Project1 用Python实现softmax多分类问题 .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 用python实现Softmax多分类问题\n",
    "\n",
    "\n",
    "### 一、 什么是softmax? \n",
    "\n",
    "在数学，尤其是概率论和相关领域中，softmax函数，是逻辑函数的一种推广。它能将一个含任意实数的K维向量“压缩”到另一个K维实向量中，使得每一个元素的范围都在0-1之间，并且使所有元素的和为1。这样，每个元素就代表了属于某个分类的概率。值越大，概率就越大，属于某一类的可能性就越大。\n",
    "\n",
    "### 二、softmax有什么用？\n",
    "\n",
    "softmax广泛应用于机器学习和深度学习中的多分类问题。在深度学习中，softmax常用于多分类问题最后一层的激活函数，用于输出某样本属于某个分类的概率值。\n",
    "\n",
    "### 三、 如何实现softmax呢？\n",
    "\n",
    "本文以tensorflow的自带数据集fashion_minist为例,fashion_minist是一个有10个分类的带label的图片数据集，使用Python（基本是靠numpy）构建一个两层的神经网络分类模型，预测图片的label。\n",
    "\n",
    "### 四、两层Softmax模型构建流程\n",
    "* step1: 明确模型框架：input layer — hidden layer  — output layer( activation = softmax)\n",
    "* step2: 参数初始化\n",
    "* step3: 循环：前向传播 - 计算损失 - 后向传播 - 更新参数（梯度下降）\n",
    "\n",
    "Notes: 这里只写了必要的过程，主要为了说明如何用Python实现softmax,其中有很多环节是可以优化的（这就变成一个分类预测问题了），说了说明我的模型的有效性，使用测试集预测准确率为80%左右。\n",
    "\n",
    "### 五、Reference\n",
    "吴恩达 Deep Learning and Neural Network on Coursera\n",
    "\n",
    "\n",
    "#######################################################################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 导入相关package和数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\littletree\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\h5py\\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import keras\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 导入多分类数据\n",
    "fashion_mnist = keras.datasets.fashion_mnist\n",
    "(train_images, train_labels), (test_images, test_labels) = fashion_mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class_names = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat',\n",
    "               'Sandal', 'Shirt', 'Sneaker', 'Bag', 'Ankle boot']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 数据探索与预处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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K7SrI8+r7YGFY3h386iNLwlVZ8HFct1NnJ9RcSExKLbF6MvZ/CNw4yfKH3X1D9ujsACYy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\n3gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.imshow(train_images[3])\n",
    "plt.colorbar()\n",
    "plt.grid(False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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53SPzOtI5d4tzboxzbqpzLj0bolgDzWfjJ0mSJQDOAXCeq+QM59zDzrlhqPwR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\n7LPRPuCAA6K96667bvTYNsaiReuHwbx585JtxxxzTLRrfVDm3wu0rm/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b55ydzPvz45Kl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\nrkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "for i in range(25):\n",
    "    plt.subplot(5,5,i+1)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.grid(False)\n",
    "    plt.imshow(train_images[i], cmap=plt.cm.binary)\n",
    "    plt.xlabel(class_names[train_labels[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training examples: m_train = 60000\n",
      "Number of testing examples: m_test = 10000\n",
      "Height/Width of each image: num_px = 28\n",
      "Each image is of size: (28, 28)\n",
      "train_images shape: (60000, 28, 28)\n",
      "train_labels shape: (60000,)\n",
      "test_images shape: (10000, 28, 28)\n",
      "test_labels shape: (10000,)\n"
     ]
    }
   ],
   "source": [
    "# Figure out the dimensions and shapes of the problem\n",
    "m_train = len(train_images)\n",
    "m_test = len(test_images)\n",
    "num_px = train_images.shape[1]\n",
    "\n",
    "print (\"Number of training examples: m_train = \" + str(m_train))\n",
    "print (\"Number of testing examples: m_test = \" + str(m_test))\n",
    "print (\"Height/Width of each image: num_px = \" + str(num_px))\n",
    "print (\"Each image is of size: (\" + str(num_px) + \", \" + str(num_px) + \")\")\n",
    "print (\"train_images shape: \" + str(train_images.shape))\n",
    "print (\"train_labels shape: \" + str(train_labels.shape))\n",
    "print (\"test_images shape: \" + str(test_images.shape))\n",
    "print (\"test_labels shape: \" + str(test_labels.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 把labels转成one-hot格式\n",
    "def convert_to_onehot(Y, C):\n",
    "    \n",
    "    Y = np.eye(C)[Y.reshape(-1)].T\n",
    "    return Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train_images_flatten shape: (784, 60000)\n",
      "train_labels_onehot shape: (10, 60000)\n",
      "test_images_flatten shape: (784, 10000)\n",
      "test_labels_onehot shape: (10, 10000)\n"
     ]
    }
   ],
   "source": [
    "# Reshape the training and test examples\n",
    "train_images_flatten = train_images.reshape(train_images.shape[0], -1).T\n",
    "test_images_flatten = test_images.reshape(test_images.shape[0], -1).T\n",
    "\n",
    "train_labels_onehot = convert_to_onehot(train_labels, 10)\n",
    "test_labels_onehot = convert_to_onehot(test_labels, 10)\n",
    "\n",
    "print (\"train_images_flatten shape: \" + str(train_images_flatten.shape))\n",
    "print (\"train_labels_onehot shape: \" + str(train_labels_onehot.shape))\n",
    "print (\"test_images_flatten shape: \" + str(test_images_flatten.shape))\n",
    "print (\"test_labels_onehot shape: \" + str(test_labels_onehot.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 对数据进行标准化处理\n",
    "train_set_x = train_images_flatten / 255.0\n",
    "test_set_x = test_images_flatten / 255.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 编写模型相关部分\n",
    "\n",
    "模型架构及参数选择：\n",
    "1. 模型框架：input layer — hidden layer (128 units, relu） — output layer(10 units, softmax)\n",
    "2. 激活函数：relu和softmax\n",
    "3. 参数初始化方式：随机初始化\n",
    "4. 损失函数：softmax交叉熵\n",
    "5. 优化算法：梯度下降"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (1) 定义激活函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def relu(Z):\n",
    "    \"\"\"\n",
    "    Implement the RELU function.\n",
    "\n",
    "    Arguments:\n",
    "    Z -- Output of the linear layer, of any shape\n",
    "\n",
    "    Returns:\n",
    "    A -- Post-activation parameter, of the same shape as Z\n",
    "    cache -- a python dictionary containing \"A\" ; stored for computing the backward pass efficiently\n",
    "    \"\"\"\n",
    "    A = np.maximum(0,Z)\n",
    "    \n",
    "    assert(A.shape == Z.shape)\n",
    "    \n",
    "    cache = Z \n",
    "    return A, cache"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 注意:exp(z)容易造成数值上溢，这个问题要处理！\n",
    "* 可以证明softmax(z) = soft(z+c),其中c为常数，即softmax对input加减一个常数项具有不变性。因此，我们在处理这个问题的时候把z-max(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def softmax(Z):\n",
    "    \"\"\"\n",
    "    softmax activation\n",
    "    \n",
    "    Arguments:\n",
    "    Z -- numpy array of any shape\n",
    "    \n",
    "    Returns:\n",
    "    A -- output of softmax(z), same shape as Z\n",
    "    cache -- returns Z as well, useful during backpropagation\n",
    "    \"\"\"\n",
    "    Z_shift = Z - np.max(Z, axis = 0)\n",
    "    A = np.exp(Z_shift)/ np.sum(np.exp(Z_shift), axis=0)\n",
    "    \n",
    "    cache = Z_shift\n",
    "    \n",
    "    return A, cache"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (2) 参数初始化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def initialize_parameters(n_x, n_h, n_y):\n",
    "    \"\"\"\n",
    "    Argument:\n",
    "    n_x -- size of the input layer\n",
    "    n_h -- size of the hidden layer\n",
    "    n_y -- size of the output layer\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    W1 -- weight matrix of shape (n_h, n_x)\n",
    "                    b1 -- bias vector of shape (n_h, 1)\n",
    "                    W2 -- weight matrix of shape (n_y, n_h)\n",
    "                    b2 -- bias vector of shape (n_y, 1)\n",
    "    \"\"\"\n",
    "    np.random.seed(1)\n",
    "    \n",
    "    W1 = np.random.randn(n_h, n_x) * 0.01   # weight matrix随机初始化\n",
    "    b1 = np.zeros((n_h, 1))                 # bias vector零初始化\n",
    "    W2 = np.random.randn(n_y, n_h) * 0.01\n",
    "    b2 = np.zeros((n_y, 1))\n",
    "    \n",
    "    assert(W1.shape == (n_h, n_x))\n",
    "    assert(b1.shape == (n_h, 1))\n",
    "    assert(W2.shape == (n_y, n_h))\n",
    "    assert(b2.shape == (n_y, 1))\n",
    "    \n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (3) Forward propagation module\n",
    "\n",
    "The linear forward module (vectorized over all the examples) computes the following equations:\n",
    "\n",
    "$$Z^{[l]} = W^{[l]}A^{[l-1]} +b^{[l]}$$\n",
    "\n",
    "where $A^{[0]} = X$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linear_forward(A, W, b):\n",
    "    \"\"\"\n",
    "    Implement the linear part of a layer's forward propagation.\n",
    "\n",
    "    Arguments:\n",
    "    A -- activations from previous layer (or input data): (size of previous layer, number of examples)\n",
    "    W -- weights matrix: numpy array of shape (size of current layer, size of previous layer)\n",
    "    b -- bias vector, numpy array of shape (size of the current layer, 1)\n",
    "\n",
    "    Returns:\n",
    "    Z -- the input of the activation function, also called pre-activation parameter \n",
    "    cache -- a python dictionary containing \"A\", \"W\" and \"b\" ; stored for computing the backward pass efficiently\n",
    "    \"\"\"\n",
    "    Z = np.dot(W, A) + b\n",
    "    \n",
    "    assert(Z.shape == (W.shape[0], A.shape[1]))\n",
    "    cache = (A, W, b)\n",
    "    \n",
    "    return Z, cache"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Implement the forward propagation of the *LINEAR->ACTIVATION* layer. Mathematical relation is: $A^{[l]} = g(Z^{[l]}) = g(W^{[l]}A^{[l-1]} +b^{[l]})$ where the activation \"g\" can be softmax() or relu()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linear_activation_forward(A_prev, W, b, activation):\n",
    "    \"\"\"\n",
    "    Implement the forward propagation for the LINEAR->ACTIVATION layer\n",
    "\n",
    "    Arguments:\n",
    "    A_prev -- activations from previous layer (or input data): (size of previous layer, number of examples)\n",
    "    W -- weights matrix: numpy array of shape (size of current layer, size of previous layer)\n",
    "    b -- bias vector, numpy array of shape (size of the current layer, 1)\n",
    "    activation -- the activation to be used in this layer, stored as a text string: \"softmax\" or \"relu\"\n",
    "\n",
    "    Returns:\n",
    "    A -- the output of the activation function, also called the post-activation value \n",
    "    cache -- a python dictionary containing \"linear_cache\" and \"activation_cache\";\n",
    "             stored for computing the backward pass efficiently\n",
    "    \"\"\"\n",
    "    \n",
    "    if activation == \"softmax\":\n",
    "        # Inputs: \"A_prev, W, b\". Outputs: \"A, activation_cache\".\n",
    "        Z, linear_cache = linear_forward(A_prev, W, b)\n",
    "        A, activation_cache = softmax(Z)\n",
    "      \n",
    "    elif activation == \"relu\":\n",
    "        # Inputs: \"A_prev, W, b\". Outputs: \"A, activation_cache\".\n",
    "        Z, linear_cache = linear_forward(A_prev, W, b)\n",
    "        A, activation_cache = relu(Z)\n",
    "    \n",
    "    assert (A.shape == (W.shape[0], A_prev.shape[1]))\n",
    "    cache = (linear_cache, activation_cache)\n",
    "\n",
    "    return A, cache"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (4) Cost Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def compute_cost(AL, Y):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    AL -- probability matrix corresponding to your label predictions, shape (classes, number of examples)\n",
    "    Y -- true \"label\" matrix, shape (classes, number of examples)\n",
    "\n",
    "    Returns:\n",
    "    cost -- softmax cross-entropy cost\n",
    "    \"\"\"\n",
    "    m = Y.shape[1]\n",
    "    cost = -(np.sum(Y * np.log(AL))) / float(m)\n",
    "    #cost = np.squeeze(cost)\n",
    "    assert(cost.shape == ())\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (5) Backward propagation module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linear_backward(dZ, cache):\n",
    "    \"\"\"\n",
    "    Implement the linear portion of backward propagation for a single layer (layer l)\n",
    "\n",
    "    Arguments:\n",
    "    dZ -- Gradient of the cost with respect to the linear output (of current layer l)\n",
    "    cache -- tuple of values (A_prev, W, b) coming from the forward propagation in the current layer\n",
    "\n",
    "    Returns:\n",
    "    dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev\n",
    "    dW -- Gradient of the cost with respect to W (current layer l), same shape as W\n",
    "    db -- Gradient of the cost with respect to b (current layer l), same shape as b\n",
    "    \"\"\"\n",
    "    A_prev, W, b = cache\n",
    "    m = A_prev.shape[1]\n",
    "\n",
    "    dW = np.dot(dZ, A_prev.T) / float(m)\n",
    "    db = np.sum(dZ, axis=1, keepdims=True) / float(m)\n",
    "    dA_prev = np.dot(W.T, dZ)\n",
    "    \n",
    "    assert (dA_prev.shape == A_prev.shape)\n",
    "    assert (dW.shape == W.shape)\n",
    "    assert (db.shape == b.shape)\n",
    "    \n",
    "    return dA_prev, dW, db"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def relu_backward(dA, cache):\n",
    "    \"\"\"\n",
    "    Implement the backward propagation for a single RELU unit.\n",
    "\n",
    "    Arguments:\n",
    "    dA -- post-activation gradient, of any shape\n",
    "    cache -- 'Z' where we store for computing backward propagation efficiently\n",
    "\n",
    "    Returns:\n",
    "    dZ -- Gradient of the cost with respect to Z\n",
    "    \"\"\"\n",
    "    Z = cache\n",
    "    dZ = np.array(dA, copy=True)  # just converting dz to a correct object.\n",
    "    \n",
    "    # When z <= 0, you should set dz to 0 as well. \n",
    "    dZ[Z <= 0] = 0\n",
    "    \n",
    "    assert (dZ.shape == Z.shape)\n",
    "    \n",
    "    return dZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def softmax_backward(Y, cache):\n",
    "    \"\"\"\n",
    "    合并求导dL/dZ = （dL/dA） * （dA/dZ）\n",
    "\n",
    "    Arguments:\n",
    "    Y -- true \"label\" matrix, shape (classes, number of examples)\n",
    "    cache -- 'Z' where we store for computing backward propagation efficiently\n",
    "\n",
    "    Returns:\n",
    "    dZ -- Gradient of the cost with respect to Z\n",
    "    \"\"\"\n",
    "    Z = cache  #注意cache中的Z实际是Z_shift\n",
    "    \n",
    "    s = np.exp(Z)/ np.sum(np.exp(Z), axis=0)\n",
    "    dZ = s - Y\n",
    "    \n",
    "    assert (dZ.shape == Z.shape)\n",
    "    \n",
    "    return dZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linear_activation_backward(dA, cache, activation):\n",
    "    \"\"\"\n",
    "    Implement the backward propagation for the LINEAR->ACTIVATION layer.\n",
    "    \n",
    "    Arguments:\n",
    "    dA -- post-activation gradient for hidden layer or Y for outputlayer!!!\n",
    "    cache -- tuple of values (linear_cache, activation_cache) we store for computing backward propagation efficiently\n",
    "    activation -- the activation to be used in this layer, stored as a text string: \"sigmoid\" or \"relu\"\n",
    "    \n",
    "    Returns:\n",
    "    dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev\n",
    "    dW -- Gradient of the cost with respect to W (current layer l), same shape as W\n",
    "    db -- Gradient of the cost with respect to b (current layer l), same shape as b\n",
    "    \"\"\"\n",
    "    linear_cache, activation_cache = cache\n",
    "    \n",
    "    if activation == \"relu\":\n",
    "        dZ = relu_backward(dA, activation_cache)\n",
    "        dA_prev, dW, db = linear_backward(dZ, linear_cache)\n",
    " \n",
    "    elif activation == \"softmax\":\n",
    "        dZ = softmax_backward(dA, activation_cache)\n",
    "        dA_prev, dW, db = linear_backward(dZ, linear_cache)\n",
    "\n",
    "    return dA_prev, dW, db"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### （6）参数更新"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def update_parameters(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters \n",
    "    grads -- python dictionary containing your gradients, output of L_model_backward\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "                  parameters[\"W\" + str(l)] = ... \n",
    "                  parameters[\"b\" + str(l)] = ...\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural network\n",
    "\n",
    "    # Update rule for each parameter. Use a for loop.\n",
    "    for l in range(1,L+1):\n",
    "        parameters['W'+str(l)] -= learning_rate * grads['dW'+str(l)]\n",
    "        parameters['b'+str(l)] -= learning_rate * grads['db'+str(l)]\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. 模型整合及有效性检测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def two_layer_model(X, Y, layers_dims, learning_rate = 0.1, num_iterations = 3000, print_cost=False):\n",
    "    \"\"\"\n",
    "    Implements a two-layer neural network: LINEAR->RELU->LINEAR->SOFTMAX.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (n_x, number of examples)\n",
    "    Y -- true \"label\", of shape (classes, number of examples)\n",
    "    layers_dims -- dimensions of the layers (n_x, n_h, n_y)\n",
    "    num_iterations -- number of iterations of the optimization loop\n",
    "    learning_rate -- learning rate of the gradient descent update rule\n",
    "    print_cost -- If set to True, this will print the cost every 100 iterations \n",
    "    \n",
    "    Returns:\n",
    "    parameters -- a dictionary containing W1, W2, b1, and b2\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(1)\n",
    "    grads = {}\n",
    "    costs = []                              # to keep track of the cost\n",
    "    m = X.shape[1]                           # number of examples\n",
    "    (n_x, n_h, n_y) = layers_dims\n",
    "    \n",
    "    # Initialize parameters dictionary, by calling one of the functions you'd previously implemented\n",
    "    parameters = initialize_parameters(n_x, n_h, n_y)\n",
    "    \n",
    "    # Get W1, b1, W2 and b2 from the dictionary parameters.\n",
    "    W1 = parameters[\"W1\"]\n",
    "    b1 = parameters[\"b1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    b2 = parameters[\"b2\"]\n",
    "    \n",
    "    # Loop (gradient descent)\n",
    "\n",
    "    for i in range(0, num_iterations):\n",
    "\n",
    "        # Forward propagation: LINEAR -> RELU -> LINEAR -> SOFTMAX. Inputs: \"X, W1, b1, W2, b2\". Output: \"A1, cache1, A2, cache2\".\n",
    "        A1, cache1 = linear_activation_forward(X, W1, b1, activation='relu')\n",
    "        A2, cache2 = linear_activation_forward(A1, W2, b2, activation='softmax')\n",
    "\n",
    "        # Compute cost\n",
    "        cost = compute_cost(A2, Y)\n",
    "        \n",
    "        # Backward propagation. Inputs: \"dA2, cache2, cache1\". Outputs: \"dA1, dW2, db2; also dA0 (not used), dW1, db1\".\n",
    "        dA1, dW2, db2 = linear_activation_backward(Y, cache2, activation='softmax')\n",
    "        dA0, dW1, db1 = linear_activation_backward(dA1, cache1, activation='relu')\n",
    "        \n",
    "        # Set grads['dWl'] to dW1, grads['db1'] to db1, grads['dW2'] to dW2, grads['db2'] to db2\n",
    "        grads['dW1'] = dW1\n",
    "        grads['db1'] = db1\n",
    "        grads['dW2'] = dW2\n",
    "        grads['db2'] = db2\n",
    "        \n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads, learning_rate)\n",
    "\n",
    "        # Retrieve W1, b1, W2, b2 from parameters\n",
    "        W1 = parameters[\"W1\"]\n",
    "        b1 = parameters[\"b1\"]\n",
    "        W2 = parameters[\"W2\"]\n",
    "        b2 = parameters[\"b2\"]\n",
    "        \n",
    "        # Print the cost every 100 training example\n",
    "        if print_cost and i % 100 == 0:\n",
    "            print(\"Cost after iteration {}: {}\".format(i, np.squeeze(cost)))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "       \n",
    "    # plot the cost\n",
    "\n",
    "    plt.plot(np.squeeze(costs))\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('iterations (per tens)')\n",
    "    plt.title(\"Learning rate =\" + str(learning_rate))\n",
    "    plt.show()\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_x = train_set_x[:,0:10000]\n",
    "train_y = train_labels_onehot[:,0:10000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 2.300682930678009\n",
      "Cost after iteration 100: 0.8947419940958851\n",
      "Cost after iteration 200: 0.7210431986278137\n",
      "Cost after iteration 300: 0.6200976623616054\n",
      "Cost after iteration 400: 0.556696247811917\n",
      "Cost after iteration 500: 0.5190547745807741\n",
      "Cost after iteration 600: 0.4931844740333001\n",
      "Cost after iteration 700: 0.4654653335667683\n",
      "Cost after iteration 800: 0.4478352055777419\n",
      "Cost after iteration 900: 0.4320776644083264\n"
     ]
    },
    {
     "data": {
      "image/png": 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AsLJSlangwtfO4MLXzgCgp7efZzbu4ukNO1mxYSdPb9jJT57dzNBNA2c01HBG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\nYt1eIZif1wYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "parameters = two_layer_model(train_x, train_y, layers_dims = (784, 128, 10), num_iterations = 1000, print_cost=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def predict_labels(X, y, parameters):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    X -- data set of examples you would like to label\n",
    "    parameters -- parameters of the trained model\n",
    "    \n",
    "    Returns:\n",
    "    predict_label -- predictions for the given dataset X\n",
    "    \"\"\"\n",
    "    m = X.shape[1]\n",
    "    \n",
    "    W1 = parameters[\"W1\"]\n",
    "    b1 = parameters[\"b1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    b2 = parameters[\"b2\"]\n",
    "    \n",
    "    # Forward propagation\n",
    "    A1, _ = linear_activation_forward(X, W1, b1, activation='relu')\n",
    "    probs, _ = linear_activation_forward(A1, W2, b2, activation='softmax')\n",
    "    \n",
    "    # convert probas to 0-9 predictions\n",
    "    predict_label = np.argmax(probs, axis=0)\n",
    "    \n",
    "    #print results\n",
    "    #print (\"predictions: \" + str(p))\n",
    "    #print (\"true labels: \" + str(y))\n",
    "    print(\"Accuracy: \"  + str(np.sum((predict_label == y)/float(m))))\n",
    "        \n",
    "    return predict_label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.8132000000000001\n"
     ]
    }
   ],
   "source": [
    "prediction = predict_labels(test_set_x, test_labels, parameters)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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