659COKgxUYA11Tc3hw6CX0TO9Qff6bZ73I4uICjDE4xEG2O5UbzPCo782y4o3M3L6CTFcKx3QaTKYrpalvc7PQBNCM3vp2Po+8ORWnwwGAy2nx7xvOZmDP8JRIxhjue3kKlf5g9T7+YIhQeSVPfTCdP192YvXjxhiWFWyjuKySQb06MWnGIv717jT8wRC2MXw6exmjB/TkoWtOq5UENu8o4aUpPzJnxUa6d8jmihPyGdSrE75AkF1llfzuqfdpl5HKeUcdwoAeeQDYtqk3kcxcspabn3offyCEAZZv2MaHM5fw3zt+QZ/O7ZvzLVRt3OKiAm776RUq7UD1YwaosANU+oPcNvsVCioK8dl7vgPlIT+fbppf6ziVoQD+UJDHln7IP4ZdUuc8QTvEtTOfZWXpFnxV51pZuoVJBT+yrGQTfjuIv+ocBeWF3PrTy9x3yPn8Y9F7zN+5DodlcWLnIdwy4HTSnB4ASoOV3DL7vywp2oAlQnnIX+ucq0u38esfnmXy2DtwWg5eWPkVC4vWV58HglRW+FgXLGRj+U66pObseQ+M4YGFb/P5pgUETQin5eCxpZN5ePhljGzft3q77b4SPtzwE5srdjG8XW/G5Q3CaTka/x8Ro6RNALZt+GHZOuas2EBuZhon5h9EZlrjq5u2bfhx2Tqm/LSc96cvImQbfIFQ9fO/+de7fPaP8bicDrYXlbGzpO7MFyHb8N2iNdV/byws4oZ/vcuWnaU4LMEfDBEM2dg15sur8AX4cu4KLnvwNf521Sn06JhDwbZdXPy3Vynz+TEmXGP4au4KfnPG4XwyaxnH9PTy9fwCLBE++mEpIw/qzpK1WygsKSc9xc1FY4dx7WmjayUDYwx/efXzWq/JGCj3Bbj/lSm8eNtFjX7P1P7Fbwd5evkU3l0/k7K9Cs2aDIaVZVtiPq6NYfr25RGf+3brElaXba0u/CGcNObvWo+h9rySIWOzumQLV854mvKQL3xsO8RHG+awsmQLLx3+GwD+sfA9Fu5aT8CEiMRgKAv6mFQwi3N6HMYHG2bXKPx3xwx+O8AF0x7jwp6Hc+NBJwHw9dYlfLF5YXViDIZsAO6Y8yqfHvMHXJaTuTvXcNOsFwkZG78d5KONc3jm5yn0Ts9jZclm+mTkcWXfcQzMar7Z8/f7BLBhexEf/bCE0gofYwb1ZuRB3QkEQ1z/r3dYum4r5b4AXreTx9/9lqduOpeDe3eO+dgGuPbxt1i0dgsVvkDEbUorfDz+7rfceNYRpHhcdT6cu6WnhK9CjDFc9/jbFGwrirJlbYvXbeXSB//Hf35/AX95dQqllbW/gLYx/Ov97wAY26Nr9WO+QJBpC1fXiNPPfz6eyTvT5nPUwX35au4KgrbNkQf3ZkNhccRzz1+1iZBt47C0L0Ey+8Oc1/hu2zJCMX1iG8cl4SLKYCgoLyTXk4HX4ebHHauoiJhsIsdgA/5QYK/HDEuKN/D2upmc3m0EX21ZFLXw381nB3h4yQd8vXUJQTv6tn47yJvrZnBo+74clnsAkwtmR4zXYJi7cy357frwx7kTa21TEfKzrryQ9eWFGGBDxQ5+2L6Ch4dfyqG5zTOZwn6dAD6bvYw/vfQZIdsmGLJ59cs55GamMWZwLxav2UJlIJy9dzfJ3D5hMnf94hhmLFlLXk4Gp48aSPvMtOrjlVWGC8mPf1iKJXDBkPbMW7mRQFU2jyRkG978Zj4zl67jv7f/gtEDezFj0Zpa+zgsoVv7LAq27eKTWctYv62oUa+zrMLHRX95uVm+fjtKKnhv+sLqvz/5cVm92y9Zt5XBvSLN+q2SwfqyQr7f/nNcCn+nWJzadRjPLJ8Cxdv483dfYxvDBT1H08GTgdty1rkCd4oDgyFo9v5OGoJE/p4+uPh9VpZuxo7xNQSNzewdq+ickk1psDLCucIqQwHeWf8Dh+UegB3l3OHIDEuKN7IzUBbl+T3/VlYloDeO/F1MsTZkv710q/AF+PN/P8MXCFZXt2zbsHVXKe9OW1hd+Ne0ZVcpNz81idenzuOJd6dx0l3PMn3xGiBcZfvVw6/zvy/nsHVXKZt3llLhC9Zb+O8WCIYo2FbEG1/P4/7LTmRQr054Xc7qppaQbZi5dC3n3f9fnpk8o9Gv1TbRrnvib1Nh45KV2r+sLtsac8HZWGlOD7meTF5dOw2DoSLkx2cHeHPtDEqDlTj2uokrQKrTQ0dPFh7LBYBDLLyWi2M6Dq73XJM3zKG9p/5OGDX57SCbKnbRwZNZ3bMpkm+2LuHzTfPxOtxYRL7PNrlgFr+a8SSBemoUNa0t21Zv7aMx9tsE8OPy9VhN7Pq1W8g2/O6p9wnZNt8uWMXG7UX4g017432BIFNmLyczzcvzt17IVScfirNGW3vQNuEbwnbkL5PDElqow0+jzF+9maKyykSHoRKkZ2pu1CvgfdUtNZf/rZlG5V5NN5V2gPcLZvHo8Mtp504nxeHG63DRLbU9zxx2Da8d8Vt+c+AJjMo9gNO7juD50ddx66Az6j1XZchPR08mXocLp4SLRbc4cEj0IjJgBzmu08Hk1pM4QsbmD/Mm8s2WJbUSpVMsPOIk3eHhk03zG5VCUxyeeuNqjP22CcjpsLCjFKaNEQjazFyyloVrNlMepZ0/Vmkp7urff1xegD8Y+xcnM81Lx+x0lq3ftk8xNLc3vp7H29/O59Frz2DUgJ6JDke1sEh945uD23JyZMf+PLvii4jPFwcqGNauFx+Nu5OVpVtwi5MeabnVXTsv6jWGi3qNqbXPiZ2H8NmmeVELW6dl8b8xNzFx7XRWl27lkJwevLf+R7b7SiJuLwivr5tRpxkqEr+pvY3XcoHAFl/k+2vReC0XF/Yc3eRxDXvbb2sA+Qd0I2g3z5XJztJKurTPJMXd9HyZ4nZywdFDqv/2uGLv2iUCT95wDqs2FTb5/LuPM/Kgblx/xuG4nY5mqVEEgqFw974Jk/FFaFZT+zcRwRGlaaOp3JaT9p50zu8xin7peRG36ZnWAUssLLE4IKMzPdM7NFgo3j34bIbl9I74nNdycWLnIXRNbcctA07j3yOvZHy/46LcaA6zMTEV/pGUh/yUB6Mfe2+pDg9uy8mpXYdzTb9jm3TOSPbbGoDb5eSw/j1qda9sqjGDeuF0WDzx7jQgtv/wnPQUfIEQAgRCIc498hCOGbrnzv05RxzMrGUFVPgbrlWkuF3079GRVI+bomDDzS0el5NrTx3FEYN788oXPzFt0WrSvG46Zmfw1CUnYVnCySP7M2nGIrbtKqWkwsecFRsJhEJ0aZfJsoKm1TJmLS9gzKBeTdpXtU0OsRibN5Avtiza52NZCF1Scji92wjO6zGKDFcKvxtwKjfPeqnWdh7LxS0DTmv08b0ON08fdg2vrZ7Gv5d/ijE2IQwpDjf90vM4vVvdJXOH5/Tm221Lm/yaomnsfZMnR15Jz7QOpLuaNjI6mv02AQBcccJIZv9cUGvg1W4njDiIz39aRkOtRKeM7E92eni03vO3XsDdL3zCzxu2EXkJe3A5LMYO7cffrzyF2T8XsKOknKF9u9QZ5XvUwX04c8wg3pm2AEvC7fvlvsjJpXuH8EjIK08cyWPvfBtxG4dl4XU7OPWwgZxzxMEc2C08WvFPl51Qvc3UqVOrbzx3zc3iutMPr3OcN7+ex8NvTo3p5vbe7Gaqcam25c5BZzN16xJCMdwL8FouLu9zNF9sXsjasm3V3S6dYpHryeS1I27C63BVbz+8XR+eOvRqfpr+Ax08mfRK68CvDziOQ3Ka3tx4ce8jOKJjf94vmEWhr4QxHQ6KOuDqxoNOblQCsBCkRo3IKRa2MbUKfJc4SHV6KArEthpurieDQdndY46hMfbrBDDiwG6cd+QhvPnNfGzbDg89B/525cnkH9idOSsK2FZUu+uVJeBwWKR7PVxx4kh+eeyeYd19u+Qy8e5fUlhUxjcLV1G8YQWZqR7KfQHcTgtjhD6d2/HHi4/FsoSRB0X/TxMRbr9gHBeNHcas5evJSvUyacYivl+6jkCNG81et5PLjg9fmfzyuBEsXruFT2fXHhzTqV0GZx0+mF+MG0pG6r5dIfzn45lNLPwN+fW8XrX/ynKn8sdBZ/P3xe/X2yTisZxc2udIruw7jot7HcGEFZ/z4YY5hEyIsXmDuOGgE2sV/rsNyu7OttSVfDj23GaLuUdabvUgrfr0Su/AyZ2H8ummeXvdxHXAXt1NHWIxKKs7XUrbcXj2gYSMzcldhjFn52o+rpquImTb9MvoxKW9j+RP89+sNWI6Eqc4eHT4ZU1+nQ3ZrxMAwO/PO5qzxgxm+qI1eD0ujh12ADlVV/Rv3HMZr34xm09+XIYAY4f249enjiLV6673mO2z0jh7zMFMnVrI1EfOZtWmQlZs3E633GwG9OjYqBs0PTpm06Nj+Ar/0AE9uG3CZOat3IDL6SAQDPHLY0dw0siDgHDS+PvVp3LbBeP4ZNZSMlI8jB3aj4yqQWTNYXtxbFcluwnh5rYHrjiRFHfdL69KDqd2G4HbcnLP/DciNm94LCf/N+yXHJrbDxEhxenmpv6ncFP/UxIQbePcNfhsioMVzCpciatq7MHRHQfQL70Tz6/6CmdVwd4nI4+Hhl3C/Bmz+Gf+FdX7n9J1GNf0O5ZlxZvonJJNv4zwuJmiQAVPLPuYkLEJmhDDc3pz58Cz+GrrQubsWMNBmZ05p/th5Hoz4/ba9vsEANCnc/uIc9ZkpXm5/owxXH/GmAh77fvxGysjxcPTN53LxsIitu4qpW/n9hGv6NtlpnLxMdEnnGqqL+f8TNS2rb04LKFrbhanHTaAMw4fTMfs9GaPR7Ut6a4U3A5nnW6bAMY23Dn3Ndp5Mnj60Kvp6G07Ewl6HS4eG3E5G8p3sK5sO73TO9KpaoK683uOZnnJRtq7M6oniYukozerzms+q/tITu06jA3lO8h2p5HtDg86/WXvo/hl76Pi94JqSGgCEJFbgIeBDsaY7YmMpTXp0j6rxWfa3LqrlLtf+CSmW1OpHhf/vO5MbfJR1ebvXMs/Fr8XsfAH8BPCHwpRWb6Du+dN5NnDft3CEe67rqnt6nR7TXd5Gd6uT5OP6bKc9ErvuK+hNVnCEoCIdAdOANYlKga1x2ezlmFivPoPBEP075G4D61qXV5dPY1nfp7SYHs2hHu/LC4qYIevlHYerTUmWiLHATwG3E7iZjFQNZRV+mvdfK5PyLYj9qxSyWeXv5ynfv4spsJ/t6Ad4oOCWdhxGkGsYiexXvU160lFzgSOMcbcJCJrgPxoTUAiMh4YD5CXlzdi4sSJLRdoA0pLS0lPbztXMfXFW+EPsHbLzlhvAdA+MzXu7f5t6f1tS7FC88VbGqxkY8XOJhXmXoeb7qntY5rWoC29v60x1nHjxs02xtQZ6BC3JiAR+RyINE3k3cAfCDf/NMgYMwGYAJCfn2/Gjh3bXCHus6lTp9Ka4mlIffEaY7j3pU/5cs6KmAanHdStA/+7u/GDcRqjLb2/bSlWaL54fyxcySM/vUJZ1Tz7NQkNV+8zQl5eOvw3dEutvxNFW3p/21KscWsCMsYcZ4wZvPcPsAroDcyruvrvBvwkIjqncAKJCPdffiL/uPoURh7Uvc5Mi3vr3D5+XdNU2zG8XW88EfruQ2xtuyXBSh5aPKl5g1Ixa/F7AMaYBcaYjsaYXsaYXkABMNwYs7mlY1G1iQhHHtyHp286l9GDetU7X1F9g9xU8nCIxb9HXkl7d3rU6Y4b8mPhymaOSsVqv50MTjWdiPDQNady+qhBZKREHhT3zOTvY75prPZv/TI68fqRN9PUCSpdEr81b1X9Ej4QrKoWoFqRTTuK+dX/vU5phS/qUpfF5ZUcduMTeFxOThs1gN+fezQpHh0JnKxc4qyaA6duw0/Nx/d+1iUOTuoyNO7xqci0BqDquPfFT9leXEa5L9BgO64vEGTSjMXc9P/ea5HYVOuU4nQzNKd3nR49Aoxo15uvj7+Pz4+9lwPSO+G1XKQ43KQ43PTP6tImpoPYXyW8BqBal7JKP/NWbWzUYjqBYIiFazazvGBb9SykKvn86ZDzuPr7pyn0lVRPkmaA+TvX8euZE3hu1LW8MuZGFhcVsLpsG73TOjAwq1uzLW6iGk9rAKoWu4njQhyWsHrzjmaORrUled4s/p1/ZZ3H/SbImrJtfLl5IX47yMCsbpzWdTiDsrtr4Z9gmgBULRkpniZdxVf6g3TLbTsTfKn4WLBrHa4Ii6RXhPz8ZeE7HD3lzxz3xQO8uHJqzFOPqPjRBKDqOG3UgEbvYxvDi5/9GIdoVFuwaNd6bv3pZZ76eQr+UORpQirtADaGkmAlz6/8iudWftnCUaq9aQJQtSwv2MYT70xr9H7GwLcLV7OtqDQOUanWbMa25Vz7w3/4dusStvmKCdHwtBCVdoBXVn9L0NauxImkCUDV8uoXP+FvYv9+t9PB5h0lzRyRas2MMTy4+H18dt0eYxZCqiP6YkVBY1MSrIhvgKpemgBULRsLi5t8IzgQDNGzY04zR6Ras4qQny2VRRGfc1kOxuUNipoEPJaTTFdqPMNTDdAEoGo5tH93nFbje2Z43U4uOHoImWn7tiaxalvcljPqSF6/HeKzzfMojzBRnNfhYny/42KaCVTFj777qpbzjxpCqJEVgPaZqdx8zlHcfE7LLGOnWg+n5eDMbvl49ur54xALgyEQoY2/S0oOdww4kwt7Hd5SYaoodCCYqsUSwWEJwUZkgYE98rjg6CFxjEq1Zr/tfzKlwUqmbF6Ay3LgCwUJmsj3kVyWg+dGXUt7T0YLR6ki0RqAqiXF68LpiPyxiNYwtLNUb+QlM5fl5E+HnM/ksXdyXvdROOqZFTRgh/jd7JeYXDBbVwRrBTQBqFpcDgfnHzUEr7t25dDjckRMDB6Xk3FD+7VUeKoV21q5izfWTcdn6l8udGnxRh5c/D73L3i7hSJT0WgCUHVcd/rhZKel1HosGLK5YOxQvG5n9bS/HpeTvJx0zj/qkAREqVqLylCAG358jqtmPE1FKLa1gX12kM82zWNt6bY4R6fqowlA1fHJrKUUldVu1gnZhg9mLOas0YNJ93pI9bg4cnAv/nvHL0hPid7XW+3/nlr+GXN3rm3wyn9vQWPz1ZZFcYpKxUITgKpj8ozFVPjrfplLK328890CSip8lPsCTFu0hnte/ETndElyH2yYjd+OXvjX16n4v6u/oTLGWoNqfpoAVB2OKOMAbNvUGiVc6Q8ya9l6FqzW1TyTWX2FP0CKFXlVOQBfKMCUTfObOyQVI00Aqo4zxwwmxR1bD+FAyGbuyg1xjki1ZgOzutX7vM8ORu0ZFDAhZu3QNYETRROAqmPMwF50apdZ/ZV1OR24nQ5cjrojPt1OB+0z01o2QNVq+O0gK0vqrwFmulM4sUvkcSIuy0HXlHbxCE3FIGEJQERuFJGlIrJIRB5KVByqtgp/gMsemkjB9qI9k3sZw9ghfSI2DTksi2O0G2jS+m7bMkL13APyWi5+0fNw7jn4PDp6MqvWB97DKeGRxCoxEpIARGQccCYwxBgzCHg4EXGouj6auYRtRaUEarT1B0I2n83+mcpA7bZeS4QHrzlVF4NPYkX+8qgDuiyEU7oO49I+R+MQi/+MupaBWd1wW068los8bxaPjbicvJTsFo5a7ZaoqSCuA/5hjPEBGGO2JigOtZeZS9dRGaEHUCRiCV/NXcGoAT3jHJVqrYa1642pMxE0eCwXdww6k9O6Dq9+rFNKNi+Mvo7tlcX47CBdUnJ0ScgEk0R04RORucD7wElAJXCrMSbiclIiMh4YD5CXlzdi4sSJLRZnQ0pLS0lPT090GDGLJd6tu0opLC6P+Zgup0W/Lrn7GlpEben9bUuxQvPGu7lyF0WB8uruwILgdbjomdb4pUWjaUvvb2uMddy4cbONMXXa2uJWAxCRz4FOEZ66u+q87YBRwEjgDRHpYyJkI2PMBGACQH5+vhk7dmy8Qm60qVOn0priaUgs8a7ZvINz7nsp5mMe2C2Xqy+u/5hN1Zbe37YUKzRvvMYYPt+8gHfX/0BlKMDJXYZyZveRuCOsDdxUben9bUuxxi0BGGOOi/aciFwHvFNV4P8gIjaQC+i48AQqr/Rz538+bNQ+J4/sH6doVFshIhzf+RCO76xTgrQ1ieoF9B4wDkBEDgTcwPYExaKqPP/pD6zcVBjz9iKwSZeAVKrNStRN4OeB50VkIeAHLo/U/KNa1sc/LCVkx/7fYAwsWbcljhGptmJj+U4eWzqZ77f/jNtyclrXEVx34Al4HdpDrDVLSAIwxviBXybi3Co6y2p8hbBP5/ZxiES1JcWBCq6Y8WT4RjDhkb8T107nh8IVvDbmt7V6+uzyl7O8ZCMdPZn0Su+YuKAVoCuCqRrOGD2QZyZ/36hF4b+Zv5KdJeXkZOji3snqg4LZlAf9tTqDGgwrS7dw7cxnefqwawB4dMlk3lo/s2oomHBgZmf+OeIKst362UkUnQpCVbvs+HwG985r1D7F5T6e+/iHOEWk2oLFRevxR5kKes6uNVzy3RP8d9U3vL5uBiFjEzQ2QRNicVEBd8x5pYWjVTVpAlDVPC4nL9x6EY9ffyZD+3apdxrf3UK24at5K+Iem2q9DsjojFXPp2VF6Rae/PnTiM/N3bmWnf7SeIWmGqAJQNVSWuln+YZt2LYhzesmyszQtaR6ok/3q/Z/Z3bPj+liIRKDoSRQ2azxqNjpPQBVraTCx8V/fYVtxWX4A+G5gCwRLAG3y4E/EKpzf8DrdnLRuKGJCFe1EkuLNhKKMB1ErLqm6mygiaI1AFXtja/n1ir8AWxjcDktnr/lQj7861X07dyeFI+LNK8bt9PBSSP7c/aYgxMYtUq0P81/o8n7usWhK4IlkNYAVLVv5q+qVfjv5nQ4KPP56d+jI2/ccykL12xm685SBvTMo0v7zAREqloL29jsCsQ+d9Te/CbEK6u/4dcHHN+MUalYaQ1AVWuXEXlhl5Btk5OeAoSH/R/cuzPHDj9AC39VZ37/pvhk47xmiEQ1hSYAVe2SY4fh3WspSIcldO+QrQO+VEQiwvCc3vt0DLdVd6U51TI0Aahq+Qd257dnH4HH5STN68brdtKnc3ue+M1ZiQ5NtWIPD7+UTt7atcF0pxc3DRfsDoRzexwWr9BUA/QegKrlorHDOH3UIJau30p2mpe+cZrrX+0/0l1eJo29k7k7VvPTjjUMzu7Oobn9mFW4kgcXv09B+Q4cCHkp2awv3zPZoIUwpmN/zumuCSBRNAGoOtK8bkYc0C3RYag2Zmi73gxtt6c5KL99X9488vdUBP24LAdOy8H2ymI+2jgXMIzucCAHZHROXMBKE4BSKr5SnHsGCuZ6M7msz1EJjEbVpPcAlFIqSWkCUEqpJKUJQCmlkpQmAKWUSlKaAJRSKklJW1qKV0S2AWsTHUcNubStxew13vhpS7GCxhtPrTHWnsaYDns/2KYSQGsjIrOMMfmJjiNWGm/8tKVYveFvbQAABIJJREFUQeONp7YUqzYBKaVUktIEoJRSSUoTwL6ZkOgAGknjjZ+2FCtovPHUZmLVewBKKZWktAaglFJJShOAUkolKU0AzUBEbhSRpSKySEQeSnQ8sRCRW0TEiEirnfBfRP6v6n2dLyLvikh2omOKREROEpFlIrJCRO5MdDzRiEh3EflKRBZXfVZvSnRMsRARh4jMEZHJiY6lISKSLSJvVX1ul4jI6ETHVB9NAPtIRMYBZwJDjDGDgIcTHFKDRKQ7cAKwLtGxNGAKMNgYcwiwHLgrwfHUISIO4EngZGAg8AsRGZjYqKIK8v/bu5sQq8oAjOP/h8oMp4KECJxgDDKJIhJGAikqW0SJbV303SZJSwiilBZFiyKohDaBThsnIkrKRWlf0CacJEm03IQbRwrdSELUJD4tzimmmPs1I/Oe8Ty/1ZxzZ/Fwufd93vNy7nvgWds3ArcBTzU463TPAEdLh+jTdmCv7ZXALTQ8dwpg7jYCr9r+E8D2ycJ5+vEm8BzQ6DsAbH9u+2x9uB9o4lNqVgM/2z5mewp4n2pC0Di2f7F9sP77DNXgtKxsqu4kDQP3AztKZ+lF0pXAHcBOANtTtk+XTdVdCmDuVgC3S5qQ9I2k0dKBupH0AHDC9qHSWQb0OPBZ6RAzWAYcn3Y8ScMHVQBJI8CtwETZJD29RTVZOVc6SB+WA6eAd+slqx2SlpQO1U2eCNYHSV8C18zw0jaq9/AqqkvqUeADSde54P21PfJupVr+aYRuWW1/Uv/PNqrli/H5zHahkjQEfARssf1b6TydSFoHnLT9vaQ7S+fpw8XAKmCz7QlJ24HngRfLxuosBdAH2/d0ek3SRmB3PeB/J+kc1WZQp+Yr3/91yivpZqpZyiFJUC2pHJS02vav8xjxX93eWwBJjwLrgLUlS7WLE8C1046H63ONJOkSqsF/3Pbu0nl6WAOsl3QfsBi4QtIu2w8WztXJJDBp+5+rqg+pCqCxsgQ0dx8DdwFIWgEsonk7AQJg+7Dtq22P2B6h+sCuKjX49yLpXqrL//W2fy+dp4MDwPWSlktaBGwA9hTONCNVrb8TOGr7jdJ5erH9gu3h+rO6Afi6wYM/9ffouKQb6lNrgZ8KRuopVwBzNwaMSToCTAGPNHSmuhC9DVwKfFFfsey3/WTZSP9l+6ykTcA+4CJgzPaPhWN1sgZ4CDgs6Yf63FbbnxbMdKHZDIzXk4FjwGOF83SVrSAiIloqS0ARES2VAoiIaKkUQERES6UAIiJaKgUQEdFSKYCI80TSXkmnF8KulRGQAog4n16nus8+YkFIAUQMSNJo/YyCxZKW1Hvr32T7K+BM6XwR/covgSMGZPuApD3AK8BlwC7bRwrHihhYCiBidl6m2gfoD+DpwlkiZiVLQBGzsxQYAi6n2qkyYsFJAUTMzjtU+7yPA68VzhIxK1kCihiQpIeBv2y/Vz8T+FtJdwMvASuBIUmTwBO295XMGtFNdgONiGipLAFFRLRUCiAioqVSABERLZUCiIhoqRRARERLpQAiIloqBRAR0VJ/A8LR5HOQ6B8cAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Generating a synthetic dataset with four classes\n",
    "nsamples = 300\n",
    "\n",
    "data = dataset_utils.corners(N = nsamples,scale = 0.5,gapwidth = 3,cornerwidth = 4) # linear dataset\n",
    "#data = dataset_utils.crescent_full_moon(N = nsamples,r1 = 5,r2 = 10,r3 = 15) #non-linear dataset\n",
    "\n",
    "# Separating features (X) and labels (Y)\n",
    "Y = data[:,-1].astype(int) # Labels\n",
    "X = data[:,:-1] # Features\n",
    "\n",
    "#Number of classes\n",
    "k = np.unique(Y).size\n",
    "\n",
    "colors = np.array(['r','y','b','g'])\n",
    "#Displaying the dataset\n",
    "plt.scatter(X[:,0],X[:,1],c=Y)\n",
    "\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.grid()\n",
    "plt.title(\"Dataset\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train, Validation and Test Sets Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First we will shuffle the samples\n",
    "indexes = np.arange(X.shape[0])\n",
    "np.random.shuffle(indexes)\n",
    "X = X[indexes,:]\n",
    "Y = Y[indexes]\n",
    "\n",
    "# Then, we split our data into train/val/test sets\n",
    "train_split = np.int(0.5*Y.size)\n",
    "val_split = np.int(0.75*Y.size)\n",
    "\n",
    "X_train = X[:train_split,:]\n",
    "Y_train = Y[:train_split]\n",
    "\n",
    "X_val = X[train_split:val_split,:]\n",
    "Y_val = Y[train_split:val_split]\n",
    "\n",
    "X_test = X[val_split:,:]\n",
    "Y_test = Y[val_split:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# min-max data normalization\n",
    "x_train_min = X_train.min(axis = 0, keepdims = True)\n",
    "x_train_max = X_train.max(axis = 0, keepdims = True)\n",
    "\n",
    "X_train = (X_train - x_train_min)/(x_train_max - x_train_min)\n",
    "X_val = (X_val - x_train_min)/(x_train_max - x_train_min)\n",
    "X_test = (X_test - x_train_min)/(x_train_max - x_train_min)\n",
    "\n",
    "\n",
    "#####################################################################################\n",
    "#Activity suggestion:\n",
    "# Change the min-max normalization above by standardization ((X - mean)/(std))\n",
    "####################################################################################\n",
    "\n",
    "\n",
    "#Displaying the normalized train set\n",
    "plt.scatter(X_train[:,0],X_train[:,1],c=Y_train)\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.grid()\n",
    "plt.title(\"Normalized Train Set\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representing Labels using one-hot-ecoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y_train[:5]:\n",
      "[0 3 3 3 3]\n",
      "\n",
      "Y_oh_train[:5]=\n",
      "[[1. 0. 0. 0.]\n",
      " [0. 0. 0. 1.]\n",
      " [0. 0. 0. 1.]\n",
      " [0. 0. 0. 1.]\n",
      " [0. 0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "Y_oh_train = to_categorical(Y_train, k) \n",
    "Y_oh_val = to_categorical(Y_val, k) \n",
    "Y_oh_test = to_categorical(Y_test, k)\n",
    "# Displaying the 5 first elemnts\n",
    "print('Y_train[:5]:')\n",
    "print(Y_train[:5])\n",
    "print('\\nY_oh_train[:5]=')\n",
    "print(Y_oh_train[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining a Fully Connected Neural Network with Keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_model(k,learning_rate = 0.15):\n",
    "    inputs = Input(shape=(2,))\n",
    "    out1 = Dense(k, activation='softmax')(inputs)\n",
    "    model = Model(inputs=inputs, outputs=out1)\n",
    "    sgd = SGD(lr=learning_rate)\n",
    "    model.compile(optimizer=sgd, loss='categorical_crossentropy', metrics = [\"accuracy\"]) \n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"model\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         [(None, 2)]               0         \n",
      "_________________________________________________________________\n",
      "dense (Dense)                (None, 4)                 12        \n",
      "=================================================================\n",
      "Total params: 12\n",
      "Trainable params: 12\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "model = my_model(k)\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/100\n",
      "1/1 [==============================] - 0s 98ms/step - loss: 1.3479 - accuracy: 0.2027 - val_loss: 1.4047 - val_accuracy: 0.2027\n",
      "Epoch 2/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.3391 - accuracy: 0.2297 - val_loss: 1.3927 - val_accuracy: 0.2162\n",
      "Epoch 3/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.3306 - accuracy: 0.2905 - val_loss: 1.3812 - val_accuracy: 0.2703\n",
      "Epoch 4/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.3225 - accuracy: 0.3716 - val_loss: 1.3703 - val_accuracy: 0.3243\n",
      "Epoch 5/100\n",
      "1/1 [==============================] - 0s 17ms/step - loss: 1.3147 - accuracy: 0.4122 - val_loss: 1.3599 - val_accuracy: 0.3649\n",
      "Epoch 6/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.3072 - accuracy: 0.4459 - val_loss: 1.3499 - val_accuracy: 0.3919\n",
      "Epoch 7/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.3001 - accuracy: 0.4595 - val_loss: 1.3404 - val_accuracy: 0.3919\n",
      "Epoch 8/100\n",
      "1/1 [==============================] - 0s 18ms/step - loss: 1.2931 - accuracy: 0.4797 - val_loss: 1.3312 - val_accuracy: 0.3919\n",
      "Epoch 9/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2864 - accuracy: 0.4865 - val_loss: 1.3224 - val_accuracy: 0.3919\n",
      "Epoch 10/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2800 - accuracy: 0.5068 - val_loss: 1.3140 - val_accuracy: 0.3919\n",
      "Epoch 11/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2737 - accuracy: 0.5135 - val_loss: 1.3058 - val_accuracy: 0.4054\n",
      "Epoch 12/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2676 - accuracy: 0.5135 - val_loss: 1.2980 - val_accuracy: 0.4054\n",
      "Epoch 13/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2617 - accuracy: 0.5135 - val_loss: 1.2904 - val_accuracy: 0.4054\n",
      "Epoch 14/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2559 - accuracy: 0.5135 - val_loss: 1.2831 - val_accuracy: 0.4054\n",
      "Epoch 15/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2502 - accuracy: 0.5473 - val_loss: 1.2761 - val_accuracy: 0.4595\n",
      "Epoch 16/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2447 - accuracy: 0.5608 - val_loss: 1.2692 - val_accuracy: 0.4595\n",
      "Epoch 17/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2393 - accuracy: 0.5608 - val_loss: 1.2626 - val_accuracy: 0.4595\n",
      "Epoch 18/100\n",
      "1/1 [==============================] - 0s 18ms/step - loss: 1.2341 - accuracy: 0.5608 - val_loss: 1.2561 - val_accuracy: 0.4595\n",
      "Epoch 19/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2289 - accuracy: 0.5608 - val_loss: 1.2499 - val_accuracy: 0.4595\n",
      "Epoch 20/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2238 - accuracy: 0.5608 - val_loss: 1.2438 - val_accuracy: 0.4595\n",
      "Epoch 21/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2188 - accuracy: 0.5608 - val_loss: 1.2378 - val_accuracy: 0.4595\n",
      "Epoch 22/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2138 - accuracy: 0.5608 - val_loss: 1.2320 - val_accuracy: 0.4595\n",
      "Epoch 23/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2090 - accuracy: 0.5608 - val_loss: 1.2264 - val_accuracy: 0.4595\n",
      "Epoch 24/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.2042 - accuracy: 0.5608 - val_loss: 1.2208 - val_accuracy: 0.4595\n",
      "Epoch 25/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1995 - accuracy: 0.5608 - val_loss: 1.2154 - val_accuracy: 0.4595\n",
      "Epoch 26/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1948 - accuracy: 0.5608 - val_loss: 1.2101 - val_accuracy: 0.4595\n",
      "Epoch 27/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1902 - accuracy: 0.5608 - val_loss: 1.2049 - val_accuracy: 0.4595\n",
      "Epoch 28/100\n",
      "1/1 [==============================] - 0s 18ms/step - loss: 1.1857 - accuracy: 0.5608 - val_loss: 1.1998 - val_accuracy: 0.4595\n",
      "Epoch 29/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1812 - accuracy: 0.5608 - val_loss: 1.1948 - val_accuracy: 0.4595\n",
      "Epoch 30/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1767 - accuracy: 0.5608 - val_loss: 1.1899 - val_accuracy: 0.4730\n",
      "Epoch 31/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1723 - accuracy: 0.5608 - val_loss: 1.1851 - val_accuracy: 0.4730\n",
      "Epoch 32/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1679 - accuracy: 0.5608 - val_loss: 1.1803 - val_accuracy: 0.4730\n",
      "Epoch 33/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1636 - accuracy: 0.5676 - val_loss: 1.1756 - val_accuracy: 0.4730\n",
      "Epoch 34/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1593 - accuracy: 0.5676 - val_loss: 1.1710 - val_accuracy: 0.4730\n",
      "Epoch 35/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1550 - accuracy: 0.5676 - val_loss: 1.1665 - val_accuracy: 0.4730\n",
      "Epoch 36/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.1508 - accuracy: 0.5676 - val_loss: 1.1620 - val_accuracy: 0.4730\n",
      "Epoch 37/100\n",
      "1/1 [==============================] - 0s 19ms/step - loss: 1.1466 - accuracy: 0.5676 - val_loss: 1.1576 - val_accuracy: 0.4730\n",
      "Epoch 38/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.1425 - accuracy: 0.5743 - val_loss: 1.1533 - val_accuracy: 0.4730\n",
      "Epoch 39/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.1384 - accuracy: 0.5743 - val_loss: 1.1490 - val_accuracy: 0.4730\n",
      "Epoch 40/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.1343 - accuracy: 0.5743 - val_loss: 1.1447 - val_accuracy: 0.4865\n",
      "Epoch 41/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1302 - accuracy: 0.5743 - val_loss: 1.1405 - val_accuracy: 0.4865\n",
      "Epoch 42/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1262 - accuracy: 0.5743 - val_loss: 1.1364 - val_accuracy: 0.4865\n",
      "Epoch 43/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1222 - accuracy: 0.5811 - val_loss: 1.1322 - val_accuracy: 0.5000\n",
      "Epoch 44/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.1182 - accuracy: 0.5811 - val_loss: 1.1282 - val_accuracy: 0.5000\n",
      "Epoch 45/100\n",
      "1/1 [==============================] - 0s 14ms/step - loss: 1.1143 - accuracy: 0.6081 - val_loss: 1.1242 - val_accuracy: 0.5270\n",
      "Epoch 46/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.1104 - accuracy: 0.6284 - val_loss: 1.1202 - val_accuracy: 0.5270\n",
      "Epoch 47/100\n",
      "1/1 [==============================] - 0s 19ms/step - loss: 1.1065 - accuracy: 0.6351 - val_loss: 1.1162 - val_accuracy: 0.5270\n",
      "Epoch 48/100\n",
      "1/1 [==============================] - 0s 58ms/step - loss: 1.1026 - accuracy: 0.6419 - val_loss: 1.1123 - val_accuracy: 0.5270\n",
      "Epoch 49/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0988 - accuracy: 0.6486 - val_loss: 1.1085 - val_accuracy: 0.5405\n",
      "Epoch 50/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0949 - accuracy: 0.6757 - val_loss: 1.1046 - val_accuracy: 0.5811\n",
      "Epoch 51/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0911 - accuracy: 0.6892 - val_loss: 1.1008 - val_accuracy: 0.5946\n",
      "Epoch 52/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0874 - accuracy: 0.6959 - val_loss: 1.0971 - val_accuracy: 0.6081\n",
      "Epoch 53/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0836 - accuracy: 0.7162 - val_loss: 1.0933 - val_accuracy: 0.6757\n",
      "Epoch 54/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0799 - accuracy: 0.7230 - val_loss: 1.0896 - val_accuracy: 0.6892\n",
      "Epoch 55/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0762 - accuracy: 0.7365 - val_loss: 1.0859 - val_accuracy: 0.7027\n",
      "Epoch 56/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0725 - accuracy: 0.7568 - val_loss: 1.0823 - val_accuracy: 0.7162\n",
      "Epoch 57/100\n",
      "1/1 [==============================] - 0s 19ms/step - loss: 1.0689 - accuracy: 0.7703 - val_loss: 1.0787 - val_accuracy: 0.7162\n",
      "Epoch 58/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0652 - accuracy: 0.7703 - val_loss: 1.0751 - val_accuracy: 0.7297\n",
      "Epoch 59/100\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0616 - accuracy: 0.7703 - val_loss: 1.0715 - val_accuracy: 0.7568\n",
      "Epoch 60/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0580 - accuracy: 0.7703 - val_loss: 1.0680 - val_accuracy: 0.7703\n",
      "Epoch 61/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0545 - accuracy: 0.7905 - val_loss: 1.0645 - val_accuracy: 0.7838\n",
      "Epoch 62/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0509 - accuracy: 0.8243 - val_loss: 1.0610 - val_accuracy: 0.8243\n",
      "Epoch 63/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0474 - accuracy: 0.8311 - val_loss: 1.0575 - val_accuracy: 0.8378\n",
      "Epoch 64/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0439 - accuracy: 0.8446 - val_loss: 1.0541 - val_accuracy: 0.8378\n",
      "Epoch 65/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0404 - accuracy: 0.8581 - val_loss: 1.0507 - val_accuracy: 0.8378\n",
      "Epoch 66/100\n",
      "1/1 [==============================] - 0s 18ms/step - loss: 1.0369 - accuracy: 0.8649 - val_loss: 1.0473 - val_accuracy: 0.8514\n",
      "Epoch 67/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0335 - accuracy: 0.8716 - val_loss: 1.0439 - val_accuracy: 0.8514\n",
      "Epoch 68/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0301 - accuracy: 0.8716 - val_loss: 1.0406 - val_accuracy: 0.8514\n",
      "Epoch 69/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0267 - accuracy: 0.8716 - val_loss: 1.0372 - val_accuracy: 0.8514\n",
      "Epoch 70/100\n",
      "1/1 [==============================] - 0s 18ms/step - loss: 1.0233 - accuracy: 0.8716 - val_loss: 1.0339 - val_accuracy: 0.8514\n",
      "Epoch 71/100\n",
      "1/1 [==============================] - 0s 17ms/step - loss: 1.0199 - accuracy: 0.8716 - val_loss: 1.0307 - val_accuracy: 0.8649\n",
      "Epoch 72/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 1.0166 - accuracy: 0.8716 - val_loss: 1.0274 - val_accuracy: 0.8649\n",
      "Epoch 73/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0132 - accuracy: 0.8716 - val_loss: 1.0241 - val_accuracy: 0.8649\n",
      "Epoch 74/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0099 - accuracy: 0.8716 - val_loss: 1.0209 - val_accuracy: 0.8784\n",
      "Epoch 75/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0066 - accuracy: 0.8716 - val_loss: 1.0177 - val_accuracy: 0.8784\n",
      "Epoch 76/100\n",
      "1/1 [==============================] - 0s 18ms/step - loss: 1.0034 - accuracy: 0.8716 - val_loss: 1.0145 - val_accuracy: 0.8784\n",
      "Epoch 77/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 1.0001 - accuracy: 0.8784 - val_loss: 1.0114 - val_accuracy: 0.8784\n",
      "Epoch 78/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9969 - accuracy: 0.8986 - val_loss: 1.0082 - val_accuracy: 0.9054\n",
      "Epoch 79/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9937 - accuracy: 0.8986 - val_loss: 1.0051 - val_accuracy: 0.9189\n",
      "Epoch 80/100\n",
      "1/1 [==============================] - 0s 17ms/step - loss: 0.9905 - accuracy: 0.8986 - val_loss: 1.0020 - val_accuracy: 0.9189\n",
      "Epoch 81/100\n",
      "1/1 [==============================] - 0s 17ms/step - loss: 0.9873 - accuracy: 0.8986 - val_loss: 0.9989 - val_accuracy: 0.9189\n",
      "Epoch 82/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9841 - accuracy: 0.9122 - val_loss: 0.9958 - val_accuracy: 0.9189\n",
      "Epoch 83/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9810 - accuracy: 0.9122 - val_loss: 0.9928 - val_accuracy: 0.9189\n",
      "Epoch 84/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9778 - accuracy: 0.9122 - val_loss: 0.9897 - val_accuracy: 0.9459\n",
      "Epoch 85/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9747 - accuracy: 0.9189 - val_loss: 0.9867 - val_accuracy: 0.9459\n",
      "Epoch 86/100\n",
      "1/1 [==============================] - 0s 19ms/step - loss: 0.9716 - accuracy: 0.9189 - val_loss: 0.9837 - val_accuracy: 0.9459\n",
      "Epoch 87/100\n",
      "1/1 [==============================] - 0s 17ms/step - loss: 0.9686 - accuracy: 0.9189 - val_loss: 0.9807 - val_accuracy: 0.9595\n",
      "Epoch 88/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 0.9655 - accuracy: 0.9189 - val_loss: 0.9777 - val_accuracy: 0.9595\n",
      "Epoch 89/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 0.9625 - accuracy: 0.9189 - val_loss: 0.9748 - val_accuracy: 0.9595\n",
      "Epoch 90/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 0.9594 - accuracy: 0.9189 - val_loss: 0.9718 - val_accuracy: 0.9595\n",
      "Epoch 91/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 0.9564 - accuracy: 0.9189 - val_loss: 0.9689 - val_accuracy: 0.9730\n",
      "Epoch 92/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 0.9534 - accuracy: 0.9189 - val_loss: 0.9660 - val_accuracy: 0.9730\n",
      "Epoch 93/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 0.9505 - accuracy: 0.9257 - val_loss: 0.9631 - val_accuracy: 0.9730\n",
      "Epoch 94/100\n",
      "1/1 [==============================] - 0s 15ms/step - loss: 0.9475 - accuracy: 0.9257 - val_loss: 0.9602 - val_accuracy: 0.9865\n",
      "Epoch 95/100\n",
      "1/1 [==============================] - 0s 20ms/step - loss: 0.9446 - accuracy: 0.9257 - val_loss: 0.9574 - val_accuracy: 0.9865\n",
      "Epoch 96/100\n",
      "1/1 [==============================] - 0s 17ms/step - loss: 0.9416 - accuracy: 0.9324 - val_loss: 0.9545 - val_accuracy: 0.9865\n",
      "Epoch 97/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9387 - accuracy: 0.9324 - val_loss: 0.9517 - val_accuracy: 0.9865\n",
      "Epoch 98/100\n",
      "1/1 [==============================] - 0s 17ms/step - loss: 0.9358 - accuracy: 0.9324 - val_loss: 0.9489 - val_accuracy: 0.9865\n",
      "Epoch 99/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9330 - accuracy: 0.9392 - val_loss: 0.9461 - val_accuracy: 0.9865\n",
      "Epoch 100/100\n",
      "1/1 [==============================] - 0s 16ms/step - loss: 0.9301 - accuracy: 0.9459 - val_loss: 0.9433 - val_accuracy: 0.9865\n"
     ]
    }
   ],
   "source": [
    "batch_size = train_split\n",
    "nb_epoch = 100\n",
    "n = X_train.shape[0] # number of training examples\n",
    "history = model.fit(X_train, Y_oh_train, validation_data=(X_val,Y_oh_val), \\\n",
    "                    batch_size=batch_size, epochs=nb_epoch,verbose=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prininting Loss and estimated weights (Ws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final loss (cross-entropy and accuracy): [0.9351743459701538, 0.9054054021835327]\n",
      "\n",
      "Layer 0\n",
      "Bias:\n",
      " [-0.3811083   0.5073468  -0.11489844 -0.01133997]\n",
      "W:\n",
      " [[ 0.6958021  -0.13924785  1.4662881  -1.5514398 ]\n",
      " [ 0.31671807 -1.2081363  -1.0485553   1.1792164 ]]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "loss = model.evaluate(X_test, Y_oh_test, verbose=0)\n",
    "print('Final loss (cross-entropy and accuracy):',loss)\n",
    "print()\n",
    "W = model.get_weights()\n",
    "for ii in range(len(W)//2):\n",
    "    print(\"Layer %d\" %ii)\n",
    "    print('Bias:\\n', W[2*ii + 1])\n",
    "    print('W:\\n', W[2*ii])\n",
    "    print()\n",
    "\n",
    "plt.plot(history.history['loss'], label = \"Train loss\")\n",
    "plt.plot(history.history['val_loss'], label = \"Val loss\")\n",
    "plt.xlabel(\"Epoch (iteration)\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.plot(history.history['accuracy'], label = \"Train accuarcy\")\n",
    "plt.plot(history.history['val_accuracy'], label = \"Val accuarcy\")\n",
    "plt.xlabel(\"Epoch (iteration)\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classifier Decision Boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = .02  # step size in the mesh\n",
    "slack = 0.1\n",
    "# Calcula a grade para o espaço de atributos\n",
    "\n",
    "x_min, x_max = X_train.min(axis=0) - slack, X_train.max(axis=0) + slack\n",
    "xx, yy = np.meshgrid(np.arange(x_min[0], x_max[0], h), np.arange(x_min[1], x_max[1], h))\n",
    "X_grid = np.c_[xx.ravel(), yy.ravel()]\n",
    "\n",
    "# Prediction of all samples in our grid\n",
    "Z = model.predict(X_grid).argmax(axis = 1)\n",
    "Z = Z.reshape(xx.shape)\n",
    "\n",
    "# Display decision boundary\n",
    "plt.figure(1, figsize=(6, 5))\n",
    "plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "\n",
    "# Display training samples\n",
    "plt.scatter(X_train[:,0], X_train[:,1], c=colors[Y_train], edgecolors='k', cmap=plt.cm.Paired)\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Suggested activities\n",
    "- Repeat the example without normalizing the data or using standardization (i.e., subtract from the mean and divide by the standard-deviation);\n",
    "- Experiment with other datasets\n",
    "- Change the neural network architecture\n",
    "- ..."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}