{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 構建自動編碼器(Autoencoder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意: 這篇文章的內容需要一些對Keras的理解, 這先確認你/妳己先閱讀並練習過以下的連結內容:\n",
    "\n",
    "* [1.1-keras-functional-api](https://github.com/erhwenkuo/deep-learning-with-keras-notebooks/blob/master/1.1-keras-functional-api.ipynb)\n",
    "\n",
    "為了獲得最好的學習效果與理解, 強烈建議先行聆聽以下的線上課程:\n",
    "* [台大李宏毅 - (ML Lecture 16: Unsupervised Learning - Auto-encoder)](https://www.youtube.com/watch?v=Tk5B4seA-AU&lc=z13atbuzfxjtzx1nf23iw5thtrrdxjnga04)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在本教程中，我們將回答關於autoencoders的一些常見問題，我們將介紹以下模型的代碼示例：\n",
    "* 一個基於完全連接層(fully-connected layer)的簡單的自動編碼器\n",
    "* 一個深度完全連接(deep fully-connected)的自動編碼器\n",
    "* 一個深度卷積(deep convolutional)自動編碼器\n",
    "* 圖像去噪(denoising)模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 什麼是自動編碼器？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![auto-encoder](https://blog.keras.io/img/ae/autoencoder_schema.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "“自動編碼(Autoencoding)”是一種數據壓縮算法，其中壓縮和解壓縮功能是:\n",
    "1. 針對特定的數據\n",
    "2. 有損的\n",
    "3. 自動從數據中學習而不是由人工設計\n",
    "\n",
    "另外，在幾乎所有使用術語“自動編碼器”的情況下，壓縮和解壓縮功能都是用神經網絡來實現的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 針對特定的數據\n",
    "\n",
    "自動編碼器是針對特定的數據，這意味著它們只能壓縮類似於他們所訓練的數據。這與例如MPEG-2音頻層壓縮算法不同，後者通常只保留關於“聲音”的假設，而不涉及特定類型的聲音。在\"臉部\"圖片上訓練的自動編碼器在壓縮\"樹\"的圖片方面做得相當差，因為它將學習的特徵是\"臉部\"特定的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 有損的\n",
    "\n",
    "自動編碼器是有損失的壓縮，這意味著與原始輸入相比，解壓縮的輸出會降低（類似於MP3或JPEG壓縮）。這與無損壓縮算法不同。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 自動從數據中學習而不是由人工設計\n",
    "\n",
    "自動編碼器是從數據中自動學習的，這是一很有用的特性：這意味著很容易訓練出特定的算法實例，在特定類型的輸入上運行良好。它不需要任何新的工程，只需要適當的訓練數據。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "要構建一個自動編碼器，需要三件事：編碼函數，解碼函數和數據壓縮表示與解壓縮表示（即“丟失”函數）之間的信息損失量之間的距離函數。\n",
    "\n",
    "編碼器和解碼器將被選擇為參數函數（通常為神經網絡），並且相對於距離函數是可微分的，因此可以優化編碼/解碼函數的參數以最小化重構損失，使用隨機梯度下降。這很簡單！而且你甚至不需要理解這些詞語就可以在實踐中開始使用自動編碼器。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 他們擅長數據壓縮嗎？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一般來說並不擅長。例如在圖片壓縮中，訓練一個比JPEG這樣的基本算法效果更好的自動編碼器是相當困難的，而且通常可以實現的唯一方法是將自己限制在一個非常特定類型的圖片上（例如用於哪個JPEG做不好）。自動編碼器是用特定的 數據所訓練出來的事實使得它們對於不能有效的解決現實世界中的數據壓縮問題：您只能將它們用於與其所訓練的數據類似的數據，並使其更加通用，因此需要大量的訓練數據。但是誰知道，未來的進展可能會改變這一點。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 那麼自動編碼器擅長？\n",
    "\n",
    "自動編碼器在實際應用中很少被使用。在2012年，它們被發現可以應用於一種用於深層卷積神經網絡的貪心分層預訓練上[1]，但是隨著我們開始意識到更好的隨機加權初始化方案足以從頭開始訓練深度網絡，它很快就又被拋棄了。在2014年，批量標準化(batch normalization)[2]開始允許更深層次的網絡，從2015年下半年起，我們可以使用殘差學習(residual learning)從頭開始任意深度訓練網絡[3]。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "今天自動編碼器的兩個有趣的實際應用是數據去噪（我們在後面將會介紹）和數據可視化的降維。通過適當的維度和稀疏性約束，自動編碼器可以學習比PCA或其他基本技術更有趣的數據投影。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "對於2D可視化而言，t-SNE（發音為“tee-snee”）可能是最好的算法，但它通常需要相對較低維的數據。因此，在高維數據中可視化相似關係的一個好方法是先使用自動編碼器將數據壓縮到低維空間（例如32維），然後使用t-SNE將壓縮數據映射到2D平面。請注意，Keras中的一個很好的參數實現t-SNE是由Kyle McDonald開發的，可在Github上找到。否則scikit-learn也有一個簡單實用的實現。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 那麼autoencoders有什麼大不了的？\n",
    "\n",
    "他們的主要聲譽來自於在線提供的許多入門機器學習課程中的特色。因此，這個領域的很多新手絕對喜歡自動編碼器，但卻苦於不知該如何入門。這就是本教程存在的原因！\n",
    "\n",
    "另外吸引如此多研究和關注的一個原因是因為它們一直被認為是解決無監督學習問題的潛在途徑，即無需標籤就可以學習有用的表示(representation)。但是，自動編碼器不是一個真正的無監督學習技術（這將意味著完全不同的學習過程），它們是一個自我監督的技術，一個監督學習的特定實例，其中目標是從輸入數據生成的。為了獲得自我監督的模型來學習有趣的特徵，你必須提出一個有趣的合成目標和損失函數，這就是問題出現的地方：僅僅學習重新構造你的輸入可能不是一個正確的選擇。在這一點上，有重要的證據表明，例如，重點放在像素級的圖像重建不能有效地學習標籤監督學習所引起的有趣的抽象特徵（其中目標是相當抽象的概念） “由諸如”狗“，”汽車“等人類）。實際上，有人可能會爭辯說，在這方面，autoencoder最好的特點是在那些你所感興趣的主要任務（分類，定位等等）上使用不怎麼樣的特徵輸入然而獲得高性能的精確重建。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在應用於計算機視覺的自我監督學習中，自動編碼器式輸入重建的一個潛在的而且富有成效的替代方法是使用玩具任務，例如拼圖遊戲求解或細節上下文匹配（能夠將高分辨率但小塊的圖片與他們從中提取的圖片的低分辨率版本）。下面的文章研究了拼圖遊戲的解決方法，並做了一個非常有趣的閱讀：Noroozi和Favaro（2016）通過解決拼圖遊戲的視覺表示的無監督學習。這些任務為模型提供了關於傳統自動編碼器中缺少的輸入數據的內置假設，例如“視覺宏觀結構比像素級細節更重要”。\n",
    "\n",
    "![jigsaw](https://blog.keras.io/img/ae/jigsaw-puzzle.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 我們來構建最簡單的自動編碼器\n",
    "\n",
    "我們將從簡單的開始，將一個完全連接(fully-connected)的神經層作為編碼器和解碼器："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from keras.layers import Input, Dense\n",
    "from keras.models import Model\n",
    "\n",
    "# 這是我們要進行編碼表示(representation)的大小\n",
    "encoding_dim = 32 # 32 浮點數 -> 假如我們的輸入是784個浮點數, 那麼壓縮係數為: 784/32 = 24.5\n",
    "\n",
    "# 這是我們的輸入的佔位符(place holder)\n",
    "input_img_fc = Input(shape=(784,))\n",
    "\n",
    "# \"encoded\"是輸入編碼過後的表示(representation)\n",
    "encoded_fc = Dense(encoding_dim, activation='relu')(input_img_fc)\n",
    "\n",
    "# \"decoded\"是有損失的解碼結果\n",
    "decoded_fc = Dense(784, activation='sigmoid')(encoded_fc)\n",
    "\n",
    "# 串接編碼(encoded)與解碼(decoded)的模型\n",
    "autoencoder_fc = Model(input_img_fc, decoded_fc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我們還要創建一個單獨的編碼器模型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 這個模型串接輸入到編碼表示(representation)\n",
    "encoder_fc = Model(input_img_fc, encoded_fc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以及解碼器模型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 產生一個佔位符來做為\"編碼表示(32-dimensional)\"的輸入\n",
    "encoded_input_fc = Input(shape=(encoding_dim,))\n",
    "\n",
    "# 取得autoencoder模型最後一層的神經層\n",
    "decoder_layer_fc = autoencoder_fc.layers[-1]\n",
    "\n",
    "# 產生解碼模型\n",
    "decoder_fc = Model(encoded_input_fc, decoder_layer_fc(encoded_input_fc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "現在讓我們訓練我們的自動編碼器來重建MNIST數字。\n",
    "\n",
    "首先，我們將我們的模型配置為使用每像素二進制信號(binary crossentropy)損失函數，以及Adadelta優化器："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         (None, 784)               0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 32)                25120     \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 784)               25872     \n",
      "=================================================================\n",
      "Total params: 50,992\n",
      "Trainable params: 50,992\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# 模型參數設定\n",
    "autoencoder_fc.compile(optimizer='adadelta', loss='binary_crossentropy')\n",
    "\n",
    "# 秀出模型結構\n",
    "autoencoder_fc.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "讓我們準備我們的輸入數據。我們使用的是MNIST數字，我們放棄了標籤（因為我們只對編碼/解碼輸入圖像感興趣）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from keras.datasets import mnist\n",
    "import numpy as np\n",
    "\n",
    "(x_train, _), (x_test, _) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我們將歸一化(normalize)所有像素值落於0和1之間，我們將把28x28的圖像打平變成784的向量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 784)\n",
      "(10000, 784)\n"
     ]
    }
   ],
   "source": [
    "x_train = x_train.astype('float32') / 255.\n",
    "x_test = x_test.astype('float32') / 255.\n",
    "\n",
    "x_train = x_train.reshape((len(x_train), np.prod(x_train.shape[1:])))\n",
    "x_test = x_test.reshape((len(x_test), np.prod(x_test.shape[1:])))\n",
    "\n",
    "print(x_train.shape)\n",
    "print(x_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "現在讓我們訓練我們的自動編碼器50個循環(epochs)："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/50\n",
      "60000/60000 [==============================] - 3s 45us/step - loss: 0.3856 - val_loss: 0.2742\n",
      "Epoch 2/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.2681 - val_loss: 0.2593\n",
      "Epoch 3/50\n",
      "60000/60000 [==============================] - 1s 23us/step - loss: 0.2497 - val_loss: 0.2373\n",
      "Epoch 4/50\n",
      "60000/60000 [==============================] - 1s 20us/step - loss: 0.2290 - val_loss: 0.2184\n",
      "Epoch 5/50\n",
      "60000/60000 [==============================] - 1s 25us/step - loss: 0.2129 - val_loss: 0.2048\n",
      "Epoch 6/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.2009 - val_loss: 0.1943\n",
      "Epoch 7/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1915 - val_loss: 0.1862\n",
      "Epoch 8/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1841 - val_loss: 0.1795\n",
      "Epoch 9/50\n",
      "60000/60000 [==============================] - 1s 23us/step - loss: 0.1780 - val_loss: 0.1738\n",
      "Epoch 10/50\n",
      "60000/60000 [==============================] - 1s 23us/step - loss: 0.1727 - val_loss: 0.1689\n",
      "Epoch 11/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1682 - val_loss: 0.1649\n",
      "Epoch 12/50\n",
      "60000/60000 [==============================] - 1s 23us/step - loss: 0.1641 - val_loss: 0.1608\n",
      "Epoch 13/50\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1604 - val_loss: 0.1573\n",
      "Epoch 14/50\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1570 - val_loss: 0.1540\n",
      "Epoch 15/50\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1539 - val_loss: 0.1510\n",
      "Epoch 16/50\n",
      "60000/60000 [==============================] - 1s 21us/step - loss: 0.1510 - val_loss: 0.1482\n",
      "Epoch 17/50\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1482 - val_loss: 0.1457\n",
      "Epoch 18/50\n",
      "60000/60000 [==============================] - 1s 22us/step - loss: 0.1457 - val_loss: 0.1431\n",
      "Epoch 19/50\n",
      "60000/60000 [==============================] - 1s 21us/step - loss: 0.1434 - val_loss: 0.1408\n",
      "Epoch 20/50\n",
      "60000/60000 [==============================] - 1s 22us/step - loss: 0.1411 - val_loss: 0.1387\n",
      "Epoch 21/50\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1390 - val_loss: 0.1366\n",
      "Epoch 22/50\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1370 - val_loss: 0.1345\n",
      "Epoch 23/50\n",
      "60000/60000 [==============================] - 1s 22us/step - loss: 0.1350 - val_loss: 0.1326\n",
      "Epoch 24/50\n",
      "60000/60000 [==============================] - 1s 22us/step - loss: 0.1331 - val_loss: 0.1307\n",
      "Epoch 25/50\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1313 - val_loss: 0.1290\n",
      "Epoch 26/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1296 - val_loss: 0.1273\n",
      "Epoch 27/50\n",
      "60000/60000 [==============================] - 1s 21us/step - loss: 0.1280 - val_loss: 0.1257\n",
      "Epoch 28/50\n",
      "60000/60000 [==============================] - 1s 22us/step - loss: 0.1264 - val_loss: 0.1242\n",
      "Epoch 29/50\n",
      "60000/60000 [==============================] - 1s 22us/step - loss: 0.1250 - val_loss: 0.1227\n",
      "Epoch 30/50\n",
      "60000/60000 [==============================] - 1s 23us/step - loss: 0.1236 - val_loss: 0.1214\n",
      "Epoch 31/50\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1223 - val_loss: 0.1201\n",
      "Epoch 32/50\n",
      "60000/60000 [==============================] - 1s 21us/step - loss: 0.1210 - val_loss: 0.1189\n",
      "Epoch 33/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1199 - val_loss: 0.1178\n",
      "Epoch 34/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1188 - val_loss: 0.1167\n",
      "Epoch 35/50\n",
      "60000/60000 [==============================] - 1s 22us/step - loss: 0.1178 - val_loss: 0.1158\n",
      "Epoch 36/50\n",
      "60000/60000 [==============================] - 1s 22us/step - loss: 0.1169 - val_loss: 0.1148\n",
      "Epoch 37/50\n",
      "60000/60000 [==============================] - 1s 23us/step - loss: 0.1160 - val_loss: 0.1140\n",
      "Epoch 38/50\n",
      "60000/60000 [==============================] - 1s 21us/step - loss: 0.1152 - val_loss: 0.1132\n",
      "Epoch 39/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1144 - val_loss: 0.1125\n",
      "Epoch 40/50\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1137 - val_loss: 0.1118\n",
      "Epoch 41/50\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1131 - val_loss: 0.1112\n",
      "Epoch 42/50\n",
      "60000/60000 [==============================] - 1s 20us/step - loss: 0.1125 - val_loss: 0.1106\n",
      "Epoch 43/50\n",
      "60000/60000 [==============================] - 1s 23us/step - loss: 0.1119 - val_loss: 0.1100\n",
      "Epoch 44/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1114 - val_loss: 0.1095\n",
      "Epoch 45/50\n",
      "60000/60000 [==============================] - 2s 25us/step - loss: 0.1109 - val_loss: 0.1090\n",
      "Epoch 46/50\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1104 - val_loss: 0.1086\n",
      "Epoch 47/50\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1100 - val_loss: 0.1081\n",
      "Epoch 48/50\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1096 - val_loss: 0.1077\n",
      "Epoch 49/50\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1092 - val_loss: 0.1073\n",
      "Epoch 50/50\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1088 - val_loss: 0.1070\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x204acd59f28>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "autoencoder_fc.fit(x_train, x_train,\n",
    "               epochs=50,\n",
    "               batch_size=256,\n",
    "               shuffle=True,\n",
    "               validation_data=(x_test, x_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在50個訓練循環之後，自動編碼器似乎達到穩定的訓練/測試損失值約0.11。我們可以視覺化輸入的重建和編碼表示。我們將使用Matplotlib。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 編碼與解碼一些手寫數字圖像\n",
    "encoded_imgs_fc = encoder_fc.predict(x_test)\n",
    "decoded_imgs_fc = decoder_fc.predict(encoded_imgs_fc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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u7/GYMWMyt2255ZbN7oNZeq2TV0cungfKSo+dHqtHH300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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x204b9d248d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n = 10 # 我們想展示圖像的數量\n",
    "plt.figure(figsize=(20, 4))\n",
    "\n",
    "for i in range(n):\n",
    "    # 秀出原圖像\n",
    "    ax = plt.subplot(2, n, i+1)\n",
    "    plt.imshow(x_test[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "    # 秀出重建圖像\n",
    "    ax = plt.subplot(2, n, i+1+n)\n",
    "    plt.imshow(decoded_imgs_fc[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上是我們得到的結果。上面的一行是原始數字圖像，下面一行是重建的數字圖像。如果我們所說的這個autoencoder會失去很多細節(有損的壓縮)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 深度自動編碼器 (Deep autoencoder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我們不必將自己限制在一個單獨的神經層上作為編碼器或解碼器，而是可以使用一堆神經層，例如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/100\n",
      "60000/60000 [==============================] - 2s 41us/step - loss: 0.3414 - val_loss: 0.2625\n",
      "Epoch 2/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.2551 - val_loss: 0.2453\n",
      "Epoch 3/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.2355 - val_loss: 0.2263\n",
      "Epoch 4/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.2193 - val_loss: 0.2111\n",
      "Epoch 5/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.2081 - val_loss: 0.2035\n",
      "Epoch 6/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1992 - val_loss: 0.1917\n",
      "Epoch 7/100\n",
      "60000/60000 [==============================] - 2s 37us/step - loss: 0.1875 - val_loss: 0.1815\n",
      "Epoch 8/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.1797 - val_loss: 0.1763\n",
      "Epoch 9/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1742 - val_loss: 0.1701\n",
      "Epoch 10/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1692 - val_loss: 0.1653\n",
      "Epoch 11/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1651 - val_loss: 0.1619\n",
      "Epoch 12/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1611 - val_loss: 0.1577\n",
      "Epoch 13/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1573 - val_loss: 0.1534\n",
      "Epoch 14/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1535 - val_loss: 0.1506\n",
      "Epoch 15/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1504 - val_loss: 0.1471\n",
      "Epoch 16/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1477 - val_loss: 0.1452\n",
      "Epoch 17/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1454 - val_loss: 0.1415\n",
      "Epoch 18/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1432 - val_loss: 0.1399\n",
      "Epoch 19/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1414 - val_loss: 0.1406\n",
      "Epoch 20/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1396 - val_loss: 0.1391\n",
      "Epoch 21/100\n",
      "60000/60000 [==============================] - 2s 25us/step - loss: 0.1381 - val_loss: 0.1350\n",
      "Epoch 22/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.1365 - val_loss: 0.1344\n",
      "Epoch 23/100\n",
      "60000/60000 [==============================] - 2s 31us/step - loss: 0.1351 - val_loss: 0.1342\n",
      "Epoch 24/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.1338 - val_loss: 0.1311\n",
      "Epoch 25/100\n",
      "60000/60000 [==============================] - 2s 33us/step - loss: 0.1326 - val_loss: 0.1303\n",
      "Epoch 26/100\n",
      "60000/60000 [==============================] - 2s 31us/step - loss: 0.1314 - val_loss: 0.1300\n",
      "Epoch 27/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1302 - val_loss: 0.1290\n",
      "Epoch 28/100\n",
      "60000/60000 [==============================] - 2s 34us/step - loss: 0.1289 - val_loss: 0.1265\n",
      "Epoch 29/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1278 - val_loss: 0.1265\n",
      "Epoch 30/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1267 - val_loss: 0.1252\n",
      "Epoch 31/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1259 - val_loss: 0.1237\n",
      "Epoch 32/100\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1248 - val_loss: 0.1231\n",
      "Epoch 33/100\n",
      "60000/60000 [==============================] - 2s 35us/step - loss: 0.1239 - val_loss: 0.1213\n",
      "Epoch 34/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.1231 - val_loss: 0.1219\n",
      "Epoch 35/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1223 - val_loss: 0.1213\n",
      "Epoch 36/100\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1216 - val_loss: 0.1198\n",
      "Epoch 37/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1208 - val_loss: 0.1191\n",
      "Epoch 38/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1202 - val_loss: 0.1173\n",
      "Epoch 39/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1194 - val_loss: 0.1175\n",
      "Epoch 40/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1188 - val_loss: 0.1173\n",
      "Epoch 41/100\n",
      "60000/60000 [==============================] - 2s 33us/step - loss: 0.1182 - val_loss: 0.1168\n",
      "Epoch 42/100\n",
      "60000/60000 [==============================] - 2s 34us/step - loss: 0.1175 - val_loss: 0.1159\n",
      "Epoch 43/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1170 - val_loss: 0.1143\n",
      "Epoch 44/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1165 - val_loss: 0.1146\n",
      "Epoch 45/100\n",
      "60000/60000 [==============================] - 2s 31us/step - loss: 0.1158 - val_loss: 0.1141\n",
      "Epoch 46/100\n",
      "60000/60000 [==============================] - 2s 34us/step - loss: 0.1153 - val_loss: 0.1154\n",
      "Epoch 47/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1149 - val_loss: 0.1128\n",
      "Epoch 48/100\n",
      "60000/60000 [==============================] - 2s 37us/step - loss: 0.1144 - val_loss: 0.1122\n",
      "Epoch 49/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1139 - val_loss: 0.1117\n",
      "Epoch 50/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.1135 - val_loss: 0.1119\n",
      "Epoch 51/100\n",
      "60000/60000 [==============================] - 2s 33us/step - loss: 0.1130 - val_loss: 0.1111\n",
      "Epoch 52/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1126 - val_loss: 0.1112\n",
      "Epoch 53/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1122 - val_loss: 0.1113\n",
      "Epoch 54/100\n",
      "60000/60000 [==============================] - 2s 33us/step - loss: 0.1118 - val_loss: 0.1103\n",
      "Epoch 55/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1113 - val_loss: 0.1111\n",
      "Epoch 56/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1111 - val_loss: 0.1100\n",
      "Epoch 57/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1105 - val_loss: 0.1095\n",
      "Epoch 58/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1102 - val_loss: 0.1081\n",
      "Epoch 59/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1099 - val_loss: 0.1089\n",
      "Epoch 60/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1095 - val_loss: 0.1087\n",
      "Epoch 61/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1091 - val_loss: 0.1079\n",
      "Epoch 62/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1090 - val_loss: 0.1070\n",
      "Epoch 63/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1086 - val_loss: 0.1075\n",
      "Epoch 64/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1084 - val_loss: 0.1064\n",
      "Epoch 65/100\n",
      "60000/60000 [==============================] - 2s 31us/step - loss: 0.1081 - val_loss: 0.1072\n",
      "Epoch 66/100\n",
      "60000/60000 [==============================] - 2s 25us/step - loss: 0.1078 - val_loss: 0.1063\n",
      "Epoch 67/100\n",
      "60000/60000 [==============================] - 2s 35us/step - loss: 0.1074 - val_loss: 0.1054\n",
      "Epoch 68/100\n",
      "60000/60000 [==============================] - 2s 31us/step - loss: 0.1072 - val_loss: 0.1053\n",
      "Epoch 69/100\n",
      "60000/60000 [==============================] - 2s 31us/step - loss: 0.1068 - val_loss: 0.1066\n",
      "Epoch 70/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1066 - val_loss: 0.1045\n",
      "Epoch 71/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1064 - val_loss: 0.1059\n",
      "Epoch 72/100\n",
      "60000/60000 [==============================] - 2s 35us/step - loss: 0.1061 - val_loss: 0.1057\n",
      "Epoch 73/100\n",
      "60000/60000 [==============================] - 2s 33us/step - loss: 0.1058 - val_loss: 0.1044\n",
      "Epoch 74/100\n",
      "60000/60000 [==============================] - 2s 33us/step - loss: 0.1056 - val_loss: 0.1034\n",
      "Epoch 75/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1052 - val_loss: 0.1046\n",
      "Epoch 76/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1050 - val_loss: 0.1035\n",
      "Epoch 77/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.1048 - val_loss: 0.1040\n",
      "Epoch 78/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.1045 - val_loss: 0.1027\n",
      "Epoch 79/100\n",
      "60000/60000 [==============================] - 2s 38us/step - loss: 0.1042 - val_loss: 0.1035\n",
      "Epoch 80/100\n",
      "60000/60000 [==============================] - 1s 25us/step - loss: 0.1040 - val_loss: 0.1040\n",
      "Epoch 81/100\n",
      "60000/60000 [==============================] - 2s 31us/step - loss: 0.1037 - val_loss: 0.1023\n",
      "Epoch 82/100\n",
      "60000/60000 [==============================] - 2s 32us/step - loss: 0.1035 - val_loss: 0.1015\n",
      "Epoch 83/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1031 - val_loss: 0.1007\n",
      "Epoch 84/100\n",
      "60000/60000 [==============================] - 2s 33us/step - loss: 0.1030 - val_loss: 0.1010\n",
      "Epoch 85/100\n",
      "60000/60000 [==============================] - 2s 31us/step - loss: 0.1027 - val_loss: 0.1015\n",
      "Epoch 86/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1025 - val_loss: 0.1024\n",
      "Epoch 87/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1023 - val_loss: 0.1011\n",
      "Epoch 88/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1020 - val_loss: 0.1013\n",
      "Epoch 89/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1018 - val_loss: 0.1006\n",
      "Epoch 90/100\n",
      "60000/60000 [==============================] - 1s 24us/step - loss: 0.1017 - val_loss: 0.0998\n",
      "Epoch 91/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1014 - val_loss: 0.0997\n",
      "Epoch 92/100\n",
      "60000/60000 [==============================] - 2s 29us/step - loss: 0.1012 - val_loss: 0.1002\n",
      "Epoch 93/100\n",
      "60000/60000 [==============================] - 2s 30us/step - loss: 0.1010 - val_loss: 0.1001\n",
      "Epoch 94/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1007 - val_loss: 0.1016\n",
      "Epoch 95/100\n",
      "60000/60000 [==============================] - 2s 27us/step - loss: 0.1007 - val_loss: 0.0999\n",
      "Epoch 96/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1004 - val_loss: 0.1015\n",
      "Epoch 97/100\n",
      "60000/60000 [==============================] - 2s 26us/step - loss: 0.1003 - val_loss: 0.0994\n",
      "Epoch 98/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1001 - val_loss: 0.1004\n",
      "Epoch 99/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.1000 - val_loss: 0.0986\n",
      "Epoch 100/100\n",
      "60000/60000 [==============================] - 2s 28us/step - loss: 0.0999 - val_loss: 0.0995\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x2071a5f78d0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_img_deep = Input(shape=(784,))\n",
    "\n",
    "encoded_deep = Dense(128, activation='relu')(input_img_deep)\n",
    "encoded_deep = Dense(64, activation='relu')(encoded_deep)\n",
    "encoded_deep = Dense(32, activation='relu')(encoded_deep)\n",
    "\n",
    "decoded_deep = Dense(64, activation='relu')(encoded_deep)\n",
    "decoded_deep = Dense(128, activation='relu')(decoded_deep)\n",
    "decoded_deep = Dense(784, activation='sigmoid')(decoded_deep)\n",
    "\n",
    "# 串接編碼(encoded)與解碼(decoded)的模型\n",
    "autoencoder_deep = Model(input_img_deep, decoded_deep)\n",
    "\n",
    "# 模型參數設定\n",
    "autoencoder_deep.compile(optimizer='adadelta', loss='binary_crossentropy')\n",
    "\n",
    "# 開始訓練模型\n",
    "autoencoder_deep.fit(x_train, x_train,\n",
    "               epochs=100,\n",
    "               batch_size=256,\n",
    "               shuffle=True,\n",
    "               validation_data=(x_test, x_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2072798ef98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 編碼與解碼一些手寫數字圖像\n",
    "decoded_imgs_deep = autoencoder_deep.predict(x_test)\n",
    "\n",
    "n = 10 # 我們想展示圖像的數量\n",
    "plt.figure(figsize=(20, 4))\n",
    "\n",
    "for i in range(n):\n",
    "    # 秀出原圖像\n",
    "    ax = plt.subplot(2, n, i+1)\n",
    "    plt.imshow(x_test[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "    # 秀出重建圖像\n",
    "    ax = plt.subplot(2, n, i+1+n)\n",
    "    plt.imshow(decoded_imgs_deep[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 卷積自動編碼器 (Convolutional autoencoder)\n",
    "\n",
    "由於我們的輸入是圖像，所以使用卷積神經網絡（convnets）作為編碼器和解碼器是有意義的。在實際設置中，應用於圖像的自動編碼器始終是卷積自動編碼器 - 它們只是表現得更好。\n",
    "\n",
    "我們來實現一個。編碼器將包含一堆Conv2D和MaxPooling2D層（最大池用於空間向下採樣down-sampling），而解碼器將包含一堆Conv2D和UpSampling2D層。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_4 (InputLayer)         (None, 28, 28, 1)         0         \n",
      "_________________________________________________________________\n",
      "conv2d_1 (Conv2D)            (None, 28, 28, 16)        160       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2 (None, 14, 14, 16)        0         \n",
      "_________________________________________________________________\n",
      "conv2d_2 (Conv2D)            (None, 14, 14, 8)         1160      \n",
      "_________________________________________________________________\n",
      "max_pooling2d_2 (MaxPooling2 (None, 7, 7, 8)           0         \n",
      "_________________________________________________________________\n",
      "conv2d_3 (Conv2D)            (None, 7, 7, 8)           584       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_3 (MaxPooling2 (None, 4, 4, 8)           0         \n",
      "_________________________________________________________________\n",
      "conv2d_4 (Conv2D)            (None, 4, 4, 8)           584       \n",
      "_________________________________________________________________\n",
      "up_sampling2d_1 (UpSampling2 (None, 8, 8, 8)           0         \n",
      "_________________________________________________________________\n",
      "conv2d_5 (Conv2D)            (None, 8, 8, 8)           584       \n",
      "_________________________________________________________________\n",
      "up_sampling2d_2 (UpSampling2 (None, 16, 16, 8)         0         \n",
      "_________________________________________________________________\n",
      "conv2d_6 (Conv2D)            (None, 14, 14, 16)        1168      \n",
      "_________________________________________________________________\n",
      "up_sampling2d_3 (UpSampling2 (None, 28, 28, 16)        0         \n",
      "_________________________________________________________________\n",
      "conv2d_7 (Conv2D)            (None, 28, 28, 1)         145       \n",
      "=================================================================\n",
      "Total params: 4,385\n",
      "Trainable params: 4,385\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "from keras.layers import Input, Dense, Conv2D, MaxPool2D, UpSampling2D\n",
    "from keras.models import Model\n",
    "\n",
    "input_img_cov = Input(shape=(28, 28, 1)) # 使用`channels_first`圖像數據格式\n",
    "\n",
    "x = Conv2D(16, (3, 3), activation='relu', padding='same')(input_img_cov)\n",
    "x = MaxPool2D((2, 2), padding='same')(x)\n",
    "x = Conv2D(8, (3, 3), activation='relu', padding='same')(x)\n",
    "x = MaxPool2D((2, 2), padding='same')(x)\n",
    "x = Conv2D(8, (3, 3), activation='relu', padding='same')(x)\n",
    "encoded_cov = MaxPool2D((2, 2), padding='same')(x)\n",
    "\n",
    "# 到這個節點的編碼表示的結構是 (4, 4, 8), 也可以想成是 128-dimensional\n",
    "\n",
    "x = Conv2D(8, (3, 3), activation='relu', padding='same')(encoded_cov)\n",
    "x = UpSampling2D((2, 2))(x)\n",
    "x = Conv2D(8, (3, 3), activation='relu', padding='same')(x)\n",
    "x = UpSampling2D((2, 2))(x)\n",
    "x = Conv2D(16, (3, 3), activation='relu')(x)\n",
    "x = UpSampling2D((2, 2))(x)\n",
    "decoded_cov = Conv2D(1, (3, 3), activation='sigmoid', padding='same')(x)\n",
    "\n",
    "# 串接編碼(encoded)與解碼(decoded)的模型\n",
    "autoencoder_cov = Model(input_img_cov, decoded_cov)\n",
    "\n",
    "# 模型參數設定\n",
    "autoencoder_cov.compile(optimizer='adadelta', loss='binary_crossentropy')\n",
    "\n",
    "# 秀出模型結構\n",
    "autoencoder_cov.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "為了訓練它，我們將使用原始MNIST數字（樣本,28,28），並且我們僅對像素值進行歸一化讓數值落在0和1之間。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 28, 28, 1)\n",
      "(10000, 28, 28, 1)\n"
     ]
    }
   ],
   "source": [
    "from keras.datasets import mnist\n",
    "import numpy as np\n",
    "\n",
    "(x_train, _), (x_test, _) = mnist.load_data()\n",
    "\n",
    "x_train = x_train.astype('float32') / 255.\n",
    "x_test = x_test.astype('float32') / 255.\n",
    "\n",
    "x_train = np.reshape(x_train, (len(x_train), 28, 28, 1))  # 使用`channels_first`圖像數據格式\n",
    "x_test = np.reshape(x_test, (len(x_test), 28, 28, 1))  # 使用`channels_first`圖像數據格式\n",
    "\n",
    "print(x_train.shape)\n",
    "print(x_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "讓我們訓練這個模型50個循環。為了演示如何在訓練過程中顯示模型的結果，我們將使用TensorFlow後端和TensorBoard回調。\n",
    "\n",
    "首先，打開一個終端並啟動一個TensorBoard服務器，該服務器將讀取存儲在/tmp/autoencoder中的日誌。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/50\n",
      "60000/60000 [==============================] - 6s 97us/step - loss: 0.2409 - val_loss: 0.1732\n",
      "Epoch 2/50\n",
      "60000/60000 [==============================] - 5s 75us/step - loss: 0.1648 - val_loss: 0.1551\n",
      "Epoch 3/50\n",
      "60000/60000 [==============================] - 4s 71us/step - loss: 0.1477 - val_loss: 0.1390\n",
      "Epoch 4/50\n",
      "60000/60000 [==============================] - 4s 74us/step - loss: 0.1376 - val_loss: 0.1317\n",
      "Epoch 5/50\n",
      "60000/60000 [==============================] - 4s 74us/step - loss: 0.1313 - val_loss: 0.1305\n",
      "Epoch 6/50\n",
      "60000/60000 [==============================] - 5s 80us/step - loss: 0.1264 - val_loss: 0.1224\n",
      "Epoch 7/50\n",
      "60000/60000 [==============================] - 4s 67us/step - loss: 0.1235 - val_loss: 0.1205\n",
      "Epoch 8/50\n",
      "60000/60000 [==============================] - 4s 70us/step - loss: 0.1209 - val_loss: 0.1187\n",
      "Epoch 9/50\n",
      "60000/60000 [==============================] - 5s 76us/step - loss: 0.1192 - val_loss: 0.1189\n",
      "Epoch 10/50\n",
      "60000/60000 [==============================] - 5s 75us/step - loss: 0.1177 - val_loss: 0.1178\n",
      "Epoch 11/50\n",
      "60000/60000 [==============================] - 4s 72us/step - loss: 0.1160 - val_loss: 0.1152\n",
      "Epoch 12/50\n",
      "60000/60000 [==============================] - 4s 72us/step - loss: 0.1140 - val_loss: 0.1147\n",
      "Epoch 13/50\n",
      "60000/60000 [==============================] - 5s 84us/step - loss: 0.1131 - val_loss: 0.1106\n",
      "Epoch 14/50\n",
      "60000/60000 [==============================] - 4s 70us/step - loss: 0.1124 - val_loss: 0.1100\n",
      "Epoch 15/50\n",
      "60000/60000 [==============================] - 5s 77us/step - loss: 0.1118 - val_loss: 0.1094\n",
      "Epoch 16/50\n",
      "60000/60000 [==============================] - 4s 68us/step - loss: 0.1105 - val_loss: 0.1111\n",
      "Epoch 17/50\n",
      "60000/60000 [==============================] - 4s 68us/step - loss: 0.1099 - val_loss: 0.1073\n",
      "Epoch 18/50\n",
      "60000/60000 [==============================] - 4s 75us/step - loss: 0.1094 - val_loss: 0.1105\n",
      "Epoch 19/50\n",
      "60000/60000 [==============================] - 4s 70us/step - loss: 0.1089 - val_loss: 0.1089\n",
      "Epoch 20/50\n",
      "60000/60000 [==============================] - 5s 81us/step - loss: 0.1077 - val_loss: 0.1065\n",
      "Epoch 21/50\n",
      "60000/60000 [==============================] - 5s 82us/step - loss: 0.1075 - val_loss: 0.1052\n",
      "Epoch 22/50\n",
      "60000/60000 [==============================] - 5s 79us/step - loss: 0.1071 - val_loss: 0.1041\n",
      "Epoch 23/50\n",
      "60000/60000 [==============================] - 5s 75us/step - loss: 0.1065 - val_loss: 0.1049\n",
      "Epoch 24/50\n",
      "60000/60000 [==============================] - 5s 79us/step - loss: 0.1062 - val_loss: 0.1070\n",
      "Epoch 25/50\n",
      "60000/60000 [==============================] - 4s 73us/step - loss: 0.1056 - val_loss: 0.1042\n",
      "Epoch 26/50\n",
      "60000/60000 [==============================] - 5s 78us/step - loss: 0.1053 - val_loss: 0.1040\n",
      "Epoch 27/50\n",
      "60000/60000 [==============================] - 5s 76us/step - loss: 0.1048 - val_loss: 0.1038\n",
      "Epoch 28/50\n",
      "60000/60000 [==============================] - 5s 77us/step - loss: 0.1044 - val_loss: 0.1026\n",
      "Epoch 29/50\n",
      "60000/60000 [==============================] - 5s 79us/step - loss: 0.1045 - val_loss: 0.1020\n",
      "Epoch 30/50\n",
      "60000/60000 [==============================] - 5s 75us/step - loss: 0.1041 - val_loss: 0.1018\n",
      "Epoch 31/50\n",
      "60000/60000 [==============================] - 4s 74us/step - loss: 0.1036 - val_loss: 0.1029\n",
      "Epoch 32/50\n",
      "60000/60000 [==============================] - 5s 78us/step - loss: 0.1033 - val_loss: 0.1020\n",
      "Epoch 33/50\n",
      "60000/60000 [==============================] - 4s 72us/step - loss: 0.1031 - val_loss: 0.1009\n",
      "Epoch 34/50\n",
      "60000/60000 [==============================] - 4s 73us/step - loss: 0.1031 - val_loss: 0.1009\n",
      "Epoch 35/50\n",
      "60000/60000 [==============================] - 4s 74us/step - loss: 0.1027 - val_loss: 0.1018\n",
      "Epoch 36/50\n",
      "60000/60000 [==============================] - 5s 77us/step - loss: 0.1025 - val_loss: 0.1026\n",
      "Epoch 37/50\n",
      "60000/60000 [==============================] - 5s 77us/step - loss: 0.1023 - val_loss: 0.1011\n",
      "Epoch 38/50\n",
      "60000/60000 [==============================] - 4s 72us/step - loss: 0.1018 - val_loss: 0.1005\n",
      "Epoch 39/50\n",
      "60000/60000 [==============================] - 5s 79us/step - loss: 0.1016 - val_loss: 0.1009\n",
      "Epoch 40/50\n",
      "60000/60000 [==============================] - 4s 74us/step - loss: 0.1014 - val_loss: 0.0997\n",
      "Epoch 41/50\n",
      "60000/60000 [==============================] - 5s 78us/step - loss: 0.1011 - val_loss: 0.0993\n",
      "Epoch 42/50\n",
      "60000/60000 [==============================] - 5s 78us/step - loss: 0.1010 - val_loss: 0.1005\n",
      "Epoch 43/50\n",
      "60000/60000 [==============================] - 5s 76us/step - loss: 0.1009 - val_loss: 0.0998\n",
      "Epoch 44/50\n",
      "60000/60000 [==============================] - 4s 70us/step - loss: 0.1005 - val_loss: 0.0983\n",
      "Epoch 45/50\n",
      "60000/60000 [==============================] - 4s 74us/step - loss: 0.1002 - val_loss: 0.0988\n",
      "Epoch 46/50\n",
      "60000/60000 [==============================] - 5s 78us/step - loss: 0.1004 - val_loss: 0.0998\n",
      "Epoch 47/50\n",
      "60000/60000 [==============================] - 5s 86us/step - loss: 0.1003 - val_loss: 0.0986\n",
      "Epoch 48/50\n",
      "60000/60000 [==============================] - 4s 70us/step - loss: 0.1002 - val_loss: 0.0980\n",
      "Epoch 49/50\n",
      "60000/60000 [==============================] - 5s 80us/step - loss: 0.0998 - val_loss: 0.0975\n",
      "Epoch 50/50\n",
      "60000/60000 [==============================] - 5s 77us/step - loss: 0.0997 - val_loss: 0.0982\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x2072ac72cc0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 開始訓練模型\n",
    "autoencoder_cov.fit(x_train, x_train,\n",
    "                epochs=50,\n",
    "                batch_size=128,\n",
    "                shuffle=True,\n",
    "                validation_data=(x_test, x_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "該模型收斂到0.094的損失，明顯好於我們之前的模型（這在很大程度上是由於編碼表示的更高的熵容量，128維度與之前的32維度）。我們來看看重建的數字圖像："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2072ac0b198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "decoded_imgs_conv = autoencoder_cov.predict(x_test)\n",
    "\n",
    "n = 10 # 我們想展示圖像的數量\n",
    "plt.figure(figsize=(20, 4))\n",
    "\n",
    "for i in range(n):\n",
    "    # 秀出原圖像\n",
    "    ax = plt.subplot(2, n, i+1)\n",
    "    plt.imshow(x_test[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "    # 秀出重建圖像\n",
    "    ax = plt.subplot(2, n, i+1+n)\n",
    "    plt.imshow(decoded_imgs_conv[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 應用於圖像去噪 (image denoising)\n",
    "\n",
    "讓我們把我們的卷積自動編碼器工作在一個圖像去噪問題。這很簡單：我們將訓練自動編碼器將噪聲數字圖像處理成清晰的數字圖像。\n",
    "\n",
    "以下是我們如何生成合成噪聲數字圖像：我們只是應用高斯噪聲矩陣，並在0和1之間剪切圖像。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from keras.datasets import mnist\n",
    "import numpy as np\n",
    "\n",
    "(x_train, _), (x_test, _) = mnist.load_data()\n",
    "\n",
    "x_train = x_train.astype('float32') / 255.\n",
    "x_test = x_test.astype('float32') / 255.\n",
    "\n",
    "x_train = np.reshape(x_train, (len(x_train), 28, 28, 1))  # 使用`channels_first`圖像數據格式\n",
    "x_test = np.reshape(x_test, (len(x_test), 28, 28, 1))  # 使用`channels_first`圖像數據格式\n",
    "\n",
    "noise_factor = 0.5 # 噪點因子\n",
    "x_train_noisy = x_train + noise_factor * np.random.normal(loc=0.0, scale=1.0, size=x_train.shape) \n",
    "x_test_noisy = x_test + noise_factor * np.random.normal(loc=0.0, scale=1.0, size=x_test.shape) \n",
    "\n",
    "x_train_noisy = np.clip(x_train_noisy, 0., 1.)\n",
    "x_test_noisy = np.clip(x_test_noisy, 0., 1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以下是有噪點的數字圖像："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kk+E4TdtlOA2bpTOcHgxESQxLDTTlm6U+ah3O6amcEszSGyCmmf7sZz8Lbaee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\nPSPX4dB5klEbdIYtuGfPnh3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mzSDbYAJR1652qVy/gfWUbHEMRB2m\n2rtyX/r5z3++wO8EAIcccgjy0H5XFUsuuWS6Jg899FDucUVjhcelam+Zstpw1Rvn9VueK4BY46Wo\nHtKQIUNy27jeCdcSAKK97913351irUFVdK5Y/1sVnTt3Trp+rQ/GYyyvBg4QrdW15oG+zoNrY6il\np9qAZ2RzU8ahhx6aYq2BwzWauBaZ1lxh9HyMHTs2xWyXrbVBuL6W1ucqW1OkvnTo0CHVlrn55ptz\nj9N6BlwLiq1P1caYrd3VopuvF8+PajvN/YnnPK45BQATJ05MsdbC4hoju+66a4pvv/32cNxPfvKT\nFPPcCwBPPvlkinn9VOtRtiVdFLzzzjupFg7X7wJiX2c9u1K2Do7WCeIaSEX7Eu6zPGa5zg2QbycP\nAE888USKeS1U7T/3Ea7rBkSb9WeeeSbFXEcHiHsInVu571dJs2bNQm0Qhr+DWscyXbp0yW3j2jkc\nA3Efw3brWmNmwIABKe7YseMC/waI9VTK1tDQvstjmC3QgVjDaOTIkSnmOVrR+oJZX9b6ct+H3r17\npz3zTTfdFNquueaaFGvNEV4Li+A6OFpriG3X8yzAi1Bbab6G2i/5enMdGP6NQNzL6hqSV6dM12C2\nPNY1nef8shbrZeD9TVF9KoXvDXgs6j3Jddddl+IXXnghtGX1zYA4f2udPK5rwntIrfnK76f1GB98\n8MEU8/2xnkuuP6fXh+uYsQU114ACivct2XzE955VonXruH6e1pzV+rF5TJ8+PcV6Xvl6lO2XG264\nYYr1vnvo0KEpXmeddUIbr9283uk9zLBhw1L86KOPhjatJ5nB971ArNGk+2iuk1UWZ+IYY4wxxhhj\njDHGNAH8EMcYY4wxxhhjjDGmCVAvi/ElllhiGoAPF3qgqZpetVqt68IPWzi+hv9TfB2bPr6Giwe+\njk0fX8PFA1/Hpo+v4eKBr2PTx9dw8aDUdazXQxxjjDHGGGOMMcYY87/BcipjjDHGGGOMMcaYJoAf\n4hhjjDHGGGOMMcY0AfwQxxhjjDHGGGOMMaYJ4Ic4xhhjjDHGGGOMMU0AP8QxxhhjjDHGGGOMaQL4\nIY4xxhhjjDHGGGNME8APcYwxxhhjjDHGGGOaAH6IY4wxxhhjjDHGGNME8EMcY4wxxhhjjDHGmCbA\n/wcYbS+RCh5kKgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x204bb83d710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 10\n",
    "plt.figure(figsize=(20, 2))\n",
    "\n",
    "for i in range(n):\n",
    "    ax = plt.subplot(1, n, i+1)\n",
    "    plt.imshow(x_test_noisy[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果你瞇起眼睛，你仍然勉強可以認出他們。我們的自動編碼器能學會如何恢復原始數字圖像嗎？讓我們試試看。\n",
    "\n",
    "與上一個的捲積自動編碼器相比，為了提高重建質量，我們將使用稍微不同的模型，每層有更多的濾波器："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_5 (InputLayer)         (None, 28, 28, 1)         0         \n",
      "_________________________________________________________________\n",
      "conv2d_8 (Conv2D)            (None, 28, 28, 32)        320       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_4 (MaxPooling2 (None, 14, 14, 32)        0         \n",
      "_________________________________________________________________\n",
      "conv2d_9 (Conv2D)            (None, 14, 14, 32)        9248      \n",
      "_________________________________________________________________\n",
      "max_pooling2d_5 (MaxPooling2 (None, 7, 7, 32)          0         \n",
      "_________________________________________________________________\n",
      "conv2d_10 (Conv2D)           (None, 7, 7, 32)          9248      \n",
      "_________________________________________________________________\n",
      "up_sampling2d_4 (UpSampling2 (None, 14, 14, 32)        0         \n",
      "_________________________________________________________________\n",
      "conv2d_11 (Conv2D)           (None, 14, 14, 32)        9248      \n",
      "_________________________________________________________________\n",
      "up_sampling2d_5 (UpSampling2 (None, 28, 28, 32)        0         \n",
      "_________________________________________________________________\n",
      "conv2d_12 (Conv2D)           (None, 28, 28, 1)         289       \n",
      "=================================================================\n",
      "Total params: 28,353\n",
      "Trainable params: 28,353\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "input_img_conv2 = Input(shape=(28, 28, 1))\n",
    "\n",
    "x = Conv2D(32, (3, 3), activation='relu', padding='same')(input_img_conv2)\n",
    "x = MaxPool2D((2, 2), padding='same')(x)\n",
    "x = Conv2D(32, (3, 3), activation='relu', padding='same')(x)\n",
    "encoded_conv2 = MaxPool2D((2, 2), padding='same')(x)\n",
    "\n",
    "# 到這個節點的編碼表示的結構是 (7, 7, 32)\n",
    "\n",
    "x = Conv2D(32, (3, 3), activation='relu', padding='same')(encoded_conv2)\n",
    "x = UpSampling2D((2, 2))(x)\n",
    "x = Conv2D(32, (3, 3), activation='relu', padding='same')(x)\n",
    "x = UpSampling2D((2, 2))(x)\n",
    "decoded_conv2= Conv2D(1, (3, 3), activation='sigmoid', padding='same')(x)\n",
    "\n",
    "# 串接編碼(encoded)與解碼(decoded)的模型\n",
    "autoencoder_conv2 = Model(input_img_conv2, decoded_conv2)\n",
    "\n",
    "# 模型參數設定\n",
    "autoencoder_conv2.compile(optimizer='adadelta', loss='binary_crossentropy')\n",
    "\n",
    "# 模型參數設定\n",
    "autoencoder_conv2.summary()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "讓我們訓練它100個循環："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/100\n",
      "60000/60000 [==============================] - 6s 97us/step - loss: 0.2192 - val_loss: 0.1322\n",
      "Epoch 2/100\n",
      "60000/60000 [==============================] - 5s 85us/step - loss: 0.1264 - val_loss: 0.1170\n",
      "Epoch 3/100\n",
      "60000/60000 [==============================] - 5s 88us/step - loss: 0.1162 - val_loss: 0.1110\n",
      "Epoch 4/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.1113 - val_loss: 0.1074\n",
      "Epoch 5/100\n",
      "60000/60000 [==============================] - 6s 98us/step - loss: 0.1085 - val_loss: 0.1062\n",
      "Epoch 6/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.1065 - val_loss: 0.1035\n",
      "Epoch 7/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.1049 - val_loss: 0.1023\n",
      "Epoch 8/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.1039 - val_loss: 0.1021\n",
      "Epoch 9/100\n",
      "60000/60000 [==============================] - 6s 97us/step - loss: 0.1029 - val_loss: 0.1033\n",
      "Epoch 10/100\n",
      "60000/60000 [==============================] - 6s 98us/step - loss: 0.1022 - val_loss: 0.1016\n",
      "Epoch 11/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.1016 - val_loss: 0.1008\n",
      "Epoch 12/100\n",
      "60000/60000 [==============================] - 5s 89us/step - loss: 0.1012 - val_loss: 0.0993\n",
      "Epoch 13/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.1007 - val_loss: 0.0990\n",
      "Epoch 14/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.1002 - val_loss: 0.0998\n",
      "Epoch 15/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.1000 - val_loss: 0.0983\n",
      "Epoch 16/100\n",
      "60000/60000 [==============================] - 6s 97us/step - loss: 0.0997 - val_loss: 0.0985\n",
      "Epoch 17/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0994 - val_loss: 0.0982\n",
      "Epoch 18/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0991 - val_loss: 0.0976\n",
      "Epoch 19/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0988 - val_loss: 0.0984\n",
      "Epoch 20/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.0988 - val_loss: 0.0976\n",
      "Epoch 21/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.0985 - val_loss: 0.0981\n",
      "Epoch 22/100\n",
      "60000/60000 [==============================] - 5s 89us/step - loss: 0.0984 - val_loss: 0.0984\n",
      "Epoch 23/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.0982 - val_loss: 0.0969\n",
      "Epoch 24/100\n",
      "60000/60000 [==============================] - 5s 88us/step - loss: 0.0980 - val_loss: 0.0977\n",
      "Epoch 25/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0979 - val_loss: 0.0969\n",
      "Epoch 26/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0978 - val_loss: 0.0967\n",
      "Epoch 27/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0975 - val_loss: 0.0973\n",
      "Epoch 28/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.0974 - val_loss: 0.0967\n",
      "Epoch 29/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0973 - val_loss: 0.0970\n",
      "Epoch 30/100\n",
      "60000/60000 [==============================] - 5s 88us/step - loss: 0.0972 - val_loss: 0.0961\n",
      "Epoch 31/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0971 - val_loss: 0.0965\n",
      "Epoch 32/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0970 - val_loss: 0.0960\n",
      "Epoch 33/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0969 - val_loss: 0.0959\n",
      "Epoch 34/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0969 - val_loss: 0.0960\n",
      "Epoch 35/100\n",
      "60000/60000 [==============================] - 6s 102us/step - loss: 0.0968 - val_loss: 0.0960\n",
      "Epoch 36/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0966 - val_loss: 0.0955\n",
      "Epoch 37/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.0965 - val_loss: 0.0956\n",
      "Epoch 38/100\n",
      "60000/60000 [==============================] - 6s 97us/step - loss: 0.0965 - val_loss: 0.0965\n",
      "Epoch 39/100\n",
      "60000/60000 [==============================] - 6s 98us/step - loss: 0.0964 - val_loss: 0.0959\n",
      "Epoch 40/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0963 - val_loss: 0.0952\n",
      "Epoch 41/100\n",
      "60000/60000 [==============================] - 5s 89us/step - loss: 0.0963 - val_loss: 0.0954\n",
      "Epoch 42/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.0961 - val_loss: 0.0951\n",
      "Epoch 43/100\n",
      "60000/60000 [==============================] - 5s 90us/step - loss: 0.0961 - val_loss: 0.0951\n",
      "Epoch 44/100\n",
      "60000/60000 [==============================] - 5s 88us/step - loss: 0.0960 - val_loss: 0.0950\n",
      "Epoch 45/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0960 - val_loss: 0.0951\n",
      "Epoch 46/100\n",
      "60000/60000 [==============================] - 6s 102us/step - loss: 0.0959 - val_loss: 0.0963\n",
      "Epoch 47/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0958 - val_loss: 0.0956\n",
      "Epoch 48/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0958 - val_loss: 0.0949\n",
      "Epoch 49/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0958 - val_loss: 0.0950\n",
      "Epoch 50/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0957 - val_loss: 0.0948\n",
      "Epoch 51/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0956 - val_loss: 0.0967\n",
      "Epoch 52/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0956 - val_loss: 0.0950\n",
      "Epoch 53/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.0955 - val_loss: 0.0956\n",
      "Epoch 54/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0955 - val_loss: 0.0948\n",
      "Epoch 55/100\n",
      "60000/60000 [==============================] - 5s 90us/step - loss: 0.0955 - val_loss: 0.0946\n",
      "Epoch 56/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0954 - val_loss: 0.0950\n",
      "Epoch 57/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0953 - val_loss: 0.0950\n",
      "Epoch 58/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0953 - val_loss: 0.0947\n",
      "Epoch 59/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0953 - val_loss: 0.0947\n",
      "Epoch 60/100\n",
      "60000/60000 [==============================] - 6s 97us/step - loss: 0.0952 - val_loss: 0.0952\n",
      "Epoch 61/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.0952 - val_loss: 0.0945\n",
      "Epoch 62/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0952 - val_loss: 0.0944\n",
      "Epoch 63/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.0951 - val_loss: 0.0944\n",
      "Epoch 64/100\n",
      "60000/60000 [==============================] - 5s 87us/step - loss: 0.0950 - val_loss: 0.0945\n",
      "Epoch 65/100\n",
      "60000/60000 [==============================] - 5s 90us/step - loss: 0.0950 - val_loss: 0.0948\n",
      "Epoch 66/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0951 - val_loss: 0.0949\n",
      "Epoch 67/100\n",
      "60000/60000 [==============================] - 6s 99us/step - loss: 0.0949 - val_loss: 0.0950\n",
      "Epoch 68/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0950 - val_loss: 0.0949\n",
      "Epoch 69/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.0949 - val_loss: 0.0945\n",
      "Epoch 70/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0948 - val_loss: 0.0948\n",
      "Epoch 71/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0949 - val_loss: 0.0947\n",
      "Epoch 72/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0948 - val_loss: 0.0945\n",
      "Epoch 73/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.0948 - val_loss: 0.0943\n",
      "Epoch 74/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0947 - val_loss: 0.0947\n",
      "Epoch 75/100\n",
      "60000/60000 [==============================] - 6s 98us/step - loss: 0.0948 - val_loss: 0.0942\n",
      "Epoch 76/100\n",
      "60000/60000 [==============================] - 6s 98us/step - loss: 0.0946 - val_loss: 0.0942\n",
      "Epoch 77/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0947 - val_loss: 0.0946\n",
      "Epoch 78/100\n",
      "60000/60000 [==============================] - 5s 90us/step - loss: 0.0946 - val_loss: 0.0952\n",
      "Epoch 79/100\n",
      "60000/60000 [==============================] - 5s 92us/step - loss: 0.0946 - val_loss: 0.0948\n",
      "Epoch 80/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0946 - val_loss: 0.0939\n",
      "Epoch 81/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0945 - val_loss: 0.0940\n",
      "Epoch 82/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0945 - val_loss: 0.0938\n",
      "Epoch 83/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0946 - val_loss: 0.0939\n",
      "Epoch 84/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.0945 - val_loss: 0.0943\n",
      "Epoch 85/100\n",
      "60000/60000 [==============================] - 6s 95us/step - loss: 0.0945 - val_loss: 0.0940\n",
      "Epoch 86/100\n",
      "60000/60000 [==============================] - 5s 90us/step - loss: 0.0945 - val_loss: 0.0938\n",
      "Epoch 87/100\n",
      "60000/60000 [==============================] - 5s 90us/step - loss: 0.0944 - val_loss: 0.0943\n",
      "Epoch 88/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0944 - val_loss: 0.0937\n",
      "Epoch 89/100\n",
      "60000/60000 [==============================] - 5s 88us/step - loss: 0.0944 - val_loss: 0.0938\n",
      "Epoch 90/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.0943 - val_loss: 0.0947\n",
      "Epoch 91/100\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0943 - val_loss: 0.0944\n",
      "Epoch 92/100\n",
      "60000/60000 [==============================] - 6s 100us/step - loss: 0.0944 - val_loss: 0.0937\n",
      "Epoch 93/100\n",
      "60000/60000 [==============================] - 6s 101us/step - loss: 0.0943 - val_loss: 0.0938\n",
      "Epoch 94/100\n",
      "60000/60000 [==============================] - 6s 98us/step - loss: 0.0943 - val_loss: 0.0940\n",
      "Epoch 95/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0943 - val_loss: 0.0940\n",
      "Epoch 96/100\n",
      "60000/60000 [==============================] - 6s 92us/step - loss: 0.0942 - val_loss: 0.0945\n",
      "Epoch 97/100\n",
      "60000/60000 [==============================] - 6s 98us/step - loss: 0.0942 - val_loss: 0.0941\n",
      "Epoch 98/100\n",
      "60000/60000 [==============================] - 6s 93us/step - loss: 0.0942 - val_loss: 0.0940\n",
      "Epoch 99/100\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0943 - val_loss: 0.0936\n",
      "Epoch 100/100\n",
      "60000/60000 [==============================] - 6s 96us/step - loss: 0.0941 - val_loss: 0.0936\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x2072e3dba58>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "autoencoder_conv2.fit(x_train_noisy, x_train,\n",
    "                     epochs=100,\n",
    "                     batch_size=128,\n",
    "                     shuffle=True,\n",
    "                     validation_data=(x_test_noisy, x_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Vl0r8/PPPh+M0bZfhNGyWznB6MBAlMSw10JRvlvqodTinp3JKMEtvgJhm+pe/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\n99xzzxSrVfTjjz8OYIZ1XCWYOnVq+u2q92advepNuQ4O12X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      "text/plain": [
       "<matplotlib.figure.Figure at 0x204acb0fc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "decoded_imgs_conv2 = autoencoder_conv2.predict(x_test_noisy)\n",
    "\n",
    "n = 10 # 我們想展示圖像的數量\n",
    "plt.figure(figsize=(20, 4))\n",
    "\n",
    "for i in range(n):\n",
    "    # 秀出原圖像\n",
    "    ax = plt.subplot(2, n, i+1)\n",
    "    plt.imshow(x_test_noisy[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "    # 秀出重建圖像\n",
    "    ax = plt.subplot(2, n, i+1+n)\n",
    "    plt.imshow(decoded_imgs_conv2[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "現在我們來看看結果。第一行展現的是有噪點的數字圖像，以及第二行由網絡重建的數字圖像。\n",
    "它似乎效果很好。如果您將此過程擴展為更大的卷積網絡，那麼就可以開始構建文檔去噪或音頻去噪的模型。"
   ]
  },
  {
   "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",
    "* Autoencoder的概念在深度學習有很多的應用, 不管是在圖像、語音甚至自然語言的處理上\n",
    "* 了解autoencoder的構建可以做為學習構建更複雜的深度學習的網絡結構"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "參考:\n",
    "* [Building Autoencoders in Keras](https://blog.keras.io/building-autoencoders-in-keras.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MIT License\n",
    "\n",
    "Copyright (c) 2017 François Chollet\n",
    "\n",
    "Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n",
    "\n",
    "The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n",
    "\n",
    "THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
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}