correlation_and_convolution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation & Convolution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from keras.datasets.mnist import load_data\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, y_train), (x_test, y_test) = load_data(\"/data/mnist.npz\",)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, y_train, x_test, y_test = x_train.reshape(60000,-1)/256, np.eye(10)[y_train], x_test.reshape(10000,-1)/256, np.eye(10)[y_test]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# you don't have to worry the following piece of code in this cell\n",
    "# We simply build a function, to plot number arrays to image\n",
    "# The visualization isn't the point of this class\n",
    "# just load the function, then you can use plot(input_image_array), and shift enter, it will show the image in notebook\n",
    "def plots(ims, interp=False, titles=None):\n",
    "    ims=np.array(ims)\n",
    "    mn,mx=ims.min(),ims.max()\n",
    "    f = plt.figure(figsize=(12,24))\n",
    "    for i in range(len(ims)):\n",
    "        sp=f.add_subplot(1, len(ims), i+1)\n",
    "        if not titles is None: sp.set_title(titles[i], fontsize=18)\n",
    "        plt.imshow(ims[i], interpolation=None if interp else 'none', vmin=mn,vmax=mx)\n",
    "\n",
    "def plot(im, interp=False):\n",
    "    f = plt.figure(figsize=(3,6), frameon=True)\n",
    "    plt.imshow(im, interpolation=None if interp else 'none')\n",
    "\n",
    "plt.gray()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(None, array([0., 1., 0., 0., 0., 0., 0., 0., 0., 0.]))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAADKCAYAAAAGucTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAACblJREFUeJzt3V+IHeUdxvHnSVovbAsxSIOoaUwimCAxBSOFSkiRllTU6E0wYEmhsLmo2IVeGAQxFAqh1LaBFMO2DaZgFcF/QUptkELaG3EV0U2yTVQMJqyJkovG3IjZXy/ObLtZ5uye3zmz58+c7weWM/vb2Zl3CE/eOe/OeV9HhAC0bkmvGwAMGkIDJBEaIInQAEmEBkgiNEASoQGSCA2QRGiApK908su2t0raJ2mppD9GxN4F9ufxA/StiHAr+7ndx2hsL5V0UtL3JZ2R9KakHRFxfJ7fITToW62GppPbszskvR8RH0bEF5Kek7Stg+MBA6GT0Fwv6eNZ358palewPWJ73PZ4B+cC+kZH72laERFjksYkbs9QD530NGcl3Tjr+xuKGlBrnYTmTUk3277J9lWSHpR0uJpmAf2r7duziPjS9sOSXlNjyPlgRByrrGVAn2p7yLmtk/GeBn2sG0POwFAiNEASoQGSCA2QRGiAJEIDJBEaIInQAEmEBkgiNEASoQGSCA2QRGiAJEIDJBEaIGnR5whA6/bt21daf+SRR0rrExMTpfV77rmntH769On2GoYr0NMASYQGSCI0QBKhAZIIDZDU6aoBH0m6KOmypC8j4vYqGlV3q1atKq0/9NBDpfXp6enS+rp160rrt9xyS2md0bNqVDHk/L2I+KyC4wADgdszIKnT0ISkv9t+y/ZI2Q6sGoC66fT27M6IOGv7m5KO2J6MiKOzd2DVANRNRz1NRJwtXs9LekmNhZ6AWmu7p7H9NUlLIuJisf0DSb+orGU19umnn5bWjx49Wlq/7777FrM5SOrk9myFpJdszxznLxHxt0paBfSxTpba+FDSbRW2BRgIDDkDSYQGSCI0QBKf3OyBS5culdZ5Nmww0NMASYQGSCI0QBKhAZIIDZDE6FkPLFu2rLR+2208YDEI6GmAJEIDJBEaIInQAEmEBkhi9KwHrr766tL6ypUrKzn+pk2bSuuTk5OldZ55y6GnAZIIDZBEaIAkQgMkLRga2wdtn7c9Mau23PYR26eK12sWt5lA/3DE/JNe2t4s6XNJf46IW4varyRdiIi9tndLuiYiHl3wZMywOa/HH3+8tL5nz57S+kL/dnONjo6W1vfv3586Tl1FhFvZb8Gepphm9sKc8jZJh4rtQ5LuT7UOGGDtvqdZERFTxfYnakwcCAyFjv+4GREx321XsZpA6YoCwCBqt6c5Z/s6SSpezzfbMSLGIuJ2VklDXbQbmsOSdhbbOyW9Uk1zgP7XyujZs5K2SLpW0jlJT0h6WdLzklZKOi1pe0TMHSwoOxajZ224fPlyaZ3Rs2q1Onq24HuaiNjR5Ed3pVoE1ARPBABJhAZIIjRAEqEBkvjk5gBYsqT8/7bp6ekutwQSPQ2QRmiAJEIDJBEaIInQAEmMng2AZqNk2WfPUA16GiCJ0ABJhAZIIjRAEqEBkggNkERogCRCAyQRGiCJ0ABJ7a4asMf2WdvvFF93L24zgf7RSk/ztKStJfXfRsTG4uuv1TYL6F/trhoADK1O3tM8bPvd4vaNRZ0wNNoNzVOS1kjaKGlK0pPNdrQ9Ynvc9nib5wL6SluhiYhzEXE5IqYl/UHSHfPsy6oBqJW2QjOzzEbhAUkTzfYF6mbBT27OXjXA9hk1Vg3YYnujpJD0kaRdi9jGoVfVvGebN28urbNqQE67qwb8aRHaAgwEnggAkggNkERogCRCAyQtuOZmpSdjzc22VLXmZjMbNmworR8/fryS4w+KVtfcpKcBkggNkERogCRCAyQRGiCJVQMGwIEDB0rru3ZV88jfyMhIaX10dLSS49cNPQ2QRGiAJEIDJBEaIInQAEmMng2AycnJXjcBs9DTAEmEBkgiNEASoQGSWlk14Ebb/7B93PYx2z8r6sttH7F9qnhlaloMhQU/uVlMDHhdRLxt+xuS3pJ0v6QfS7oQEXtt75Z0TUQ8usCx+ORmhU6ePFlaX7NmTeo4zeZVW7t2bWn9gw8+SB1/UFT2yc2ImIqIt4vti5JOSLpe0jZJh4rdDqkRJKD2Uu9pbK+S9G1Jb0haERFTxY8+kbSi0pYBfarlP27a/rqkFySNRsR/7P/3ZBERzW69bI9IKn/2HBhALfU0tr+qRmCeiYgXi/K5mYnQi9fzZb/LqgGom1ZGz6zG3M0nIuI3s350WNLOYnunpFeqbx7Qf1q5PfuupB9Jes/2O0XtMUl7JT1v+yeSTkvavjhNRDPHjh0rra9evTp1nOzqA8OulVUD/iWp2VDcXdU2B+h/PBEAJBEaIInQAEmEBkjik5sDbGxsrLR+7733drklw4WeBkgiNEASoQGSCA2QRGiAJEbPBlizNTFPnDhRWl+3bt1iNmdo0NMASYQGSCI0QBKhAZIIDZC04LxnlZ6Mec/Qxyqb9wzAlQgNkERogCRCAyR1smrAHttnbb9TfN29+M0Feq+TVQO2S/o8In7d8skYPUMfa3X0rJV5z6YkTRXbF23PrBoADKVOVg2QpIdtv2v7IIs6YVi0HJq5qwZIekrSGkkb1eiJnmzyeyO2x22PV9BeoOdaeiKgWDXgVUmvzZkEfebnqyS9GhG3LnAc3tOgb1X2RECzVQNmltkoPCBpIttIYBC1Mnp2p6R/SnpP0sz08o9J2qHGrVlI+kjSrlkrozU7Fj0N+larPQ0PbAIFHtgEFgmhAZIIDZBEaIAkQgMkERogidAASYQGSCI0QBKhAZK6vWrAZ5JOF9vXFt8PC663v32r1R27+uzZFSe2xyPi9p6cvAe43vrg9gxIIjRAUi9DM9bDc/cC11sTPXtPAwwqbs+ApK6HxvZW2/+2/b7t3d0+fzcUU1qdtz0xq7bc9hHbp4rXWkx5Nc8MrLW8XqnLobG9VNLvJf1Q0npJO2yv72YbuuRpSVvn1HZLej0ibpb0evF9HXwp6ecRsV7SdyT9tPg3rev1dr2nuUPS+xHxYUR8Iek5Sdu63IZFFxFHJV2YU94m6VCxfUiNqX0HXkRMRcTbxfZFSTMzsNbyeqXuh+Z6SR/P+v6MhmeK2xWzZuv5RNKKXjZmMcyZgbW218tAQA9EY8iyVsOWJTOw/k/drrfboTkr6cZZ399Q1IbBuZkJFovX8z1uT2WKGVhfkPRMRLxYlGt7vd0OzZuSbrZ9k+2rJD0o6XCX29ArhyXtLLZ3Snqlh22pTLMZWFXT65V68MfNYvGn30laKulgRPyyqw3oAtvPStqixpO+5yQ9IellSc9LWqnGk97bI2LuYMHAmWcG1jdUw+uVeCIASGMgAEgiNEASoQGSCA2QRGiAJEIDJBEaIInQAEn/BXhN2hsKFDpKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x_train[6].reshape(28,28)),y_train[6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure = x_train[5].reshape(28,28)\n",
    "plot(figure)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "filter1 = np.array([[0,0.5,0],\n",
    "                    [0.5,-1,0.5],\n",
    "                    [0,0.5,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(filter1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.signal import correlate2d\n",
    "plot(correlate2d(figure,filter1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "filter2 = np.array([[1,0.5,1],\n",
    "                    [0.5,-1,0.5],\n",
    "                    [1,0.5,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(filter2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(correlate2d(figure,filter2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "filter_edge = np.array([[1,0.5,0],\n",
    "                    [0.5,0,-0.5],\n",
    "                    [0,-0.5,-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(filter_edge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(None, None, None, None)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAADKCAYAAADHPo59AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAACaxJREFUeJzt3X+o3fddx/Hny+4uUFZtNYOmP2wnhuKYQrfSTQZrcCu0YayCFdo/3A82bhkrOnHgplBBEKp/KI7JJGxFK7JNnMwIgdGxxU50pbcl+9GWbrEgTVasSzU1ZLpG3/5xvnWndze9Yef7Pj/ufT7gkvPjk/v5XMKTm3PyzfumqpDU40cWfQBpJzMwqZGBSY0MTGpkYFIjA5MazRRYkh9P8kCSbw2/Xnaedf+T5NjwcXiWPaVVkln+HSzJHwDPVdW9ST4MXFZVv7nFujNV9aoZzimtpFkDexI4UFXPJNkHHK2q67ZYZ2DalWYN7D+q6tLhdoB/f/H+pnXngGPAOeDeqvrceT7fOrAOsLa29oa9e/f+0Gdbdpdccsmij9Bqp399jzzyyHeq6tXbrXvFdguSfAG4fIunfnv6TlVVkvPVek1VnUzyU8AXk3y9qv5586KqOgQcArjiiivqrrvu2u54K+vAgQOLPkKrm266adFHaJXkXy5k3baBVdXbXmaTf02yb+qviM+e53OcHH59KslR4HrgBwKTdppZ36Y/DLxruP0u4G83L0hyWZI9w+29wJuBx2fcV1oJswZ2L3Bzkm8Bbxvuk+SGJJ8Y1vwMsJHkq8CXmLwGMzDtCtv+FfHlVNUp4K1bPL4BvG+4/Y/Az86yj7SqvJJDamRgUiMDkxoZmNTIwKRGBiY1MjCpkYFJjQxMamRgUiMDkxoZmNTIwKRGBiY1MjCpkYFJjQxMamRgUiMDkxqNEliSW5I8meT4MEJ78/N7knxmeP6hJNeOsa+07GYOLMlFwJ8AtwKvBe5M8tpNy97LZOrvTwN/BPz+rPtKq2CM72A3Aser6qmq+h7waeC2TWtuA/58uP3XwFuHUdvSjjZGYFcCT0/dPzE8tuWaqjoHnAZ+YvMnSrKeZCPJxtmzZ0c4mrRYS/UmR1UdqqobquqGiy++eNHHkWY2RmAngaun7l81PLblmiSvAH4MODXC3tJSGyOwh4H9SV6T5JXAHUxm1k+bnmF/O/DFmuXnJkkrYqbR2TB5TZXkbuDzwEXAfVX1WJLfBTaq6jDwSeAvkhwHnmMSobTjzRwYQFUdAY5seuyeqdv/BfzyGHtJq2Sp3uSQdhoDkxoZmNTIwKRGBiY1MjCpkYFJjQxMamRgUiMDkxoZmNTIwKRGBiY1MjCpkYFJjQxMamRgUiMDkxoZmNRoXrPp353k35IcGz7eN8a+0rKbeejN1Gz6m5lM9X04yeGqenzT0s9U1d2z7ietknnNppd2pTHGtm01m/6NW6z7pSRvAb4J/HpVPb15QZJ1YB1gz549HD16dITjSYszrzc5/g64tqp+DniA7/+klZeYnk2/trY2p6NJfeYym76qTlXVfw93PwG8YYR9paU3l9n0SfZN3X0H8MQI+0pLb16z6X81yTuAc0xm07971n2lVTCv2fQfAT4yxl7SKvFKDqmRgUmNDExqZGBSIwOTGhmY1MjApEYGJjUyMKmRgUmNDExqZGBSIwOTGhmY1MjApEYGJjUyMKmRgUmNDExqNNZs+vuSPJvkG+d5Pkk+Osyu/1qS14+xr7TsxvoO9mfALS/z/K3A/uFjHfj4SPtKS22UwKrqQSbj2M7nNuD+mvgKcOmmWYnSjjSv12Bbza+/cvOiJOtJNpJsvPDCC3M6mtRnqd7kcDa9dpp5Bbbt/HppJ5pXYIeBdw7vJr4JOF1Vz8xpb2lhRhmdneRTwAFgb5ITwO8AawBV9adMxmofBI4DZ4H3jLGvtOzGmk1/5zbPF/CBMfaSVslSvckh7TQGJjUyMKmRgUmNDExqZGBSIwOTGhmY1MjApEYGJjUyMKmRgUmNDExqZGBSIwOTGhmY1MjApEYGJjUyMKnRvGbTH0hyOsmx4eOeMfaVlt0oQ2+YzKb/GHD/y6z5clW9faT9pJUwr9n00q401newC/HzSb4KfBv4UFU9tnlBknUmP30FgKNHj87vdFKDeQX2KHBNVZ1JchD4HJMfZfQSVXUIOASQpOZ0NqnNXN5FrKrnq+rMcPsIsJZk7zz2lhZpLoEluTxJhts3Dvuemsfe0iLNazb97cD7k5wDvgvcMYzTlna0ec2m/xiTt/GlXcUrOaRGBiY1MjCpkYFJjQxMamRgUiMDkxoZmNTIwKRGBiY1MjCpkYFJjQxMamRgUiMDkxoZmNTIwKRGBiY1MjCp0cyBJbk6yZeSPJ7ksSS/tsWaJPlokuNJvpbk9bPuK62CMYbenAN+o6oeTXIJ8EiSB6rq8ak1tzIZNLofeCPw8eFXaUeb+TtYVT1TVY8Ot/8TeAK4ctOy24D7a+IrwKVJ9s26t7TsRn0NluRa4HrgoU1PXQk8PXX/BD8YIUnWk2wk2RjzXNKijDabPsmrgM8CH6yq53+Yz+Fseu00Y/0AvjUmcf1lVf3NFktOAldP3b9qeEza0cZ4FzHAJ4EnquoPz7PsMPDO4d3ENwGnq+qZWfeWlt0Yf0V8M/ArwNeTHBse+y3gJ+H/Z9MfAQ4Cx4GzwHtG2FdaejMHVlX/AGSbNQV8YNa9pFXjlRxSIwOTGhmY1MjApEYGJjUyMKmRgUmNDExqZGBSIwOTGhmY1MjApEYGJjUyMKmRgUmNDExqZGBSIwOTGhmY1Ghes+kPJDmd5Njwcc+s+0qrYF6z6QG+XFVvH2E/aWXMaza9tCtlMlFtpE82mU3/IPC66fHZSQ4wmfx7Avg28KGqemyL378OrA93rwOeHO1w29sLfGeO+82bX9+4rqmqV2+3aLTAhtn0fw/83ubx2Ul+FPjfqjqT5CDwx1W1f5SNR5Jko6puWPQ5uvj1LcZcZtNX1fNVdWa4fQRYS7J3jL2lZTaX2fRJLh/WkeTGYd9Ts+4tLbt5zaa/HXh/knPAd4E7aswXf+M4tOgDNPPrW4BR3+SQ9FJeySE1MjCpkYEBSW5J8mSS40k+vOjzjCnJfUmeTfKNRZ+lw4VcqrdIu/41WJKLgG8CNzP5h/CHgTu3uNRrJSV5C3AGuL+qXrfo84wtyT5g3/SlesAvLsufn9/B4EbgeFU9VVXfAz4N3LbgM42mqh4Enlv0Obos+6V6Bjb5w3h66v4JlugPSBduuFTveuChxZ7k+wxMO8Jwqd5ngQ9OXwe7aAYGJ4Grp+5fNTymFbHdpXqLZGCTNzX2J3lNklcCdwCHF3wmXaALuVRvkXZ9YFV1Drgb+DyTF8h/tdV/pVlVST4F/BNwXZITSd676DON7MVL9X5h6n/MH1z0oV6069+mlzrt+u9gUicDkxoZmNTIwKRGBiY1MjCpkYFJjf4PrpcHqlNbuvwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAADKCAYAAADHPo59AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAACatJREFUeJzt3W2Ipeddx/Hvz3RbCNUkuiHZPFdcisUH2oa0pdAstoEklK5ghOSFfaBlQmnQigVbhQiCEH2hWCuV0AaNSFuxUldYKJF2bEVbMoZN2ySkXQOS3QaTbnSTZatl9e+Lc6ceJ7OZoef+n4eZ7wcOc+5zrsx1DcOXM+fOvddJVSGpxw8tegHSbmZgUiMDkxoZmNTIwKRGBiY1mimwJD+a5IEk3xq+XnKecf+d5NhwOzLLnNIqySz/HyzJ7wHPVtU9ST4MXFJVv77FuDNV9coZ1imtpFkDexw4VFVPJTkArFfVq7cYZ2Dak2YN7D+q6uLhfoB/f+F407hzwDHgHHBPVX3uPN9vDVgD2Ldv3+v379//A69t2T3//POLXkKrM2fOLHoJ3b5TVZduN+hl2w1I8nfA5Vs89ZvTB1VVSc5X67VVdTLJjwNfSPL1qvqXzYOq6l7gXoArrrii7rzzzu2Wt7LW19cXvYRWu/3nA/51J4O2Dayq3na+55L8W5IDU38iPn2e73Fy+PpEknXgtcCLApN2m1lP0x8B3jXcfxfwN5sHJLkkySuG+/uBNwOPzjivtBJmDewe4KYk3wLeNhyT5PoknxjG/CSwkeRh4ItM3oMZmPaEbf9EfClVdQp46xaPbwDvG+7/I/DTs8wjrSqv5JAaGZjUyMCkRgYmNTIwqZGBSY0MTGpkYFIjA5MaGZjUyMCkRgYmNTIwqZGBSY0MTGpkYFIjA5MaGZjUyMCkRqMEluTmJI8nOT5sob35+Vck+czw/FeTXDfGvNKymzmwJBcAfwzcArwGuCPJazYNey+TXX9/AvgD4HdnnVdaBWO8gt0AHK+qJ6rqe8CngcObxhwG/my4/1fAW4ettqVdbYzArgSenDo+MTy25ZiqOgecBn5s8zdKspZkI8nG2bNnR1iatFhLdZKjqu6tquur6voLL7xw0cuRZjZGYCeBq6eOrxoe23JMkpcBFwGnRphbWmpjBPYgcDDJq5K8HLidyZ7106b3sL8N+ELN8rlJ0oqYaetsmLynSnIX8HngAuC+qnokyW8DG1V1BPgk8OdJjgPPMolQ2vVmDgygqo4CRzc9dvfU/f8EfnGMuaRVslQnOaTdxsCkRgYmNTIwqZGBSY0MTGpkYFIjA5MaGZjUyMCkRgYmNTIwqZGBSY0MTGpkYFIjA5MaGZjUyMCkRgYmNZrX3vTvTvJMkmPD7X1jzCstu5k3vZnam/4mJrv6PpjkSFU9umnoZ6rqrlnnk1bJvPaml/akMbZt22pv+jdsMe4XkrwF+Cbwq1X15OYBSdaANYDLLruMQ4cOjbA8aXzr6+s7Gjevkxx/C1xXVT8DPMD/fdLK/zO9N/1FF100p6VJfeayN31Vnaqq/xoOPwG8foR5paU3l73pkxyYOnwH8NgI80pLb1570/9ykncA55jsTf/uWeeVVsG89qb/CPCRMeaSVolXckiNDExqZGBSIwOTGhmY1MjApEYGJjUyMKmRgUmNDExqZGBSIwOTGhmY1MjApEYGJjUyMKmRgUmNDExqZGBSo7H2pr8vydNJvnGe55Pko8Pe9V9L8rox5pWW3VivYH8K3PwSz98CHBxua8DHR5pXWmqjBFZVX2KyHdv5HAbur4mvABdv2itR2pXm9R5sq/3rr9w8KMlako0kG6dPn57T0qQ+S3WSw73ptdvMK7Bt96+XdqN5BXYEeOdwNvGNwOmqempOc0sLM8rW2Uk+BRwC9ic5AfwWsA+gqv6EybbatwLHgbPAe8aYV1p2Y+1Nf8c2zxfwgTHmklbJUp3kkHYbA5MaGZjUyMCkRgYmNTIwqZGBSY0MTGpkYFIjA5MaGZjUyMCkRgYmNTIwqZGBSY0MTGpkYFIjA5MaGZjUaF570x9KcjrJseF29xjzSstulE1vmOxN/zHg/pcY8+WqevtI80krYV5700t70livYDvxpiQPA98GPlRVj2wekGSNyaevcM0113DjjTfOcXnSzq2vr+9o3LxOcjwEXFtVPwv8EfC5rQZN701/6aWXzmlpUp+5BFZVz1XVmeH+UWBfkv3zmFtapLkEluTyJBnu3zDMe2oec0uLNK+96W8D3p/kHPBd4PZhO21pV5vX3vQfY3IaX9pTvJJDamRgUiMDkxoZmNTIwKRGBiY1MjCpkYFJjQxMamRgUiMDkxoZmNTIwKRGBiY1MjCpkYFJjQxMamRgUiMDkxrNHFiSq5N8McmjSR5J8itbjEmSjyY5nuRrSV4367zSKhhj05tzwK9V1UNJfhj45yQPVNWjU2NuAQ4OtzcAHx++SrvazK9gVfVUVT003H8eeAy4ctOww8D9NfEV4OIkB2adW1p2o74HS3Id8Frgq5ueuhJ4cur4BC+OkCRrSTaSbDzzzDNjLk1aiNECS/JK4LPAB6vquR/ke7g3vXabsT6Abx+TuP6iqv56iyEngaunjq8aHpN2tTHOIgb4JPBYVf3+eYYdAd45nE18I3C6qp6adW5p2Y1xFvHNwC8BX09ybHjsN4Br4Pt70x8FbgWOA2eB94wwr7T0Zg6sqv4ByDZjCvjArHNJq8YrOaRGBiY1MjCpkYFJjQxMamRgUiMDkxoZmNTIwKRGBiY1MjCpkYFJjQxMamRgUiMDkxoZmNTIwKRGBiY1MjCp0bz2pj+U5HSSY8Pt7lnnlVbBvPamB/hyVb19hPmklTGvvemlPWmMV7Dve4m96QHelORh4NvAh6rqkS3++zVgbTg8k+TxMde3jf3Ad+Y437z5843r2p0MymTLwtkNe9P/PfA7m7fPTvIjwP9U1ZkktwJ/WFUHR5l4JEk2qur6Ra+jiz/fYsxlb/qqeq6qzgz3jwL7kuwfY25pmc1lb/oklw/jSHLDMO+pWeeWlt289qa/DXh/knPAd4Hba6y/Tcdz76IX0MyfbwFGew8m6cW8kkNqZGBSIwMDktyc5PEkx5N8eNHrGVOS+5I8neQbi15Lh51cqrdIe/49WJILgG8CNzH5cPYHgTu2uNRrJSV5C3AGuL+qfmrR6xlbkgPAgelL9YCfX5bfn69gcANwvKqeqKrvAZ8GDi94TaOpqi8Bzy56HV2W/VI9A5v8Mp6cOj7BEv2CtHPbXKq3EAamXWG4VO+zwAer6rlFr+cFBgYngaunjq8aHtOK2O5SvUUysMlJjYNJXpXk5cDtwJEFr0k7tJNL9RZpzwdWVeeAu4DPM3mD/Jdb/VOaVZXkU8A/Aa9OciLJexe9ppG9cKnez039i/lbF72oF+z50/RSpz3/CiZ1MjCpkYFJjQxMamRgUiMDkxoZmNTofwE6chIMsheckgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fe_1 = filter_edge\n",
    "fe_2 = fe_1.T[:,::-1]\n",
    "fe_3 = fe_2.T[:,::-1]\n",
    "fe_4 = fe_3.T[:,::-1]\n",
    "plot(fe_1),plot(fe_2),plot(fe_3),plot(fe_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(None, None, None, None)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(correlate2d(figure,fe_1)),plot(correlate2d(figure,fe_2)),plot(correlate2d(figure,fe_3)),plot(correlate2d(figure,fe_4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(correlate2d(correlate2d(correlate2d(correlate2d(figure,fe_1),fe_2),fe_3),fe_4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MNIST Hacking\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.layers import *\n",
    "from keras.models import Model,Sequential"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard MLP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "md=Sequential([\n",
    "    Dense(512,activation=\"relu\",input_shape=(784,)),# relu is like max(x,0) in excel\n",
    "    Dense(10,activation=\"softmax\"),#output layer neuron number must be 10 to match y's dimension\n",
    "])\n",
    "md.compile(loss=\"categorical_crossentropy\",\n",
    "           optimizer=\"Adam\", \n",
    "           metrics=[\"accuracy\"]\n",
    "          )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/10\n",
      "60000/60000 [==============================] - 7s 122us/step - loss: 0.2330 - acc: 0.9331 - val_loss: 0.1199 - val_acc: 0.9636\n",
      "Epoch 2/10\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0911 - acc: 0.9728 - val_loss: 0.0867 - val_acc: 0.9739\n",
      "Epoch 3/10\n",
      "60000/60000 [==============================] - 3s 55us/step - loss: 0.0582 - acc: 0.9820 - val_loss: 0.0708 - val_acc: 0.9779\n",
      "Epoch 4/10\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0408 - acc: 0.9874 - val_loss: 0.0622 - val_acc: 0.9798\n",
      "Epoch 5/10\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0301 - acc: 0.9911 - val_loss: 0.0653 - val_acc: 0.9787\n",
      "Epoch 6/10\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0223 - acc: 0.9930 - val_loss: 0.0626 - val_acc: 0.9805\n",
      "Epoch 7/10\n",
      "60000/60000 [==============================] - 3s 56us/step - loss: 0.0172 - acc: 0.9945 - val_loss: 0.0670 - val_acc: 0.9794\n",
      "Epoch 8/10\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0131 - acc: 0.9960 - val_loss: 0.0620 - val_acc: 0.9826\n",
      "Epoch 9/10\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0121 - acc: 0.9964 - val_loss: 0.0765 - val_acc: 0.9796\n",
      "Epoch 10/10\n",
      "60000/60000 [==============================] - 3s 54us/step - loss: 0.0110 - acc: 0.9962 - val_loss: 0.0719 - val_acc: 0.9808\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f1659963a58>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md.fit(x_train,y_train,\n",
    "       validation_data=(x_test,y_test), # validation data, not involved in training, but exam the model for each epoch\n",
    "       epochs=10,# how many time we are going to run through the entire training data\n",
    "       batch_size=64,#how many image's we process per batch\n",
    "      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convolution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_ = Input((784,))\n",
    "x = Reshape((28,28,1))(input_)\n",
    "x = Convolution2D(filters=64,kernel_size=3,padding=\"same\",activation=\"relu\")(x)\n",
    "x = Convolution2D(filters=64,kernel_size=3,padding=\"same\")(x)\n",
    "x = MaxPool2D()(x)\n",
    "x = Convolution2D(filters=64,kernel_size=3,padding=\"same\",activation=\"relu\")(x)\n",
    "x = Convolution2D(filters=64,kernel_size=3,padding=\"same\")(x)\n",
    "x = MaxPool2D()(x)\n",
    "x = Convolution2D(filters=128,kernel_size=3,padding=\"same\",activation=\"relu\")(x)\n",
    "x = Convolution2D(filters=128,kernel_size=3,padding=\"same\",activation=\"relu\")(x)\n",
    "x = Convolution2D(filters=128,kernel_size=3,padding=\"same\")(x)\n",
    "x = MaxPool2D()(x)\n",
    "x = Flatten()(x)\n",
    "x = Dense(256,activation=\"relu\")(x)\n",
    "x = Dense(10,activation=\"softmax\")(x)\n",
    "\n",
    "md = Model(input_,x)\n",
    "md.compile(loss=\"categorical_crossentropy\",\n",
    "           optimizer=\"Adam\", \n",
    "           metrics=[\"accuracy\"]\n",
    "          )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/5\n",
      "60000/60000 [==============================] - 16s 269us/step - loss: 0.1302 - acc: 0.9589 - val_loss: 0.0333 - val_acc: 0.9886\n",
      "Epoch 2/5\n",
      "60000/60000 [==============================] - 13s 225us/step - loss: 0.0430 - acc: 0.9868 - val_loss: 0.0303 - val_acc: 0.9902\n",
      "Epoch 3/5\n",
      "60000/60000 [==============================] - 14s 225us/step - loss: 0.0345 - acc: 0.9890 - val_loss: 0.0342 - val_acc: 0.9892\n",
      "Epoch 4/5\n",
      "60000/60000 [==============================] - 13s 224us/step - loss: 0.0265 - acc: 0.9920 - val_loss: 0.0398 - val_acc: 0.9897\n",
      "Epoch 5/5\n",
      "60000/60000 [==============================] - 13s 224us/step - loss: 0.0259 - acc: 0.9921 - val_loss: 0.0310 - val_acc: 0.9897\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f165848e160>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md.fit(x_train,y_train,\n",
    "       validation_data=(x_test,y_test), # validation data, not involved in training, but exam the model for each epoch\n",
    "       epochs=5,# how many time we are going to run through the entire training data\n",
    "       batch_size=64,#how many image's we process per batch\n",
    "      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BatchNorm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def conv_bn(x,f_nb, ks=3,act=True):\n",
    "    x = Convolution2D(filters=f_nb,kernel_size=ks,padding=\"same\")(x)\n",
    "    x = BatchNormalization()(x)\n",
    "    if act:x = ReLU()(x)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_ = Input((784,))\n",
    "x = Reshape((28,28,1))(input_)\n",
    "x = conv_bn(x,32)\n",
    "x = conv_bn(x,32,act=False)\n",
    "x = MaxPool2D()(x)\n",
    "x = conv_bn(x,64)\n",
    "x = conv_bn(x,64,act=False)\n",
    "x = MaxPool2D()(x)\n",
    "x = conv_bn(x,128)\n",
    "x = conv_bn(x,128)\n",
    "x = conv_bn(x,128,act=False)\n",
    "x = MaxPool2D()(x)\n",
    "x = Flatten()(x)\n",
    "x = Dense(256,activation=\"relu\")(x)\n",
    "x = Dropout(.3)(x)\n",
    "x = Dense(10,activation=\"softmax\")(x)\n",
    "\n",
    "md = Model(input_,x)\n",
    "md.compile(loss=\"categorical_crossentropy\",\n",
    "           optimizer=\"Adam\", \n",
    "           metrics=[\"accuracy\"]\n",
    "          )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "60000/60000 [==============================] - 16s 272us/step - loss: 0.0251 - acc: 0.9922 - val_loss: 0.0369 - val_acc: 0.9904\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f15bed40390>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md.fit(x_train,y_train,\n",
    "       validation_data=(x_test,y_test), # validation data, not involved in training, but exam the model for each epoch\n",
    "       epochs=1,# how many time we are going to run through the entire training data\n",
    "       batch_size=64,#how many image's we process per batch\n",
    "      )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/4\n",
      "60000/60000 [==============================] - 16s 273us/step - loss: 0.0199 - acc: 0.9940 - val_loss: 0.0242 - val_acc: 0.9919\n",
      "Epoch 2/4\n",
      "60000/60000 [==============================] - 16s 273us/step - loss: 0.0161 - acc: 0.9950 - val_loss: 0.0304 - val_acc: 0.9925\n",
      "Epoch 3/4\n",
      "60000/60000 [==============================] - 16s 272us/step - loss: 0.0153 - acc: 0.9953 - val_loss: 0.0316 - val_acc: 0.9912\n",
      "Epoch 4/4\n",
      "60000/60000 [==============================] - 16s 273us/step - loss: 0.0126 - acc: 0.9961 - val_loss: 0.0290 - val_acc: 0.9932\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f15bed409e8>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md.fit(x_train,y_train,\n",
    "       validation_data=(x_test,y_test), # validation data, not involved in training, but exam the model for each epoch\n",
    "       epochs=4,# how many time we are going to run through the entire training data\n",
    "       batch_size=64,#how many image's we process per batch\n",
    "      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Augmentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.preprocessing.image import apply_affine_transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(apply_affine_transform(x_train[0].reshape(28,28,1),theta=15,tx = 3).reshape(28,28))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "def aug_x(x):\n",
    "    random_aug = (np.random.rand(4)-0.5)*np.array([20,5,5,10])\n",
    "\n",
    "    aug_conf = {\"theta\":random_aug[0],\n",
    "     \"tx\":random_aug[1],\n",
    "     \"ty\":random_aug[2],\n",
    "     \"shear\":random_aug[3],}\n",
    "\n",
    "    x = apply_affine_transform(x.reshape(28,28,1),**aug_conf).reshape(28,28)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "def aug_xs(x_train):\n",
    "    x_train = x_train.reshape(-1,28,28)\n",
    "    train_len = x_train.shape[0]\n",
    "    for i in range(train_len):\n",
    "        x_train[i] = aug_x(x_train[i])\n",
    "\n",
    "    return x_train.reshape(-1,784)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_ = Input((784,))\n",
    "x = Reshape((28,28,1))(input_)\n",
    "x = conv_bn(x,32)\n",
    "x = conv_bn(x,32,act=False)\n",
    "x = MaxPool2D()(x)\n",
    "x = conv_bn(x,64)\n",
    "x = conv_bn(x,64,act=False)\n",
    "x = MaxPool2D()(x)\n",
    "x = conv_bn(x,128)\n",
    "x = conv_bn(x,128)\n",
    "x = conv_bn(x,128,act=False)\n",
    "x = MaxPool2D()(x)\n",
    "x = Flatten()(x)\n",
    "x = Dense(256,activation=\"relu\")(x)\n",
    "x = Dropout(.3)(x)\n",
    "x = Dense(10,activation=\"softmax\")(x)\n",
    "\n",
    "md = Model(input_,x)\n",
    "md.compile(loss=\"categorical_crossentropy\",\n",
    "           optimizer=\"Adam\", \n",
    "           metrics=[\"accuracy\"]\n",
    "          )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 37s 309us/step - loss: 0.1116 - acc: 0.9660 - val_loss: 0.0391 - val_acc: 0.9887\n",
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 33s 273us/step - loss: 0.0491 - acc: 0.9857 - val_loss: 0.0336 - val_acc: 0.9896\n",
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 33s 273us/step - loss: 0.0388 - acc: 0.9888 - val_loss: 0.0422 - val_acc: 0.9875\n",
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 33s 273us/step - loss: 0.0336 - acc: 0.9902 - val_loss: 0.0250 - val_acc: 0.9937\n",
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 33s 273us/step - loss: 0.0289 - acc: 0.9919 - val_loss: 0.0277 - val_acc: 0.9917\n",
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 33s 273us/step - loss: 0.0258 - acc: 0.9923 - val_loss: 0.0223 - val_acc: 0.9937\n",
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 33s 273us/step - loss: 0.0250 - acc: 0.9929 - val_loss: 0.0208 - val_acc: 0.9944\n",
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 33s 273us/step - loss: 0.0204 - acc: 0.9938 - val_loss: 0.0320 - val_acc: 0.9904\n"
     ]
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    x_aug = aug_xs(x_train.copy())\n",
    "    md.fit(np.concatenate([x_aug,x_train],axis=0),np.concatenate([y_train,y_train],axis=0),\n",
    "       validation_data=(x_test,y_test), # validation data, not involved in training, but exam the model for each epoch\n",
    "       epochs=1,# how many time we are going to run through the entire training data\n",
    "       batch_size=64,#how many image's we process per batch\n",
    "      )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 120000 samples, validate on 10000 samples\n",
      "Epoch 1/1\n",
      "120000/120000 [==============================] - 33s 273us/step - loss: 0.0197 - acc: 0.9943 - val_loss: 0.0276 - val_acc: 0.9931\n"
     ]
    }
   ],
   "source": [
    "for i in range(1):\n",
    "    x_aug = aug_xs(x_train.copy())\n",
    "    md.fit(np.concatenate([x_aug,x_train],axis=0),np.concatenate([y_train,y_train],axis=0),\n",
    "       validation_data=(x_test,y_test), # validation data, not involved in training, but exam the model for each epoch\n",
    "       epochs=1,# how many time we are going to run through the entire training data\n",
    "       batch_size=64,#how many image's we process per batch\n",
    "      )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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