06_deep_neural_network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第 6 章：深层神经网络"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from skimage import io\n",
    "plt.rcParams['font.sans-serif']=['SimHei']\n",
    "plt.rcParams['axes.unicode_minus']=False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数据集"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "猫狗数据集：\n",
    "\n",
    "- 训练图片 500 张，猫狗各占 250\n",
    "\n",
    "- 测试图片 200 张，猫狗各占 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "训练样本数量：500\n",
      "测试样本数量：200\n",
      "每张图片的维度：(64, 64, 3)\n"
     ]
    }
   ],
   "source": [
    "# 训练样本\n",
    "file='./datasets/ch06/train/*.jpg'\n",
    "coll = io.ImageCollection(file)\n",
    "X_train = np.asarray(coll)                                   # 500 个训练样本，250 个猫图片，250 个非猫图片\n",
    "Y_train = np.hstack((np.ones((1,250)),np.zeros((1,250))))            # 输出标签 \n",
    "\n",
    "# 测试样本\n",
    "file='./datasets/ch06/test/*.jpg'\n",
    "coll = io.ImageCollection(file)\n",
    "X_test = np.asarray(coll)                                   # 200 个测试样本，100 个猫图片，100 个非猫图片\n",
    "Y_test = np.hstack((np.ones((1,100)),np.zeros((1,100))))            # 输出标签 \n",
    "\n",
    "m_train = X_train.shape[0]\n",
    "m_test = X_test.shape[0]\n",
    "w, h, d = X_train.shape[1], X_train.shape[2], X_train.shape[3]\n",
    "\n",
    "print('训练样本数量：%d' % m_train)\n",
    "print('测试样本数量：%d' % m_test)\n",
    "print('每张图片的维度：(%d, %d, %d)' % (w, h, d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从训练样本中随机选择 10 张图片显示，y = 1 表示是猫类图片；y = 0 表示狗类图片。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = [np.random.choice(m_train) for _ in range(10)]  # 随机选择 10 张图片\n",
    "label = Y_train[0,idx]\n",
    "for i in range(2):\n",
    "    for j in range(5):\n",
    "        plt.subplot(2, 5, 5*i+j+1)\n",
    "        plt.imshow(X_train[idx[5*i+j]])\n",
    "        plt.title(\"y = \"+str(label[5*i+j]))\n",
    "        plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 图片数据预处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "训练样本维度：(12288, 500)\n",
      "测试样本维度：(12288, 200)\n"
     ]
    }
   ],
   "source": [
    "# 图片矩阵转化为一维向量\n",
    "X_train = X_train.reshape(m_train, -1).T\n",
    "X_test = X_test.reshape(m_test, -1).T\n",
    "\n",
    "print('训练样本维度：' + str(X_train.shape))\n",
    "print('测试样本维度：' + str(X_test.shape))\n",
    "\n",
    "# 图片像素归一化到 [0,1] 之间\n",
    "X_train = X_train / 255\n",
    "X_test = X_test / 255"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 参数初始化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于 $L$ 层神经网络，各层 $W^{[l]}$ 和 $b^{[l]}$ 都要初始化：$W^{[1]},b^{[1]},W^{[2]},b^{[2]},\\cdots,W^{[L]},b^{[L]}$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_parameters(layer_dims):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - layer_dims：列表，神经网络各层神经元个数，包含输入层\n",
    "    函数输出：\n",
    "        - parameters：存储参数字典\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(5)\n",
    "    \n",
    "    parameters = {}          # 存储参数 W 和 b 的字典\n",
    "    L = len(layer_dims)      # 神经网络的层数，包含输入层\n",
    "\n",
    "    for l in range(1, L):\n",
    "        parameters['W' + str(l)] = np.random.randn(layer_dims[l],layer_dims[l-1]) * 0.1    # 随机初始化\n",
    "        parameters['b' + str(l)] = np.zeros((layer_dims[l],1))    # 初始化为零\n",
    "       \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 前向传播"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义 Sigmoid 激活函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(Z):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - Z：激活函数输入，神经元线性输出\n",
    "    函数输出：\n",
    "        - A：激活函数输出，神经元非线性输出\n",
    "    \"\"\"\n",
    "    \n",
    "    A = 1 / (1 + np.exp(-Z))\n",
    "    \n",
    "    return A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义 ReLU 激活函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def relu(Z):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - Z：激活函数输入，神经元线性输出\n",
    "    函数输出：\n",
    "        - A：激活函数输出，神经元非线性输出\n",
    "    \"\"\"\n",
    "    \n",
    "    A = np.maximum(0,Z)\n",
    "    \n",
    "    return A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "单层神经网络计算 $Z$ 和 $A$："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def single_layer_forward(A_prev, W, b, activation):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - A_prev：该层网络的输入，上一层网络的输出\n",
    "        - W：该层网络的权重参数\n",
    "        - b：该层网络的偏置参数\n",
    "        - activation：该层网络使用的激活函数\n",
    "    函数输出：\n",
    "        - A：该层网络输出\n",
    "        - cache：存储所有的中间变量 A_prev, W, b, Z\n",
    "    \"\"\"\n",
    "    \n",
    "    Z = np.dot(W, A_prev) + b        # 线性输出\n",
    "    if activation == \"sigmoid\":\n",
    "        A = sigmoid(Z)\n",
    "    elif activation == \"relu\":\n",
    "        A = relu(Z) \n",
    "    cache = (A_prev, W, b, Z)\n",
    "    \n",
    "    return A, cache"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$L$ 层神经网络前向传播："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "迭代更新公式：\n",
    "\n",
    "$$Z^{[l]}=W^{[l]}A^{[l-1]}+b^{[l]}$$\n",
    "$$A^{[l]}=g(Z^{[l]})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_propagation(X, parameters):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - X：神经网络输入\n",
    "        - parameters：该层网络的权重参数\n",
    "    函数输出：\n",
    "        - A：该层网络输出\n",
    "        - caches：存储各层网络所有的中间变量\n",
    "    \"\"\"\n",
    "\n",
    "    caches = []\n",
    "    A = X\n",
    "    L = len(parameters) // 2                  # 神经网络层数 L\n",
    "\n",
    "    # L-1 层使用 ReLU\n",
    "    for l in range(1, L):\n",
    "        A_prev = A \n",
    "        A, cache = single_layer_forward(A_prev, parameters['W' + str(l)], parameters['b' + str(l)], \"relu\")\n",
    "        caches.append(cache)\n",
    "\n",
    "    # L 层使用 Sigmoid\n",
    "    AL, cache = single_layer_forward(A, parameters['W' + str(L)], parameters['b' + str(L)], \"sigmoid\")\n",
    "    caches.append(cache)\n",
    "\n",
    "    return AL, caches"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 损失函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "交叉熵损失：\n",
    "\n",
    "$$J=-\\frac1m\\sum_{i=1}^my^{(i)}log\\hat y^{(i)}+(1-y^{(i)})log(1-\\hat y^{(i)})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "计算损失函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(AL, Y):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - AL：神经网络输出层输出\n",
    "        - Y：神经网络真实标签\n",
    "    函数输出：\n",
    "        - cost：交叉熵损失\n",
    "    \"\"\"\n",
    "\n",
    "    m = AL.shape[1]\n",
    "    cross_entropy = -(Y * np.log(AL) + (1 - Y) * np.log(1 - AL))\n",
    "    cost = 1.0 / m * np.sum(cross_entropy)\n",
    "\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 反向传播"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反向传播梯度递推公式：\n",
    "\n",
    "$$dZ^{[l]}=dA^{[l]}*g'(Z^{[l]})$$\n",
    "$$ dW^{[l]} =  \\frac{1}{m} dZ^{[l]} A^{[l-1] T} $$\n",
    "$$ db^{[l]} =  \\frac{1}{m} \\sum_{i = 1}^{m} dZ^{[l](i)} $$\n",
    "$$ dA^{[l-1]} =  W^{[l] T} dZ^{[l]} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义 ReLU 函数的反向传播：dA --> dZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def relu_backward(dA, Z):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - dA：A 的梯度\n",
    "        - Z：神经网络线性输出\n",
    "    函数输出：\n",
    "        - dZ：Z 的梯度\n",
    "    \"\"\"\n",
    "\n",
    "    dZ = np.array(dA, copy=True)  \n",
    "    dZ[Z <= 0] = 0\n",
    "\n",
    "    return dZ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义 Sigmoid 函数的反向传播：dA --> dZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid_backward(dA, Z):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - dA：A 的梯度\n",
    "        - Z：神经网络线性输出\n",
    "    函数输出：\n",
    "        - dZ：Z 的梯度\n",
    "    \"\"\"\n",
    "\n",
    "    s = 1/(1 + np.exp(-Z))\n",
    "    dZ = dA * s * (1-s)\n",
    "\n",
    "    return dZ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "单层神经网络反向传播："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def single_layer_backward(dA, cache, activation):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - dA：A 的梯度\n",
    "        - cache：存储所有的中间变量 A_prev, W, b, Z\n",
    "        - activation：选择的激活函数\n",
    "    函数输出：\n",
    "        - dA_prev：上一层 A_prev 的梯度\n",
    "        - dW：参数 W 的梯度\n",
    "        - db：参数 b 的梯度\n",
    "    \"\"\"\n",
    "\n",
    "    A_prev, W, b, Z = cache\n",
    "\n",
    "    if activation == \"relu\":\n",
    "        dZ = relu_backward(dA, Z)\n",
    "    elif activation == 'sigmoid':\n",
    "        dZ = sigmoid_backward(dA, Z)\n",
    "\n",
    "    m = dA.shape[1]\n",
    "    dW = 1/m*np.dot(dZ,A_prev.T)\n",
    "    db = 1/m*np.sum(dZ,axis=1,keepdims=True)\n",
    "    dA_prev = np.dot(W.T,dZ)\n",
    "\n",
    "    return dA_prev, dW, db"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$L$ 层神经网络反向传播："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward_propagation(AL, Y, caches):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - AL：神经网络输出层输出\n",
    "        - caches：存储所有的中间变量 A_prev, W, b, Z\n",
    "        - Y：神经网络真实标签\n",
    "    函数输出：\n",
    "        - grads：所有参数梯度\n",
    "    \"\"\"\n",
    "\n",
    "    grads = {}\n",
    "    L = len(caches)         # 神经网络层数\n",
    "    m = AL.shape[1]         # 样本个数\n",
    "    \n",
    "    # AL 值\n",
    "    dAL = -(np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))\n",
    "\n",
    "    # 第 L 层，激活函数是 Sigmoid\n",
    "    current_cache = caches[L-1]\n",
    "    grads[\"dA\" + str(L-1)], grads[\"dW\" + str(L)], grads[\"db\" + str(L)] = single_layer_backward(dAL, current_cache, activation = \"sigmoid\")\n",
    "\n",
    "    # 前 L-1 层，激活函数是 ReLU\n",
    "    for l in reversed(range(L-1)):\n",
    "        current_cache = caches[l]\n",
    "        dA_prev_temp, dW_temp, db_temp = single_layer_backward(grads[\"dA\" + str(l + 1)], current_cache, activation = \"relu\")\n",
    "        grads[\"dA\" + str(l)] = dA_prev_temp\n",
    "        grads[\"dW\" + str(l + 1)] = dW_temp\n",
    "        grads[\"db\" + str(l + 1)] = db_temp\n",
    "\n",
    "    return grads"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 更新参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_parameters(parameters, grads, learning_rate=0.1):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - parameters: 网络参数\n",
    "        - grads: 神经网络参数梯度\n",
    "    函数输出：\n",
    "        - parameters: 网络参数\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2    # 神经网络层数 L\n",
    "    for l in range(L):\n",
    "        parameters['W'+str(l+1)] -= learning_rate * grads['dW'+str(l+1)]\n",
    "        parameters['b'+str(l+1)] -=learning_rate * grads['db'+str(l+1)]\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 构建神经网络模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义整个模型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nn_model(X, Y, layers_dims, learning_rate = 0.01, num_iterations = 3000):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - X：神经网络输入\n",
    "        - Y：样本真实标签\n",
    "        - layers_dim: 列表，神经网络各层神经元个数，包含输入层和输出层\n",
    "        - num_iterations: 训练次数\n",
    "        - learning_rate: 学习率\n",
    "    函数输出：\n",
    "        - parameters: 训练完成后的网络参数\n",
    "    \"\"\"\n",
    "\n",
    "    np.random.seed(1)\n",
    "    costs = []                         \n",
    "\n",
    "    # 参数初始化\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # 迭代训练\n",
    "    for i in range(0, num_iterations):\n",
    "\n",
    "        # 正向传播\n",
    "        AL, caches = forward_propagation(X, parameters)\n",
    "\n",
    "        # 计算损失函数\n",
    "        cost = compute_cost(AL, Y)\n",
    "\n",
    "        # 反向传播\n",
    "        grads = backward_propagation(AL, Y, caches)\n",
    "\n",
    "        # 更新参数\n",
    "        parameters = update_parameters(parameters, grads, learning_rate)\n",
    "\n",
    "        # 每迭代 100 次，打印 cost\n",
    "        if (i+1) % 100 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" %(i+1, cost))\n",
    "            costs.append(cost)\n",
    "\n",
    "    # 绘制 cost 趋势图\n",
    "    plt.plot(np.squeeze(costs))\n",
    "    plt.ylabel('交叉熵损失cost')\n",
    "    plt.xlabel('迭代训练次数（百次）')\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义预测函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(X, parameters):\n",
    "    \"\"\"\n",
    "    函数输入：\n",
    "        - X：神经网络输入\n",
    "        - parameters: 训练完成后的网络参数\n",
    "    函数输出：\n",
    "        - Y_pred: 预测样本标签\n",
    "    \"\"\"\n",
    "    \n",
    "    # L 层模型前向传播\n",
    "    AL, caches = forward_propagation(X, parameters)\n",
    "    # 预测标签\n",
    "    Y_pred = np.zeros((1, X.shape[1]))    # 初始化 Y_pred\n",
    "    Y_pred[AL > 0.5] = 1    # Y_hat 大于 0.5 的预测为正类\n",
    "    \n",
    "    return Y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 使用简单的 2 层神经网络训练"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "训练："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 100: 0.684486\n",
      "Cost after iteration 200: 0.674664\n",
      "Cost after iteration 300: 0.662584\n",
      "Cost after iteration 400: 0.646598\n",
      "Cost after iteration 500: 0.626021\n",
      "Cost after iteration 600: 0.600818\n",
      "Cost after iteration 700: 0.573096\n",
      "Cost after iteration 800: 0.542202\n",
      "Cost after iteration 900: 0.508659\n",
      "Cost after iteration 1000: 0.486468\n",
      "Cost after iteration 1100: 0.476841\n",
      "Cost after iteration 1200: 0.459816\n",
      "Cost after iteration 1300: 0.440341\n",
      "Cost after iteration 1400: 0.422442\n",
      "Cost after iteration 1500: 0.401162\n",
      "Cost after iteration 1600: 0.379927\n",
      "Cost after iteration 1700: 0.350352\n",
      "Cost after iteration 1800: 0.341812\n",
      "Cost after iteration 1900: 0.323652\n",
      "Cost after iteration 2000: 0.299465\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "layers_dims = [12288, 10, 1]    # 2-layer model\n",
    "parameters = nn_model(X_train, Y_train, layers_dims, \n",
    "                      num_iterations=2000, \n",
    "                      learning_rate=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "计算训练样本的准确率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.858\n"
     ]
    }
   ],
   "source": [
    "Y_train_pred = predict(X_train, parameters)\n",
    "acc_train = np.mean(Y_train_pred == Y_train)\n",
    "print(acc_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "计算测试样本的准确率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.57\n"
     ]
    }
   ],
   "source": [
    "Y_test_pred = predict(X_test, parameters)\n",
    "acc_test = np.mean(Y_test_pred == Y_test)\n",
    "print(acc_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 使用更深的 5 层神经网络训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 100: 0.688680\n",
      "Cost after iteration 200: 0.678262\n",
      "Cost after iteration 300: 0.644802\n",
      "Cost after iteration 400: 0.610248\n",
      "Cost after iteration 500: 0.568977\n",
      "Cost after iteration 600: 0.505714\n",
      "Cost after iteration 700: 0.434559\n",
      "Cost after iteration 800: 0.303987\n",
      "Cost after iteration 900: 0.343186\n",
      "Cost after iteration 1000: 0.089528\n",
      "Cost after iteration 1100: 0.028418\n",
      "Cost after iteration 1200: 0.014516\n",
      "Cost after iteration 1300: 0.008889\n",
      "Cost after iteration 1400: 0.006102\n",
      "Cost after iteration 1500: 0.004537\n",
      "Cost after iteration 1600: 0.003547\n",
      "Cost after iteration 1700: 0.002877\n",
      "Cost after iteration 1800: 0.002404\n",
      "Cost after iteration 1900: 0.002041\n",
      "Cost after iteration 2000: 0.001767\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "layers_dims = [12288, 200, 100, 20, 6, 1] #  5-layer model\n",
    "parameters = nn_model(X_train, Y_train, layers_dims, \n",
    "                      num_iterations=2000, \n",
    "                      learning_rate=0.02)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "预测，计算训练样本的准确率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "Y_train_pred = predict(X_train, parameters)\n",
    "acc_train = np.mean(Y_train_pred == Y_train)\n",
    "print(acc_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "计算测试样本的准确率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.64\n"
     ]
    }
   ],
   "source": [
    "Y_test_pred = predict(X_test, parameters)\n",
    "acc_test = np.mean(Y_test_pred == Y_test)\n",
    "print(acc_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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