1 导入所需的包
import time import numpy as np import h5py import matplotlib.pyplot as plt import scipy from PIL import Image from scipy import ndimage from dnn_app_utils_v2 import * plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plots plt.rcParams['image.interpolation'] = 'nearest' plt.rcParams['image.cmap'] = 'gray' np.random.seed(1)
包介绍:
- numpy 用Python进行科学计算的基本软件包。
- matplotlib 是一个用于在Python中绘制图表的库。
- h5py 是与存储在H5文件中的数据集进行交互的常见包。
- PIL and scipy 用来通过自己的图片来测试模型。
- dnn_app_utils 提供在上一篇文章 Building your Deep Neural Network Step by Step 中构建的一些函数。
2 数据集
加载数据,重塑它们的维度,使其标准化
# Load data train_x_orig, train_y, test_x_orig, test_y, classes = load_data() # Explore dataset m_train = train_x_orig.shape[0] num_px = train_x_orig.shape[1] m_test = test_x_orig.shape[0] # Reshape the training and test examples # The "-1" makes reshape flatten the remaining dimensions train_x_flatten = train_x_orig.reshape(train_x_orig.shape[0], -1).T test_x_flatten = test_x_orig.reshape(test_x_orig.shape[0], -1).T # Standardize data to have feature values between 0 and 1. train_x = train_x_flatten/255. test_x = test_x_flatten/255.
3 模型结构
3.1 2层神经网络的结构
模型结构为: INPUT -> LINEAR -> RELU -> LINEAR -> SIGMOID -> OUTPUT
3.2 L层神经网络的结构
模型结构为: [LINEAR -> RELU] × (L-1) -> LINEAR -> SIGMOID
3.3 建立模型的一般方法
构建模型的一般方法:
- 初始化参数/定义超参数
- 循环:
- 前向传播
- 计算成本
- 反向传播
- 更新参数 (使用反向传播中计算的参数和梯度)
- 使用训练参数来进行预测
4 2层神经网络
以下函数在之前的 Building your Deep Neural Network Step by Step 中已经实现,接下来要使用这些函数来构建一个2层神经网络
def initialize_parameters(n_x, n_h, n_y): ... return parameters def linear_activation_forward(A_prev, W, b, activation): ... return A, cache def compute_cost(AL, Y): ... return cost def linear_activation_backward(dA, cache, activation): ... return dA_prev, dW, db def update_parameters(parameters, grads, learning_rate): ... return parameters
建立2层神经网络模型如下:
### CONSTANTS DEFINING THE MODEL #### n_x = 12288 # num_px * num_px * 3 n_h = 7 n_y = 1 layers_dims = (n_x, n_h, n_y)
# GRADED FUNCTION: two_layer_model def two_layer_model(X, Y, layers_dims, learning_rate=0.0075, num_iterations=3000, print_cost=False): """ Implements a two-layer neural network: LINEAR->RELU->LINEAR->SIGMOID. Arguments: X -- input data, of shape (n_x, number of examples) Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples) layers_dims -- dimensions of the layers (n_x, n_h, n_y) num_iterations -- number of iterations of the optimization loop learning_rate -- learning rate of the gradient descent update rule print_cost -- If set to True, this will print the cost every 100 iterations Returns: parameters -- a dictionary containing W1, W2, b1, and b2 """ np.random.seed(1) grads = {} costs = [] # to keep track of the cost m = X.shape[1] # number of examples (n_x, n_h, n_y) = layers_dims # Initialize parameters dictionary, by calling one of the functions you'd previously implemented parameters = initialize_parameters(n_x, n_h, n_y) # Get W1, b1, W2 and b2 from the dictionary parameters. W1 = parameters["W1"] b1 = parameters["b1"] W2 = parameters["W2"] b2 = parameters["b2"] # Loop (gradient descent) for i in range(0, num_iterations): # Forward propagation: LINEAR -> RELU -> LINEAR -> SIGMOID. Inputs: "X, W1, b1". Output: "A1, cache1, A2, cache2". A1, cache1 = linear_activation_forward(X, W1, b1, "relu") A2, cache2 = linear_activation_forward(A1, W2, b2, "sigmoid") # Compute cost cost = compute_cost(A2, Y) # Initializing backward propagation dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2)) # Backward propagation. Inputs: "dA2, cache2, cache1". Outputs: "dA1, dW2, db2; also dA0 (not used), dW1, db1". dA1, dW2, db2 = linear_activation_backward(dA2, cache2, "sigmoid") dA0, dW1, db1 = linear_activation_backward(dA1, cache1, "relu") # Set grads['dWl'] to dW1, grads['db1'] to db1, grads['dW2'] to dW2, grads['db2'] to db2 grads['dW1'] = dW1 grads['db1'] = db1 grads['dW2'] = dW2 grads['db2'] = db2 # Update parameters. parameters = update_parameters(parameters, grads, learning_rate) # Retrieve W1, b1, W2, b2 from parameters W1 = parameters["W1"] b1 = parameters["b1"] W2 = parameters["W2"] b2 = parameters["b2"] # Print the cost every 100 training example if print_cost and i % 100 == 0: print("Cost after iteration {}: {}".format(i, np.squeeze(cost))) if print_cost and i % 100 == 0: costs.append(cost) # plot the cost plt.plot(np.squeeze(costs)) plt.ylabel('cost') plt.xlabel('iterations (per tens)') plt.title("Learning rate =" + str(learning_rate)) plt.show() return parameters
使用以下的代码来训练参数
parameters = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=True)
运行结果如下:
Cost after iteration 0: 0.693049735659989
Cost after iteration 100: 0.6464320953428849
Cost after iteration 200: 0.6325140647912678
Cost after iteration 300: 0.6015024920354665
Cost after iteration 400: 0.5601966311605748
Cost after iteration 500: 0.515830477276473
Cost after iteration 600: 0.4754901313943325
Cost after iteration 700: 0.43391631512257495
Cost after iteration 800: 0.4007977536203886
Cost after iteration 900: 0.35807050113237987
Cost after iteration 1000: 0.3394281538366413
Cost after iteration 1100: 0.30527536361962654
Cost after iteration 1200: 0.2749137728213015
Cost after iteration 1300: 0.24681768210614827
Cost after iteration 1400: 0.1985073503746611
Cost after iteration 1500: 0.17448318112556593
Cost after iteration 1600: 0.1708076297809661
Cost after iteration 1700: 0.11306524562164737
Cost after iteration 1800: 0.09629426845937163
Cost after iteration 1900: 0.08342617959726878
Cost after iteration 2000: 0.0743907870431909
Cost after iteration 2100: 0.06630748132267938
Cost after iteration 2200: 0.05919329501038176
Cost after iteration 2300: 0.05336140348560564
Cost after iteration 2400: 0.048554785628770226
查看在训练集和测试集上的预测:
# on train dataset predictions_train = predict(train_x, train_y, parameters) # on test dataset predictions_test = predict(test_x, test_y, parameters)
运行结果如下:
Accuracy: 1.0
Accuracy: 0.72
5 L层神经网络
以下函数在之前的 Building your Deep Neural Network Step by Step 中已经实现,接下来要使用这些函数来构建一个L层神经网络
def initialize_parameters_deep(layer_dims): ... return parameters def L_model_forward(X, parameters): ... return AL, caches def compute_cost(AL, Y): ... return cost def L_model_backward(AL, Y, caches): ... return grads def update_parameters(parameters, grads, learning_rate): ... return parameters
建立2层神经网络模型如下:
### CONSTANTS ### layers_dims = [12288, 20, 7, 5, 1] # 5-layer model
# GRADED FUNCTION: L_layer_model def L_layer_model(X, Y, layers_dims, learning_rate=0.0075, num_iterations=3000, print_cost=False): # lr was 0.009 """ Implements a L-layer neural network: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID. Arguments: X -- data, numpy array of shape (number of examples, num_px * num_px * 3) Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples) layers_dims -- list containing the input size and each layer size, of length (number of layers + 1). learning_rate -- learning rate of the gradient descent update rule num_iterations -- number of iterations of the optimization loop print_cost -- if True, it prints the cost every 100 steps Returns: parameters -- parameters learnt by the model. They can then be used to predict. """ np.random.seed(1) costs = [] # keep track of cost # Parameters initialization. parameters = initialize_parameters_deep(layers_dims) # Loop (gradient descent) for i in range(0, num_iterations): # Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID. AL, caches = L_model_forward(X, parameters) # Compute cost. cost = compute_cost(AL, Y) # Backward propagation. grads = L_model_backward(AL, Y, caches) # Update parameters. parameters = update_parameters(parameters, grads, learning_rate) # Print the cost every 100 training example if print_cost and i % 100 == 0: print("Cost after iteration %i: %f" % (i, cost)) if print_cost and i % 100 == 0: costs.append(cost) # plot the cost plt.plot(np.squeeze(costs)) plt.ylabel('cost') plt.xlabel('iterations (per tens)') plt.title("Learning rate =" + str(learning_rate)) plt.show() return parameters
使用以下的代码来训练参数(此时相当于一个5层的神经网络):
parameters = L_layer_model(train_x, train_y, layers_dims, num_iterations = 2500, print_cost = True)
运行结果如下:
Cost after iteration 0: 0.771749
Cost after iteration 100: 0.672053
Cost after iteration 200: 0.648263
Cost after iteration 300: 0.611507
Cost after iteration 400: 0.567047
Cost after iteration 500: 0.540138
Cost after iteration 600: 0.527930
Cost after iteration 700: 0.465477
Cost after iteration 800: 0.369126
Cost after iteration 900: 0.391747
Cost after iteration 1000: 0.315187
Cost after iteration 1100: 0.272700
Cost after iteration 1200: 0.237419
Cost after iteration 1300: 0.199601
Cost after iteration 1400: 0.189263
Cost after iteration 1500: 0.161189
Cost after iteration 1600: 0.148214
Cost after iteration 1700: 0.137775
Cost after iteration 1800: 0.129740
Cost after iteration 1900: 0.121225
Cost after iteration 2000: 0.113821
Cost after iteration 2100: 0.107839
Cost after iteration 2200: 0.102855
Cost after iteration 2300: 0.100897
Cost after iteration 2400: 0.092878
查看在训练集和测试集上的预测:
# on train dataset pred_train = predict(train_x, train_y, parameters) # on test dataset pred_test = predict(test_x, test_y, parameters)
运行结果如下:
Accuracy: 0.9856459330143539
Accuracy: 0.8
6 结果分析
首先,运行以下代码查看L层模型标记错误的一些图像:
print_mislabeled_images(classes, test_x, test_y, pred_test)
运行结果如下:
在L层模型上,表现往往不佳的几类图片包括:
- 猫身体处于不寻常的位置
- 猫出现在相似颜色的背景下
- 不寻常的颜色和物种的猫
- 相机角度
- 图片的亮度
- 比例变化(猫在图像中非常大或小)
参考资料:
用于自动重新加载外部模块:http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython