{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 03 王牌例子 MNIST\n",
    "\n",
    "CNN 的創始者 Yann LeCun 第一個 CNN 例子就是用來辨識手寫、印刷的 0-9 數字。這裡用 LeCun 原版資料:\n",
    "\n",
    "[MNIST 手寫辨識資料](http://yann.lecun.com/exdb/mnist/)\n",
    "\n",
    "每個手寫圖檔都是 28x28 大小的, 輸出原本是 0-9 的數字, 但我們想改成辨視資料是 0 就要輸出\n",
    "\n",
    "[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
    "\n",
    "是 3 就是\n",
    "\n",
    "[0, 0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
    "\n",
    "等等。\n",
    "\n",
    "另外我們用最傳統的 Fully Connected Feedforward 架構, 而不是用 CNN:\n",
    "\n",
    "* 輸入是一個 28x28=784 維的向量。\n",
    "* 輸出是 10 維向量 (每個數字都是 0 到 9)\n",
    "* Hidden Layer 有兩層, 每層 500 個 neuron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 套件"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using Theano backend.\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from keras.datasets import mnist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中的 `keras` 是我們選用非常方便的 deep learning 套件, 它甚至幫我們準備好了 MNIST 等這類有名的資料庫。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 讀入 MNIST 資料"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(x0_train, y0_train), (x0_test, y0_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最親切的是它還分好訓練資料和測試資料, 我們來看看各有多少筆資料。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "訓練資料筆數:  60000\n",
      "測試資料筆數:  10000\n"
     ]
    }
   ],
   "source": [
    "print(\"訓練資料筆數: \", len(x0_train))\n",
    "print(\"測試資料筆數: \", len(x0_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. 看看資料內容\n",
    "\n",
    "我們來看看資料的內容長什麼樣子。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ind = 777\n",
    "X = x0_train[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "          0,   0],\n",
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       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   6, 114, 254, 253,\n",
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       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   4,  95, 239, 253,\n",
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       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0, 175, 253, 253,  60,   0,\n",
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       "          0,   0],\n",
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       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,  20, 253, 253, 162,  13,  73,\n",
       "        226, 253, 253, 105,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,  14, 229, 253, 253, 224, 253,\n",
       "        253, 253, 185,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,  81, 227, 253, 254, 253,\n",
       "        253, 201,  34,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,  47, 155, 216, 245,\n",
       "        126,   5,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "          0,   0]], dtype=uint8)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x108edb048>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Rf+ycVXt1dYV+vz8RVuaJr041lS+LdiWwtSloXzALMPuE5X3ldXkhSpmsk5Ud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\nhIMgCFokRDgIgqBFQoSDIAha5P8HPQCDFPC016EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c03668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(X, cmap='Greys')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果堅持不要外框。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x10ac13cf8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fLGDogsALkPLpqjjcLPW4ts/F2PtGlgWnLPg493zRZEFESxhTi9XgFOQQaJWK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac134a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_axis_off()\n",
    "plt.imshow(X, cmap='Greys')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "看一下「正確答案」。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y0_train[ind]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. 互動展示 (複習)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def show(ind):\n",
    "    print(\"數字: \", y0_train[ind])\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.set_axis_off()\n",
    "    plt.imshow(x0_train[ind], cmap='Greys')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "數字:  7\n"
     ]
    },
    {
     "data": {
      "image/png": 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JuZqAW6NhPwHnz1vL1PzyZZ9yyI4AHwkShpOS5YRbV8RFQx/bnx8i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\nSBgAoCP/B0Veo9cA2FbuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105eb8ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(show, ind=(0,59999))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. 資料整理之一\n",
    "\n",
    "現在每個訓練資料都是 28x28 的矩陣, 但我們常常都是「拉平」的向量, 也就是每筆輸入可能是 784 (=28x28) 的向量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = x0_train.reshape(60000, 28*28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0], dtype=uint8)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### [練習] 把 `x0_test` 也改成「平的」向量"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. 資料整理之二\n",
    "\n",
    "輸出原本是 0-9 的數字, 但我們想改成辨視資料是 0 就要輸出\n",
    "\n",
    "[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
    "\n",
    "是 3 就是\n",
    "\n",
    "[0, 0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
    "\n",
    "等等。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y0_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from keras.utils import np_utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_train = np_utils.to_categorical(y0_train,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "改變前:  3\n",
      "改變後:  [ 0.  0.  0.  1.  0.  0.  0.  0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "ind = 10\n",
    "print(\"改變前: \", y0_train[ind])\n",
    "print(\"改變後: \", y_train[ind])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### [練習] 把 `y0_test` 也修改過來"
   ]
  }
 ],
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