m.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import keras\n",
    "from keras.datasets import mnist\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Conv2D, MaxPool2D, Flatten, Dropout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the data and pre-process it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((60000, 28, 28), (60000,), (10000, 28, 28), (10000,))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(X_train, Y_train),(X_test, Y_test) = mnist.load_data()\n",
    "\n",
    "X_train.shape, Y_train.shape, X_test.shape, Y_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2beb87b68d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(X_train[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_input_img(i):\n",
    "  plt.imshow(X_train[i], cmap='binary')\n",
    "  plt.title(Y_train[i])\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaAAAAGzCAYAAABpdMNsAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/TGe4hAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAdvElEQVR4nO3de2zV9f3H8dfh0iNge2qtvZzRYgGRyW0OpetQhtIV6kIE0eEtAWcwYjEiOk0XlcuW9CcmanAM4y4wI+AlEfA2FgQpKi2TAkHmqJR0Awctiuk5pUBp6Of3B/HMI1T4Hs7puy3PR3ISe85597z97qxPD+f0i8855wQAQDvrZr0AAODCRIAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBDQDj755BPNmjVLQ4YMUZ8+fZSbm6tf/vKX+vzzz61XA8z4OBcckHi33nqrPv74Y912220aPny46urq9Pvf/15HjhxRZWWlhg4dar0i0O4IENAONm/erGuuuUZJSUmR6/bs2aNhw4bp1ltv1SuvvGK4HWCDAAGGRo4cKUmqqqoy3gRof7wHBBhxzqm+vl7p6enWqwAmCBBgZPny5frvf/+rqVOnWq8CmOCP4AADu3fvVn5+voYMGaIPP/xQ3bt3t14JaHcECGhndXV1Gj16tFpaWlRZWalgMGi9EmCih/UCwIUkFAqpuLhYDQ0N+vDDD4kPLmgECGgnx48f18SJE/X555/r/fff11VXXWW9EmCKAAHt4OTJk5o6daoqKiq0Zs0aFRQUWK8EmCNAQDt45JFH9NZbb2nixIn6+uuvT/vF07vvvttoM8AOH0IA2sHYsWNVXl7e5u383xAXIgIEADDBL6ICAEwQIACACQIEADBBgAAAJggQAMAEAQIAmOhwv4ja2tqqAwcOKDk5WT6fz3odAIBHzjk1NjYqGAyqW7e2X+d0uAAdOHBAOTk51msAAM7T/v371bdv3zZv73ABSk5OlnRq8ZSUFONtAABehcNh5eTkRH6etyVhAVq8eLGeeeYZ1dXVacSIEXrhhRc0atSos85988duKSkpBAgAOrGzvY2SkA8hvPbaa5ozZ47mzp2rbdu2acSIERo/frwOHTqUiIcDAHRCCQnQs88+qxkzZuiee+7RVVddpRdffFG9e/fWX/7yl0Q8HACgE4p7gE6cOKGqqioVFhb+70G6dVNhYaEqKipOu39zc7PC4XDUBQDQ9cU9QF999ZVOnjypzMzMqOszMzNVV1d32v3LysoUCAQiFz4BBwAXBvNfRC0tLVUoFIpc9u/fb70SAKAdxP1TcOnp6erevbvq6+ujrq+vr1dWVtZp9/f7/fL7/fFeAwDQwcX9FVBSUpJGjhyp9evXR65rbW3V+vXrVVBQEO+HAwB0Ugn5PaA5c+Zo2rRpuuaaazRq1Cg9//zzampq0j333JOIhwMAdEIJCdDUqVP15Zdf6qmnnlJdXZ1+9KMfae3atad9MAEAcOHyOeec9RLfFg6HFQgEFAqFOBMCAHRC5/pz3PxTcACACxMBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgoof1AgDOTWNjo+eZI0eOxPRY7777rueZQ4cOeZ555JFHPM/4/X7PM+iYeAUEADBBgAAAJuIeoHnz5snn80VdBg8eHO+HAQB0cgl5D2jIkCF6//33//cgPXirCQAQLSFl6NGjh7KyshLxrQEAXURC3gPas2ePgsGg+vfvr7vuukv79u1r877Nzc0Kh8NRFwBA1xf3AOXn52vZsmVau3atlixZotraWl1//fVtfoS0rKxMgUAgcsnJyYn3SgCADijuASouLtZtt92m4cOHa/z48XrvvffU0NCg119//Yz3Ly0tVSgUilz2798f75UAAB1Qwj8dkJqaqkGDBqmmpuaMt/v9fn6xDAAuQAn/PaAjR45o7969ys7OTvRDAQA6kbgH6NFHH1V5ebn+/e9/a/PmzZo8ebK6d++uO+64I94PBQDoxOL+R3BffPGF7rjjDh0+fFiXXXaZrrvuOlVWVuqyyy6L90MBADqxuAfo1Vdfjfe3BDq02tpazzMLFy70PFNRUeF55tNPP/U8057q6uo8zyxatCgBm8AC54IDAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwk/C+kAyzs3r07prnnn3/e88wrr7zieebYsWOeZ5xznmdyc3M9z0hScnKy55nPPvvM80xbf1Py93nggQc8zwwePNjzDBKPV0AAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwwdmw0a5CoZDnmccff9zzzGuvveZ5RpLC4XBMc+1h0KBBnmf+/ve/x/RYJ06c8DwTyxmnv/zyS88zX331lecZdEy8AgIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATHAyUrSrVatWeZ754x//mIBNbA0cONDzzLp16zzP5OTkeJ6RpD179sQ0B3jBKyAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQnI0W7ev31161X+F6XX36555lRo0Z5nnn66ac9z8R6YtFY7N69u90eCxcuXgEBAEwQIACACc8B2rRpkyZOnKhgMCifz6fVq1dH3e6c01NPPaXs7Gz16tVLhYWF/N0iAIDTeA5QU1OTRowYocWLF5/x9oULF2rRokV68cUXtWXLFvXp00fjx4/X8ePHz3tZAEDX4flDCMXFxSouLj7jbc45Pf/883riiSd08803S5JefvllZWZmavXq1br99tvPb1sAQJcR1/eAamtrVVdXp8LCwsh1gUBA+fn5qqioOONMc3OzwuFw1AUA0PXFNUB1dXWSpMzMzKjrMzMzI7d9V1lZmQKBQOTSnh81BQDYMf8UXGlpqUKhUOSyf/9+65UAAO0grgHKysqSJNXX10ddX19fH7ntu/x+v1JSUqIuAICuL64BysvLU1ZWltavXx+5LhwOa8uWLSooKIjnQwEAOjnPn4I7cuSIampqIl/X1tZqx44dSktLU25urmbPnq3f/e53uuKKK5SXl6cnn3xSwWBQkyZNiufeAIBOznOAtm7dqhtuuCHy9Zw5cyRJ06ZN07Jly/TYY4+pqalJ9913nxoaGnTddddp7dq1uuiii+K3NQCg0/McoLFjx8o51+btPp9PCxYs0IIFC85rMXRNf/rTnzzPvPTSS55nioqKPM9I0sCBAz3PZGRkxPRYHdl338cFEsH8U3AAgAsTAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATHg+GzZwPoLBoOeZefPmxX8RfK/Nmzdbr4ALAK+AAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATnIwUOE+LFi3yPNPU1OR5xjnnecbn83mekaRdu3bFNOfV6NGjPc8UFBQkYBNY4BUQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCk5Giwzt69KjnmX/+858xPdaCBQs8z7z77rsxPZZX7Xky0lgEg0HPM0uXLvU80717d88z6Jh4BQQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmOBkpIhZS0uL55nt27d7npkyZYrnmQMHDniekaTevXt7nonlJJw//elPPc+sXbvW80xTU5PnmVidPHnS88ybb77peeahhx7yPJOUlOR5BonHKyAAgAkCBAAw4TlAmzZt0sSJExUMBuXz+bR69eqo26dPny6fzxd1mTBhQrz2BQB0EZ4D1NTUpBEjRmjx4sVt3mfChAk6ePBg5LJy5crzWhIA0PV4/hBCcXGxiouLv/c+fr9fWVlZMS8FAOj6EvIe0MaNG5WRkaErr7xSM2fO1OHDh9u8b3Nzs8LhcNQFAND1xT1AEyZM0Msvv6z169fr6aefVnl5uYqLi9v8iGZZWZkCgUDkkpOTE++VAAAdUNx/D+j222+P/POwYcM0fPhwDRgwQBs3btS4ceNOu39paanmzJkT+TocDhMhALgAJPxj2P3791d6erpqamrOeLvf71dKSkrUBQDQ9SU8QF988YUOHz6s7OzsRD8UAKAT8fxHcEeOHIl6NVNbW6sdO3YoLS1NaWlpmj9/vqZMmaKsrCzt3btXjz32mAYOHKjx48fHdXEAQOfmOUBbt27VDTfcEPn6m/dvpk2bpiVLlmjnzp3661//qoaGBgWDQRUVFem3v/2t/H5//LYGAHR6Puecs17i28LhsAKBgEKhEO8HtZMTJ07ENBfLyTEnT54c02N5NW/evJjmvv0fV+fquuuu8zzz9ddfe5658cYbPc98+umnnmc6uhUrVniemTRpUkyPxX84x+Zcf45zLjgAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYiPtfyQ1bLS0tnmfmzp0b02MtXLgwpjmviouLPc88+OCDMT1Wamqq55kvv/zS88xNN93keWbnzp2eZ2I9m/Njjz3meSaWM2+vWbPG88ydd97peebnP/+55xkptuNwySWXxPRYXl199dXt8jiJxCsgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEJyPtwE6ePOl55sknn/Q888wzz3iekaSLL77Y80xZWZnnmTvuuMPzTCwnFZWkTz75xPNMLCc+3bZtm+eZQYMGeZ5ZsmSJ5xlJuuGGGzzPhMNhzzObN2/2PLN8+XLPM2+99ZbnGSn2k5h6lZub63mmtrY2AZu0L14BAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmfM45Z73Et4XDYQUCAYVCIaWkpFivYyqWE0nOmjXL80yfPn08z0jSSy+95HmmqKjI88yWLVs8zyxdutTzjCS99957nmeOHTvmeWbu3LmeZ+655x7PMzk5OZ5nuqKVK1fGNBfLiU9j8dxzz3meueKKKxKwSXyc689xXgEBAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACY4GWkHlp2d7Xnm0KFDnmf8fr/nGUkaPHiw55mjR496ntmzZ4/nmfY0f/58zzOlpaWeZ7p37+55BrDAyUgBAB0aAQIAmPAUoLKyMl177bVKTk5WRkaGJk2apOrq6qj7HD9+XCUlJbr00kt18cUXa8qUKaqvr4/r0gCAzs9TgMrLy1VSUqLKykqtW7dOLS0tKioqUlNTU+Q+Dz/8sN5++2298cYbKi8v14EDB3TLLbfEfXEAQOfWw8ud165dG/X1smXLlJGRoaqqKo0ZM0ahUEh//vOftWLFCt14442STv3NlD/84Q9VWVmpn/zkJ/HbHADQqZ3Xe0ChUEiSlJaWJkmqqqpSS0uLCgsLI/cZPHiwcnNzVVFRccbv0dzcrHA4HHUBAHR9MQeotbVVs2fP1ujRozV06FBJUl1dnZKSkpSamhp138zMTNXV1Z3x+5SVlSkQCEQu/B32AHBhiDlAJSUl2rVrl1599dXzWqC0tFShUChy2b9//3l9PwBA5+DpPaBvzJo1S++88442bdqkvn37Rq7PysrSiRMn1NDQEPUqqL6+XllZWWf8Xn6/P+ZfhAQAdF6eXgE55zRr1iytWrVKGzZsUF5eXtTtI0eOVM+ePbV+/frIddXV1dq3b58KCgriszEAoEvw9AqopKREK1as0Jo1a5ScnBx5XycQCKhXr14KBAK69957NWfOHKWlpSklJUUPPvigCgoK+AQcACCKpwAtWbJEkjR27Nio65cuXarp06dLkp577jl169ZNU6ZMUXNzs8aPH68//OEPcVkWANB1cDLSDuzqq6/2PLNz584EbGLrF7/4heeZMWPGxPRYkyZN8jxz+eWXe57p0SOmt1+BToGTkQIAOjQCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCY4JS8HdimTZs8z6xevdrzzLZt2zzPSFJGRobnmV/96leeZy655BLPM0lJSZ5nALQvXgEBAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACZ8zjlnvcS3hcNhBQIBhUIhpaSkWK8DAPDoXH+O8woIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMOEpQGVlZbr22muVnJysjIwMTZo0SdXV1VH3GTt2rHw+X9Tl/vvvj+vSAIDOz1OAysvLVVJSosrKSq1bt04tLS0qKipSU1NT1P1mzJihgwcPRi4LFy6M69IAgM6vh5c7r127NurrZcuWKSMjQ1VVVRozZkzk+t69eysrKys+GwIAuqTzeg8oFApJktLS0qKuX758udLT0zV06FCVlpbq6NGjbX6P5uZmhcPhqAsAoOvz9Aro21pbWzV79myNHj1aQ4cOjVx/5513ql+/fgoGg9q5c6cef/xxVVdX68033zzj9ykrK9P8+fNjXQMA0En5nHMulsGZM2fqb3/7mz766CP17du3zftt2LBB48aNU01NjQYMGHDa7c3NzWpubo58HQ6HlZOTo1AopJSUlFhWAwAYCofDCgQCZ/05HtMroFmzZumdd97Rpk2bvjc+kpSfny9JbQbI7/fL7/fHsgYAoBPzFCDnnB588EGtWrVKGzduVF5e3llnduzYIUnKzs6OaUEAQNfkKUAlJSVasWKF1qxZo+TkZNXV1UmSAoGAevXqpb1792rFihW66aabdOmll2rnzp16+OGHNWbMGA0fPjwh/wIAgM7J03tAPp/vjNcvXbpU06dP1/79+3X33Xdr165dampqUk5OjiZPnqwnnnjinN/POdc/OwQAdEwJeQ/obK3KyclReXm5l28JALhAcS44AIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAICJHtYLfJdzTpIUDoeNNwEAxOKbn9/f/DxvS4cLUGNjoyQpJyfHeBMAwPlobGxUIBBo83afO1ui2llra6sOHDig5ORk+Xy+qNvC4bBycnK0f/9+paSkGG1oj+NwCsfhFI7DKRyHUzrCcXDOqbGxUcFgUN26tf1OT4d7BdStWzf17dv3e++TkpJyQT/BvsFxOIXjcArH4RSOwynWx+H7Xvl8gw8hAABMECAAgIlOFSC/36+5c+fK7/dbr2KK43AKx+EUjsMpHIdTOtNx6HAfQgAAXBg61SsgAEDXQYAAACYIEADABAECAJggQAAAE50mQIsXL9bll1+uiy66SPn5+frHP/5hvVK7mzdvnnw+X9Rl8ODB1msl3KZNmzRx4kQFg0H5fD6tXr066nbnnJ566illZ2erV69eKiws1J49e2yWTaCzHYfp06ef9vyYMGGCzbIJUlZWpmuvvVbJycnKyMjQpEmTVF1dHXWf48ePq6SkRJdeeqkuvvhiTZkyRfX19UYbJ8a5HIexY8ee9ny4//77jTY+s04RoNdee01z5szR3LlztW3bNo0YMULjx4/XoUOHrFdrd0OGDNHBgwcjl48++sh6pYRramrSiBEjtHjx4jPevnDhQi1atEgvvviitmzZoj59+mj8+PE6fvx4O2+aWGc7DpI0YcKEqOfHypUr23HDxCsvL1dJSYkqKyu1bt06tbS0qKioSE1NTZH7PPzww3r77bf1xhtvqLy8XAcOHNAtt9xiuHX8nctxkKQZM2ZEPR8WLlxotHEbXCcwatQoV1JSEvn65MmTLhgMurKyMsOt2t/cuXPdiBEjrNcwJcmtWrUq8nVra6vLyspyzzzzTOS6hoYG5/f73cqVKw02bB/fPQ7OOTdt2jR38803m+xj5dChQ06SKy8vd86d+t++Z8+e7o033ojc51//+peT5CoqKqzWTLjvHgfnnPvZz37mHnroIbulzkGHfwV04sQJVVVVqbCwMHJdt27dVFhYqIqKCsPNbOzZs0fBYFD9+/fXXXfdpX379lmvZKq2tlZ1dXVRz49AIKD8/PwL8vmxceNGZWRk6Morr9TMmTN1+PBh65USKhQKSZLS0tIkSVVVVWppaYl6PgwePFi5ubld+vnw3ePwjeXLlys9PV1Dhw5VaWmpjh49arFemzrc2bC/66uvvtLJkyeVmZkZdX1mZqZ2795ttJWN/Px8LVu2TFdeeaUOHjyo+fPn6/rrr9euXbuUnJxsvZ6Juro6STrj8+Ob2y4UEyZM0C233KK8vDzt3btXv/nNb1RcXKyKigp1797der24a21t1ezZszV69GgNHTpU0qnnQ1JSklJTU6Pu25WfD2c6DpJ05513ql+/fgoGg9q5c6cef/xxVVdX68033zTcNlqHDxD+p7i4OPLPw4cPV35+vvr166fXX39d9957r+Fm6Ahuv/32yD8PGzZMw4cP14ABA7Rx40aNGzfOcLPEKCkp0a5duy6I90G/T1vH4b777ov887Bhw5Sdna1x48Zp7969GjBgQHuveUYd/o/g0tPT1b1799M+xVJfX6+srCyjrTqG1NRUDRo0SDU1NdarmPnmOcDz43T9+/dXenp6l3x+zJo1S++8844++OCDqL8/LCsrSydOnFBDQ0PU/bvq86Gt43Am+fn5ktShng8dPkBJSUkaOXKk1q9fH7mutbVV69evV0FBgeFm9o4cOaK9e/cqOzvbehUzeXl5ysrKinp+hMNhbdmy5YJ/fnzxxRc6fPhwl3p+OOc0a9YsrVq1Shs2bFBeXl7U7SNHjlTPnj2jng/V1dXat29fl3o+nO04nMmOHTskqWM9H6w/BXEuXn31Vef3+92yZcvcZ5995u677z6Xmprq6urqrFdrV4888ojbuHGjq62tdR9//LErLCx06enp7tChQ9arJVRjY6Pbvn272759u5Pknn32Wbd9+3b3n//8xznn3P/93/+51NRUt2bNGrdz50538803u7y8PHfs2DHjzePr+45DY2Oje/TRR11FRYWrra1177//vvvxj3/srrjiCnf8+HHr1eNm5syZLhAIuI0bN7qDBw9GLkePHo3c5/7773e5ubluw4YNbuvWra6goMAVFBQYbh1/ZzsONTU1bsGCBW7r1q2utrbWrVmzxvXv39+NGTPGePNonSJAzjn3wgsvuNzcXJeUlORGjRrlKisrrVdqd1OnTnXZ2dkuKSnJ/eAHP3BTp051NTU11msl3AcffOAknXaZNm2ac+7UR7GffPJJl5mZ6fx+vxs3bpyrrq62XToBvu84HD161BUVFbnLLrvM9ezZ0/Xr18/NmDGjy/1H2pn+/SW5pUuXRu5z7Ngx98ADD7hLLrnE9e7d202ePNkdPHjQbukEONtx2LdvnxszZoxLS0tzfr/fDRw40P361792oVDIdvHv4O8DAgCY6PDvAQEAuiYCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAm/h/PvaiAwm7stwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "  plot_input_img(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Preprocess the data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#normalizing the image to [0,1] range\n",
    "\n",
    "X_train = X_train.astype(np.float32)/255\n",
    "X_test = X_test.astype(np.float32)/255\n",
    "\n",
    "#reshape / expand the dimensions of images to (28)\n",
    "X_train = np.expand_dims(X_train, -1)\n",
    "X_test = np.expand_dims(X_test, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 28, 28, 1)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., ..., 0., 0., 0.],\n",
       "       [1., 0., 0., ..., 0., 0., 0.],\n",
       "       [0., 0., 0., ..., 0., 0., 0.],\n",
       "       ...,\n",
       "       [0., 0., 0., ..., 0., 0., 0.],\n",
       "       [0., 0., 0., ..., 0., 0., 0.],\n",
       "       [0., 0., 0., ..., 0., 1., 0.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#convert classes to one hot vector\n",
    "Y_train = keras.utils.to_categorical(Y_train)\n",
    "Y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., ..., 1., 0., 0.],\n",
       "       [0., 0., 1., ..., 0., 0., 0.],\n",
       "       [0., 1., 0., ..., 0., 0., 0.],\n",
       "       ...,\n",
       "       [0., 0., 0., ..., 0., 0., 0.],\n",
       "       [0., 0., 0., ..., 0., 0., 0.],\n",
       "       [0., 0., 0., ..., 0., 0., 0.]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#convert class to one hot vector\n",
    "Y_test = keras.utils.to_categorical(Y_test)\n",
    "Y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\ADMIN\\AppData\\Local\\Programs\\Python\\Python311\\Lib\\site-packages\\keras\\src\\layers\\convolutional\\base_conv.py:107: UserWarning: Do not pass an `input_shape`/`input_dim` argument to a layer. When using Sequential models, prefer using an `Input(shape)` object as the first layer in the model instead.\n",
      "  super().__init__(activity_regularizer=activity_regularizer, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "model = Sequential()\n",
    "\n",
    "model.add(Conv2D(32, (3,3), activation='relu', input_shape=(28,28,1)))\n",
    "model.add(MaxPool2D((2,2)))\n",
    "\n",
    "model.add(Conv2D(64, (3,3), activation='relu'))\n",
    "model.add(MaxPool2D((2,2)))\n",
    "\n",
    "model.add(Flatten())\n",
    "\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(10, activation='softmax'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">Model: \"sequential\"</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1mModel: \"sequential\"\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Layer (type)                    </span>┃<span style=\"font-weight: bold\"> Output Shape           </span>┃<span style=\"font-weight: bold\">       Param # </span>┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
       "│ conv2d (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Conv2D</span>)                 │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">26</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">26</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">32</span>)     │           <span style=\"color: #00af00; text-decoration-color: #00af00\">320</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ max_pooling2d (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">MaxPooling2D</span>)    │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">13</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">13</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">32</span>)     │             <span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ conv2d_1 (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Conv2D</span>)               │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">11</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">11</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">64</span>)     │        <span style=\"color: #00af00; text-decoration-color: #00af00\">18,496</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ max_pooling2d_1 (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">MaxPooling2D</span>)  │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">5</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">5</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">64</span>)       │             <span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ flatten (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Flatten</span>)               │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">1600</span>)           │             <span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dropout (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dropout</span>)               │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">1600</span>)           │             <span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                   │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">10</span>)             │        <span style=\"color: #00af00; text-decoration-color: #00af00\">16,010</span> │\n",
       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mLayer (type)                   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mOutput Shape          \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1m      Param #\u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
       "│ conv2d (\u001b[38;5;33mConv2D\u001b[0m)                 │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m26\u001b[0m, \u001b[38;5;34m26\u001b[0m, \u001b[38;5;34m32\u001b[0m)     │           \u001b[38;5;34m320\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ max_pooling2d (\u001b[38;5;33mMaxPooling2D\u001b[0m)    │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m13\u001b[0m, \u001b[38;5;34m13\u001b[0m, \u001b[38;5;34m32\u001b[0m)     │             \u001b[38;5;34m0\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ conv2d_1 (\u001b[38;5;33mConv2D\u001b[0m)               │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m11\u001b[0m, \u001b[38;5;34m11\u001b[0m, \u001b[38;5;34m64\u001b[0m)     │        \u001b[38;5;34m18,496\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ max_pooling2d_1 (\u001b[38;5;33mMaxPooling2D\u001b[0m)  │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m5\u001b[0m, \u001b[38;5;34m5\u001b[0m, \u001b[38;5;34m64\u001b[0m)       │             \u001b[38;5;34m0\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ flatten (\u001b[38;5;33mFlatten\u001b[0m)               │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m1600\u001b[0m)           │             \u001b[38;5;34m0\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dropout (\u001b[38;5;33mDropout\u001b[0m)               │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m1600\u001b[0m)           │             \u001b[38;5;34m0\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense (\u001b[38;5;33mDense\u001b[0m)                   │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m10\u001b[0m)             │        \u001b[38;5;34m16,010\u001b[0m │\n",
       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Total params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">34,826</span> (136.04 KB)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Total params: \u001b[0m\u001b[38;5;34m34,826\u001b[0m (136.04 KB)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Trainable params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">34,826</span> (136.04 KB)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Trainable params: \u001b[0m\u001b[38;5;34m34,826\u001b[0m (136.04 KB)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Non-trainable params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> (0.00 B)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Non-trainable params: \u001b[0m\u001b[38;5;34m0\u001b[0m (0.00 B)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(optimizer= 'adam', loss = keras.losses.categorical_crossentropy, metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#callbacks\n",
    "\n",
    "from keras.callbacks import ModelCheckpoint, EarlyStopping\n",
    "\n",
    "#Earlystopping\n",
    "\n",
    "es = EarlyStopping(monitor='val_accuracy', min_delta=0.01, patience=4, verbose=1)\n",
    "\n",
    "#ModelCheckpoint\n",
    "\n",
    "mc = ModelCheckpoint(\"./bestmodel.keras\", monitor = \"val_accuracy\", verbose=1, save_best_only=True)\n",
    "\n",
    "cb = [es,mc]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 28, 28, 1)\n",
      "(60000, 10)\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape)\n",
    "print(Y_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/50\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 17ms/step - accuracy: 0.8541 - loss: 0.4734\n",
      "Epoch 1: val_accuracy improved from -inf to 0.97589, saving model to ./bestmodel.keras\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m30s\u001b[0m 21ms/step - accuracy: 0.8542 - loss: 0.4732 - val_accuracy: 0.9759 - val_loss: 0.0804\n",
      "Epoch 2/50\n",
      "\u001b[1m1311/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m━\u001b[0m \u001b[1m0s\u001b[0m 14ms/step - accuracy: 0.9771 - loss: 0.0787\n",
      "Epoch 2: val_accuracy improved from 0.97589 to 0.97994, saving model to ./bestmodel.keras\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m21s\u001b[0m 16ms/step - accuracy: 0.9771 - loss: 0.0786 - val_accuracy: 0.9799 - val_loss: 0.0653\n",
      "Epoch 3/50\n",
      "\u001b[1m1311/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m━\u001b[0m \u001b[1m0s\u001b[0m 20ms/step - accuracy: 0.9812 - loss: 0.0589\n",
      "Epoch 3: val_accuracy improved from 0.97994 to 0.98322, saving model to ./bestmodel.keras\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m30s\u001b[0m 23ms/step - accuracy: 0.9812 - loss: 0.0589 - val_accuracy: 0.9832 - val_loss: 0.0549\n",
      "Epoch 4/50\n",
      "\u001b[1m1311/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m━\u001b[0m \u001b[1m0s\u001b[0m 19ms/step - accuracy: 0.9852 - loss: 0.0466\n",
      "Epoch 4: val_accuracy improved from 0.98322 to 0.98650, saving model to ./bestmodel.keras\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m40s\u001b[0m 22ms/step - accuracy: 0.9852 - loss: 0.0466 - val_accuracy: 0.9865 - val_loss: 0.0488\n",
      "Epoch 5/50\n",
      "\u001b[1m1309/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m━\u001b[0m \u001b[1m0s\u001b[0m 14ms/step - accuracy: 0.9876 - loss: 0.0378\n",
      "Epoch 5: val_accuracy did not improve from 0.98650\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m21s\u001b[0m 16ms/step - accuracy: 0.9876 - loss: 0.0378 - val_accuracy: 0.9862 - val_loss: 0.0455\n",
      "Epoch 6/50\n",
      "\u001b[1m1310/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m━\u001b[0m \u001b[1m0s\u001b[0m 17ms/step - accuracy: 0.9902 - loss: 0.0323\n",
      "Epoch 6: val_accuracy did not improve from 0.98650\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m47s\u001b[0m 20ms/step - accuracy: 0.9902 - loss: 0.0323 - val_accuracy: 0.9854 - val_loss: 0.0489\n",
      "Epoch 7/50\n",
      "\u001b[1m1310/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m━\u001b[0m \u001b[1m0s\u001b[0m 15ms/step - accuracy: 0.9903 - loss: 0.0297\n",
      "Epoch 7: val_accuracy improved from 0.98650 to 0.98911, saving model to ./bestmodel.keras\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m23s\u001b[0m 17ms/step - accuracy: 0.9903 - loss: 0.0297 - val_accuracy: 0.9891 - val_loss: 0.0380\n",
      "Epoch 8/50\n",
      "\u001b[1m1310/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m━\u001b[0m \u001b[1m0s\u001b[0m 15ms/step - accuracy: 0.9913 - loss: 0.0263\n",
      "Epoch 8: val_accuracy did not improve from 0.98911\n",
      "\u001b[1m1313/1313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m22s\u001b[0m 17ms/step - accuracy: 0.9913 - loss: 0.0263 - val_accuracy: 0.9881 - val_loss: 0.0423\n",
      "Epoch 8: early stopping\n"
     ]
    }
   ],
   "source": [
    "his = model.fit(X_train, Y_train, epochs = 50, validation_split=0.3, callbacks = cb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_S = keras.models.load_model(\"./bestmodel.keras\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m2s\u001b[0m 6ms/step - accuracy: 0.9894 - loss: 0.0342\n",
      " the model accuracy is 0.9918000102043152\n"
     ]
    }
   ],
   "source": [
    "score = model_S.evaluate(X_test, Y_test)\n",
    "print(f\" the model accuracy is {score[1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}