{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST 手寫數字辨識資料集介紹 & 多層感知器模型(MLP)\n",
    "\n",
    "![MLP](http://cntk.ai/jup/cntk103c_MNIST_MLP.png)\n",
    "\n",
    "圖片出處:[CNTK_103C_MNIST_MultiLayerPerceptron](https://cntk.ai/pythondocs/CNTK_103C_MNIST_MultiLayerPerceptron.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP1. 匯入 Keras 及相關模組 \n",
    "\n",
    "首先匯入 Keras 及相關模組: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from keras.utils import np_utils  # 用來後續將 label 標籤轉為 one-hot-encoding\n",
    "\n",
    "np.random.seed(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP2. 下載 mnist 資料\n",
    "\n",
    "下載 Mnist 資料 \n",
    "我們將建立以下 Keras 程式, 下載並讀取 mnist 資料. \n",
    "\n",
    "Mnist 資料的下載路徑在 ~/.keras/datasets/mnist.npz (npz is a simple zip archive, which contains numpy files.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from keras.datasets import mnist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP3. 讀取與查看 mnist 資料"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t[Info] train data= 60,000\n",
      "\t[Info] test  data= 10,000\n"
     ]
    }
   ],
   "source": [
    "(X_train_image, y_train_label), (X_test_image, y_test_label) = mnist.load_data()\n",
    "\n",
    "print(\"\\t[Info] train data={:7,}\".format(len(X_train_image)))  \n",
    "print(\"\\t[Info] test  data={:7,}\".format(len(X_test_image))) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由上可以知道 training data 共有 60,000 筆; testing data 共有 10,000 筆。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 查看訓練資料\n",
    "\n",
    "接著我們來看載入資料的長相與格式."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP1. 訓練資料是由 images 與 labels 所組成"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t[Info] Shape of train data=(60000, 28, 28)\n",
      "\t[Info] Shape of train label=(60000,)\n"
     ]
    }
   ],
   "source": [
    "print(\"\\t[Info] Shape of train data=%s\" % (str(X_train_image.shape)))\n",
    "print(\"\\t[Info] Shape of train label=%s\" % (str(y_train_label.shape)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "訓練資料是由 images 與 labels 所組成共有 60,000 筆, 每一筆代表某個數字的影像為 28x28 pixels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP2. 定應 plot_image 函數顯示數字影像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "def plot_image(image):\n",
    "    fig = plt.gcf()\n",
    "    fig.set_size_inches(2, 2)\n",
    "    plt.imshow(image, cmap='binary') # cmap='binary' 參數設定以黑白灰階顯示\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP3. 執行 plot_image 函數查看第 0 筆數字影像與 label 資料 \n",
    "\n",
    "以下程式呼叫 plot_image 函數, 傳入 X_train_image[0], 也就是順練資料集的第 0 筆資料, 顯示結果可以看到這是一個數字 5 的圖形: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJIAAACPCAYAAAARM4LLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAACGVJREFUeJzt3V1oVOkZB/D/YzR+1a80ssRsMIuKEAp+EGuLRaPWjy5o\n8KZERass1As/WjBYUy/0woui0AuNN4uVVKwpxRp2LQuii7kQF0mCwSa7ZtVi3Cx+LaIWvdCVpxdz\ndjrPwSQnM0/OzGT+Pwg5/3OSOS/4+M4750yeEVUFUaZGZXsANDKwkMgFC4lcsJDIBQuJXLCQyAUL\niVywkMhFRoUkImtFpEdE7ojIfq9BUf6RdK9si0gRgK8BrALQB6ANwEZV/bK/3yktLdXKysq0zkfZ\n0dHR8Z2qTh/s50ZncI6fArijqv8BABH5O4BaAP0WUmVlJdrb2zM4JcVNRHqj/FwmT23lAL5JyX3B\nvvBAfisi7SLS/uTJkwxOR7ls2BfbqvqxqlaravX06YPOkJSnMimkbwFUpOT3g31UgDIppDYAc0Tk\nAxEpBlAH4FOfYVG+SXuxrarfi8guABcBFAE4pardbiOjvJLJqzao6mcAPnMaC+UxXtkmFywkcsFC\nIhcsJHLBQiIXLCRywUIiFywkcsFCIhcsJHLBQiIXGd1rKyRv3741+fnz55F/t7Gx0eRXr16Z3NPT\nY/KJEydMrq+vN7m5udnkcePGmbx////fPn/w4MHI48wEZyRywUIiFywkclEwa6T79++b/Pr1a5Ov\nXbtm8tWrV01+9uyZyefOnXMbW0VFhcm7d+82uaWlxeRJkyaZPG/ePJOXLVvmNraoOCORCxYSuWAh\nkYsRu0a6ceOGyStWrDB5KNeBvBUVFZl8+PBhkydOnGjy5s2bTZ4xY4bJ06ZNM3nu3LmZDnHIOCOR\nCxYSuWAhkYsRu0aaOXOmyaWlpSZ7rpEWL15scnjNcuXKFZOLi4tN3rJli9tYsoUzErlgIZELFhK5\nGLFrpJKSEpOPHj1q8oULF0xesGCByXv27Bnw8efPn5/cvnz5sjkWvg7U1dVl8rFjxwZ87HzEGYlc\nDFpIInJKRB6LSFfKvhIRuSQit4Pv0wZ6DBr5osxITQDWhvbtB/C5qs4B8HmQqYBFao8sIpUA/qWq\nPwlyD4AaVX0gImUAWlV10Bs81dXVmitdbV+8eGFy+D0+O3bsMPnkyZMmnzlzJrm9adMm59HlDhHp\nUNXqwX4u3TXSe6r6INh+COC9NB+HRoiMF9uamNL6ndbYHrkwpFtIj4KnNATfH/f3g2yPXBjSvY70\nKYDfAPhT8P0TtxHFZPLkyQMenzJlyoDHU9dMdXV15tioUYV3VSXKy/9mAF8AmCsifSLyERIFtEpE\nbgP4ZZCpgA06I6nqxn4OrXQeC+WxwpuDaViM2HttmTp06JDJHR0dJre2tia3w/faVq9ePVzDylmc\nkcgFC4lcsJDIRdofRZqOXLrXNlR37941eeHChcntqVOnmmPLly83ubra3qrauXOnySLiMcRhMdz3\n2ogMFhK54Mv/iGbNmmVyU1NTcnv79u3m2OnTpwfML1++NHnr1q0ml5WVpTvMrOGMRC5YSOSChUQu\nuEZK04YNG5Lbs2fPNsf27t1rcvgWSkNDg8m9vb0mHzhwwOTy8vK0xxkXzkjkgoVELlhI5IK3SIZB\nuJVy+M/Dt23bZnL432DlSvuewUuXLvkNboh4i4RixUIiFywkcsE1UhaMHTvW5Ddv3pg8ZswYky9e\nvGhyTU3NsIzrXbhGolixkMgFC4lc8F6bg5s3b5oc/giutrY2k8NrorCqqiqTly5dmsHo4sEZiVyw\nkMgFC4lccI0UUfgj1Y8fP57cPn/+vDn28OHDIT326NH2nyH8nu18aJOT+yOkvBClP1KFiFwRkS9F\npFtEfhfsZ4tkSooyI30PYK+qVgH4GYCdIlIFtkimFFEabT0A8CDY/q+IfAWgHEAtgJrgx/4KoBXA\nH4ZllDEIr2vOnj1rcmNjo8n37t1L+1yLFi0yOfwe7fXr16f92NkypDVS0G97AYDrYItkShG5kETk\nRwD+CeD3qmq6nQ/UIpntkQtDpEISkTFIFNHfVPWH17qRWiSzPXJhGHSNJImeK38B8JWq/jnlUF61\nSH706JHJ3d3dJu/atcvkW7dupX2u8EeT7tu3z+Ta2lqT8+E60WCiXJBcAmALgH+LSGew749IFNA/\ngnbJvQB+PTxDpHwQ5VXbVQD9dYJii2QCwCvb5GTE3Gt7+vSpyeGPyers7DQ53MpvqJYsWZLcDv+t\n/5o1a0weP358RufKB5yRyAULiVywkMhFXq2Rrl+/ntw+cuSIORZ+X3RfX19G55owYYLJ4Y9vT70/\nFv549kLEGYlcsJDIRV49tbW0tLxzO4rwn/isW7fO5KKiIpPr6+tNDnf3J4szErlgIZELFhK5YFsb\nGhDb2lCsWEjkgoVELlhI5IKFRC5YSOSChUQuWEjkgoVELlhI5IKFRC5ivdcmIk+Q+KvcUgDfxXbi\noeHYrJmqOmjThlgLKXlSkfYoNwKzgWNLD5/ayAULiVxkq5A+ztJ5o+DY0pCVNRKNPHxqIxexFpKI\nrBWRHhG5IyJZbacsIqdE5LGIdKXsy4ne4fnY2zy2QhKRIgAnAPwKQBWAjUG/7mxpArA2tC9Xeofn\nX29zVY3lC8DPAVxMyQ0AGuI6fz9jqgTQlZJ7AJQF22UAerI5vpRxfQJgVa6OT1VjfWorB/BNSu4L\n9uWSnOsdni+9zbnY7ocm/ttn9SVtur3NsyHOQvoWQEVKfj/Yl0si9Q6PQya9zbMhzkJqAzBHRD4Q\nkWIAdUj06s4lP/QOB7LYOzxCb3Mg13qbx7xo/BDA1wDuAjiQ5QVsMxIf1vMGifXaRwB+jMSrodsA\nLgMoydLYfoHE09ZNAJ3B14e5Mr53ffHKNrngYptcsJDIBQuJXLCQyAULiVywkMgFC4lcsJDIxf8A\njM9gOIVbmEoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xda9b748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_image(X_train_image[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_label[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 查看多筆訓練資料 images 與 labels\n",
    "\n",
    "接下來我們將建立 plot_images_labels_predict 函數, 可以顯示多筆資料的影像與 label. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP1. 建立 plot_images_labels_predict() 函數\n",
    "\n",
    "因為後續我們希望能很方便查看數字圖形, 真實的數字與預測結果, 所以我們建立了以下函數:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_images_labels_predict(images, labels, prediction, idx, num=10):  \n",
    "    fig = plt.gcf()  \n",
    "    fig.set_size_inches(12, 14)  \n",
    "    if num > 25: num = 25  \n",
    "    for i in range(0, num):  \n",
    "        ax=plt.subplot(5,5, 1+i)  \n",
    "        ax.imshow(images[idx], cmap='binary')  \n",
    "        title = \"l=\" + str(labels[idx])  \n",
    "        if len(prediction) > 0:  \n",
    "            title = \"l={},p={}\".format(str(labels[idx]), str(prediction[idx]))  \n",
    "        else:  \n",
    "            title = \"l={}\".format(str(labels[idx]))  \n",
    "        ax.set_title(title, fontsize=10)  \n",
    "        ax.set_xticks([]); ax.set_yticks([])  \n",
    "        idx+=1  \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP2. 查看訓練資料的前 10 筆資料"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sr3l82GGHJag6d91+++1Bl5Bwb731VtTvXHLJJSmoBLGy17oWEVm4cGFc+7DXwz722GPL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\nAICz/j+eXIut1A8c+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12775940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_images_labels_predict(X_train_image, y_train_label, [], 0, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 多層感知器模型資料前處理\n",
    "\n",
    "接下來我們建立 多層感知器模型 (MLP), 我們必須先將 images 與 labels 的內容進行前處理, 才能餵進去 Keras 預期的資料結構。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP1. features (數字影像的特徵值) 資料前處理\n",
    "\n",
    "首先將 image 以 reshape 轉換為二維 ndarray 並進行 normalization (Feature scaling): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t[Info] xTrain: (60000, 784)\n",
      "\t[Info] xTest: (10000, 784)\n"
     ]
    }
   ],
   "source": [
    "x_Train = X_train_image.reshape(60000, 28*28).astype('float32')\n",
    "x_Test = X_test_image.reshape(10000, 28*28).astype('float32')\n",
    "print(\"\\t[Info] xTrain: %s\" % (str(x_Train.shape)))\n",
    "print(\"\\t[Info] xTest: %s\" % (str(x_Test.shape)))\n",
    "  \n",
    "# Normalization\n",
    "x_Train_norm = x_Train/255\n",
    "x_Test_norm = x_Test/255"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP2. labels (影像數字真實的值) 資料前處理\n",
    "\n",
    "label 標籤欄位原本是 0-9 數字, 而為了配合 Keras 的資料格式, 我們必須進行 One-hot-encoding 將之轉換為 10 個 0 或 1 的組合, 例如數字 7 經過 One-hot encoding 轉換後是 0000001000, 正好對應到輸出層的 10 個神經元. 下面簡單測試過程:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_TrainOneHot = np_utils.to_categorical(y_train_label) # 將 training 的 label 進行 one-hot encoding\n",
    "y_TestOneHot = np_utils.to_categorical(y_test_label) # 將測試的 labels 進行 one-hot encoding\n",
    "\n",
    "y_train_label[0] # 檢視 training labels 第一個 label 的值\n",
    "y_TrainOneHot[:1] # 檢視第一個 label 在 one-hot encoding 後的結果, 會在第六個位置上為 1, 其他位置上為 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 建立模型\n",
    "\n",
    "我們將建立以下多層感知器 Multilayer Perceptron 模型, 輸入層 (x) 共有 28x28=784 個神經元, Hidden layers (h) 共有 256 層; 輸出層 (y) 共有 10 個 神經元:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![mlp](https://3.bp.blogspot.com/-TpTfcbPRWWY/WVW-EUCKVLI/AAAAAAAAWuE/sn9sX6qMc38UePENvSmmgLH3bA7za-3ogCLcBGAs/s1600/3946_3.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "對應代碼:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t[Info] Model summary:\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_1 (Dense)              (None, 256)               200960    \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 10)                2570      \n",
      "=================================================================\n",
      "Total params: 203,530\n",
      "Trainable params: 203,530\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from keras.models import Sequential  \n",
    "from keras.layers import Dense  \n",
    "  \n",
    "model = Sequential()  # Build Linear Model  \n",
    "  \n",
    "model.add(Dense(units=256, input_dim=784, kernel_initializer='normal', activation='relu')) # Add Input/hidden layer  \n",
    "model.add(Dense(units=10, kernel_initializer='normal', activation='softmax')) # Add Hidden/output layer  \n",
    "print(\"\\t[Info] Model summary:\")  \n",
    "model.summary()  \n",
    "print(\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summary 的相關說明:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![mlp](https://1.bp.blogspot.com/-XYUDaErijCI/WVW-IliFkOI/AAAAAAAAWuI/g4zOWWWMfpIwIEYWLq2zd0qVJHlRanTHACLcBGAs/s1600/3946_4.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 進行訓練\n",
    "\n",
    "當我們建立深度學習模型後, 就可以使用 Backpropagation 進行訓練。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP1. 定義訓練方式\n",
    "\n",
    "在訓練模型之前, 我們必須先使用 compile 方法, 對訓練模型進行設定, 代碼如下:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "參數說明如下:\n",
    "* **loss** : 設定 loss function, 在深度學習通常使用 cross_entropy (Cross entropy) 交叉摘順練效果較好.\n",
    "* **optimizer** : 設定訓練時的優化方法, 在深度學習使用 adam 可以讓訓練更快收斂, 並提高準確率.\n",
    "* **metrics** : 設定評估模型的方式是 accuracy (準確率)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP2. 開始訓練\n",
    "執行訓練的程式碼如下:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 48000 samples, validate on 12000 samples\n",
      "Epoch 1/10\n",
      "3s - loss: 0.4385 - acc: 0.8829 - val_loss: 0.2181 - val_acc: 0.9408\n",
      "Epoch 2/10\n",
      "3s - loss: 0.1907 - acc: 0.9455 - val_loss: 0.1554 - val_acc: 0.9559\n",
      "Epoch 3/10\n",
      "3s - loss: 0.1354 - acc: 0.9618 - val_loss: 0.1259 - val_acc: 0.9648\n",
      "Epoch 4/10\n",
      "3s - loss: 0.1027 - acc: 0.9704 - val_loss: 0.1121 - val_acc: 0.9678\n",
      "Epoch 5/10\n",
      "3s - loss: 0.0810 - acc: 0.9774 - val_loss: 0.0982 - val_acc: 0.9716\n",
      "Epoch 6/10\n",
      "3s - loss: 0.0659 - acc: 0.9818 - val_loss: 0.0931 - val_acc: 0.9723\n",
      "Epoch 7/10\n",
      "3s - loss: 0.0544 - acc: 0.9851 - val_loss: 0.0912 - val_acc: 0.9739\n",
      "Epoch 8/10\n",
      "3s - loss: 0.0459 - acc: 0.9876 - val_loss: 0.0822 - val_acc: 0.9760\n",
      "Epoch 9/10\n",
      "3s - loss: 0.0381 - acc: 0.9902 - val_loss: 0.0820 - val_acc: 0.9761\n",
      "Epoch 10/10\n",
      "3s - loss: 0.0317 - acc: 0.9918 - val_loss: 0.0809 - val_acc: 0.9760\n"
     ]
    }
   ],
   "source": [
    "train_history = model.fit(x=x_Train_norm, \n",
    "                          y=y_TrainOneHot, \n",
    "                          validation_split=0.2, \n",
    "                          epochs=10, \n",
    "                          batch_size=200, \n",
    "                          verbose=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上面訓練過程會儲存於 train_history 變數中, 參數說明如下: \n",
    "\n",
    "* **x = x_Train_norm** : features 數字的影像特徵值 (60,000 x 784 的陣列)\n",
    "* **y = y_Train_OneHot** : label 數字的 One-hot encoding 陣列 (60,000 x 10 的陣列)\n",
    "* **validation_split = 0.2** : 設定訓練資料與 cross validation 的資料比率. 也就是說會有 0.8 * 60,000 = 48,000 作為訓練資料; 0.2 * 60,000 = 12,000 作為驗證資料.\n",
    "* **epochs** = 10 : 執行 10 次的訓練週期.\n",
    "* **batch_size = 200** : 每一批次的訓練筆數為 200\n",
    "* **verbose = 2** : 顯示訓練過程. 共執行 10 次 epoch (訓練週期), 每批 200 筆, 也就是每次會有 240 round (48,000 / 200 = 240). 每一次的 epoch 會計算 accuracy 並記錄在 train_history 中."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP3. 建立 show_train_history 顯示訓練過程\n",
    "\n",
    "之前訓練步驟會將每一個訓練週期的 accuracy 與 loss 記錄在 train_history 變數. 我們可以使用下面程式碼讀取 train_history 以圖表顯示訓練過程:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt  \n",
    "def show_train_history(train_history, train, validation):  \n",
    "    plt.plot(train_history.history[train])  \n",
    "    plt.plot(train_history.history[validation])  \n",
    "    plt.title('Train History')  \n",
    "    plt.ylabel(train)  \n",
    "    plt.xlabel('Epoch')  \n",
    "    plt.legend(['train', 'validation'], loc='upper left')  \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "執行結果如下:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YAFBYWNhjhXfH5MmTqa2tZeTIkQwfPpwvfOELXHbZZZx22mnMmjWL4uLiY27/la98hVtu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\nAkNERLpEgSEiIl2iwBARkS75/0lnA1pcQcR4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x128ef438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_train_history(train_history, 'acc', 'val_acc')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果 \"acc 訓練的準確率\" 一直提升, 但是 \"val_acc 的準確率\" 卻一直沒有增加, 就有可能是 Overfitting 的現象 (更多說明請參考 Bias, Variance, and Overfitting). 在完成所有 (epoch) 訓練週期後, 在後面還會使用測試資料來評估模型準確率, 這是另外一組獨立的資料, 所以計算準確率會更客觀. 接著我們來看 loss 誤差的執行結果: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4kDsefZe6JvfuP26MCW8WGENt4Vfg2t/5BvgtG9QAP4CEmEjuvX4+/7J8Oi9s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\n5P8DbodGauHmTm4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x128ff320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_train_history(train_history, 'loss', 'val_loss')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "總共執行 10 個 Epoch 訓練週期, 可以發現:    \n",
    "* 不論訓練與驗證, 誤差越來越低.\n",
    "* 在 Epoch 訓練後期, \"loss 訓練的誤差\" 比 \"val_loss 驗證的誤差\" 小."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 以測試資料評估模型準確率與預測 \n",
    "\n",
    "我們已經完成訓練模型, 現在要使用 test 測試資料來評估模型準確率。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP1. 評估模型準確率\n",
    "\n",
    "使用下面代碼評估模型準確率:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 9760/10000 [============================>.] - ETA: 0s\n",
      "\t[Info] Accuracy of testing data = 97.5%\n"
     ]
    }
   ],
   "source": [
    "scores = model.evaluate(x_Test_norm, y_TestOneHot)  \n",
    "print()  \n",
    "print(\"\\t[Info] Accuracy of testing data = {:2.1f}%\".format(scores[1]*100.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP2. 進行預測\n",
    "前面我們建立模型並於訓練後達成可以接受的 97% 準確率, 接著我們將使用此模型進行預測。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t[Info] Making prediction to x_Test_norm\n",
      " 9792/10000 [============================>.] - ETA: 0s\n",
      "\t[Info] Show 10 prediction result (From 240):\n",
      "[5 9 8 7 2 3 0 2 4 2]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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PLiLSp08flVu3bq3y9u3bAz3n7NmzVf7oo4+ijvn2229VHjt2rMplypQJ9JyI75prrlF5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\nflt57+VoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12d03f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"\\t[Info] Making prediction to x_Test_norm\")  \n",
    "prediction = model.predict_classes(x_Test_norm)  # Making prediction and save result to prediction  \n",
    "print()  \n",
    "print(\"\\t[Info] Show 10 prediction result (From 240):\")  \n",
    "print(\"%s\\n\" % (prediction[240:250]))  \n",
    "  \n",
    "plot_images_labels_predict(X_test_image, y_test_label, prediction, idx=240)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上面可以發現有個預測結果為 6, 但實際 label 為 4. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 總結 (Conclusion)\n",
    "\n",
    "在這篇文章中有一些個人學習到的一些有趣的重點:\n",
    "\n",
    "* Mnist的手寫資料集雖然很簡單, 但對很多不熟悉把圖像處理的人來說, Mnist絕對是一個合適用來做練習與講解的好資料集\n",
    "* 需要了解網絡的結構與不同網絡層輸入輸出的張量的結構才能夠清楚地構建一個對的模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "參考:\n",
    "* [程式扎記 - MNIST 手寫數字辨識資料集介紹](http://puremonkey2010.blogspot.tw/2017/07/toolkit-keras-mnist-cnn.html)\n",
    "* [林大貴 - TensorFlow+Keras深度學習人工智慧實務應用](http://tensorflowkeras.blogspot.com)"
   ]
  },
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