深度学习入门-卷积神经网络（CNN）（下）

1-4、深度学习入门-卷积神经网络（CNN）（上）-CSDN博客

5、卷积神经网络（CNN）的实现

简单网络的构成是“Convolution - ReLU - Pooling - Affine - ReLU - Affine - Softmax”：

相关代码：

# 搭建进行手写数字识别的简单CNN网络
import sys, os
sys.path.append(os.pardir)
import pickle
import numpy as np
from collections import OrderedDict
from common.layers import *
from common.gradient import numerical_gradientclass SimpleConvNet:"""简单的ConvNetconv - relu - pool - affine - relu - affine - softmaxParameters----------input_size : 输入大小（MNIST的情况下为784）input_dim―输入数据的维度：（通道，高，长）conv_param―卷积层的超参数（字典）。字典的关键字如下：filter_num―滤波器的数量ilter_size―滤波器的大小stride―步幅pad―填充hidden_size―隐藏层（全连接）的神经元数量hidden_size_list : 隐藏层的神经元数量的列表（e.g. [100, 100, 100]）output_size : 输出大小（MNIST的情况下为10）activation : 'relu' or 'sigmoid'weight_init_std : 初始化时权重的标准差（e.g. 0.01）指定'relu'或'he'的情况下设定“He的初始值”指定'sigmoid'或'xavier'的情况下设定“Xavier的初始值”"""# 初始化的最开始部分def __init__(self, input_dim=(1, 28, 28),# 卷积层的超参数通过名为conv_param的字典传入，# 以{'filter_num':30,'filter_size':5, 'pad':0, 'stride':1}保存必要的超参数值conv_param={'filter_num':30, 'filter_size':5, 'pad':0, 'stride':1},hidden_size=100, output_size=10, weight_init_std=0.01):# 将由初始化参数传入的卷积层的超参数从字典中取了出来（以方便后面使用）filter_num = conv_param['filter_num']filter_size = conv_param['filter_size']filter_pad = conv_param['pad']filter_stride = conv_param['stride']input_size = input_dim[1]# 计算卷积层的输出大小conv_output_size = (input_size - filter_size + 2*filter_pad) / filter_stride + 1pool_output_size = int(filter_num * (conv_output_size/2) * (conv_output_size/2))# 初始化权重参数# 将这些参数保存在实例变量的params字典中self.params = {}# 将第1层的卷积层的权重设为关键字W1，偏置设为关键字b1self.params['W1'] = weight_init_std * \np.random.randn(filter_num, input_dim[0], filter_size, filter_size)self.params['b1'] = np.zeros(filter_num)# 分别用关键字W2、b2和关键字W3、b3来保存第2个和第3个全连接层的权重和偏置self.params['W2'] = weight_init_std * \np.random.randn(pool_output_size, hidden_size)self.params['b2'] = np.zeros(hidden_size)self.params['W3'] = weight_init_std * \np.random.randn(hidden_size, output_size)self.params['b3'] = np.zeros(output_size)# 生成层self.layers = OrderedDict()# 从最前面开始按顺序向有序字典（OrderedDict）的layers中添加层self.layers['Conv1'] = Convolution(self.params['W1'], self.params['b1'],conv_param['stride'], conv_param['pad'])self.layers['Relu1'] = Relu()self.layers['Pool1'] = Pooling(pool_h=2, pool_w=2, stride=2)self.layers['Affine1'] = Affine(self.params['W2'], self.params['b2'])self.layers['Relu2'] = Relu()self.layers['Affine2'] = Affine(self.params['W3'], self.params['b3'])# SoftmaxWithLoss层被添加到另一个变量lastLayer中self.last_layer = SoftmaxWithLoss()def predict(self, x):for layer in self.layers.values():x = layer.forward(x)return xdef loss(self, x, t):"""求损失函数参数x是输入数据、t是正确标签"""# 用于推理的predict方法从头开始依次调用已添加的层，并将结果传递给下一层y = self.predict(x)return self.last_layer.forward(y, t)def accuracy(self, x, t, batch_size=100):if t.ndim != 1 : t = np.argmax(t, axis=1)acc = 0.0for i in range(int(x.shape[0] / batch_size)):tx = x[i*batch_size:(i+1)*batch_size]tt = t[i*batch_size:(i+1)*batch_size]y = self.predict(tx)y = np.argmax(y, axis=1)acc += np.sum(y == tt) return acc / x.shape[0]def numerical_gradient(self, x, t):"""求梯度（数值微分）Parameters----------x : 输入数据t : 教师标签Returns-------具有各层的梯度的字典变量grads['W1']、grads['W2']、...是各层的权重grads['b1']、grads['b2']、...是各层的偏置"""loss_w = lambda w: self.loss(x, t)grads = {}for idx in (1, 2, 3):grads['W' + str(idx)] = numerical_gradient(loss_w, self.params['W' + str(idx)])grads['b' + str(idx)] = numerical_gradient(loss_w, self.params['b' + str(idx)])return gradsdef gradient(self, x, t):"""求梯度（误差反向传播法）Parameters----------x : 输入数据t : 教师标签Returns-------具有各层的梯度的字典变量grads['W1']、grads['W2']、...是各层的权重grads['b1']、grads['b2']、...是各层的偏置"""# forwardself.loss(x, t)# backwarddout = 1dout = self.last_layer.backward(dout)layers = list(self.layers.values())layers.reverse()for layer in layers:dout = layer.backward(dout)# 设定grads = {}grads['W1'], grads['b1'] = self.layers['Conv1'].dW, self.layers['Conv1'].dbgrads['W2'], grads['b2'] = self.layers['Affine1'].dW, self.layers['Affine1'].dbgrads['W3'], grads['b3'] = self.layers['Affine2'].dW, self.layers['Affine2'].dbreturn gradsdef save_params(self, file_name="params.pkl"):params = {}for key, val in self.params.items():params[key] = valwith open(file_name, 'wb') as f:pickle.dump(params, f)def load_params(self, file_name="params.pkl"):with open(file_name, 'rb') as f:params = pickle.load(f)for key, val in params.items():self.params[key] = valfor i, key in enumerate(['Conv1', 'Affine1', 'Affine2']):self.layers[key].W = self.params['W' + str(i+1)]self.layers[key].b = self.params['b' + str(i+1)]

# 学习
import sys, os
sys.path.append(os.pardir)
import numpy as np
import matplotlib.pyplot as plt
from dataset.mnist import load_mnist
from ch07.simple_convnet import SimpleConvNet
from common.trainer import Trainer# 读入数据
(x_train, t_train), (x_test, t_test) = load_mnist(flatten=False)# 处理花费时间较长的情况下减少数据 
#x_train, t_train = x_train[:5000], t_train[:5000]
#x_test, t_test = x_test[:1000], t_test[:1000]max_epochs = 20network = SimpleConvNet(input_dim=(1,28,28), conv_param = {'filter_num': 30, 'filter_size': 5, 'pad': 0, 'stride': 1},hidden_size=100, output_size=10, weight_init_std=0.01)trainer = Trainer(network, x_train, t_train, x_test, t_test,epochs=max_epochs, mini_batch_size=100,optimizer='Adam', optimizer_param={'lr': 0.001},evaluate_sample_num_per_epoch=1000)
trainer.train()# 保存参数
network.save_params("params.pkl")
print("Saved Network Parameters!")# 绘制图形
markers = {'train': 'o', 'test': 's'}
x = np.arange(max_epochs)
plt.plot(x, trainer.train_acc_list, marker='o', label='train', markevery=2)
plt.plot(x, trainer.test_acc_list, marker='s', label='test', markevery=2)
plt.xlabel("epochs")
plt.ylabel("accuracy")
plt.ylim(0, 1.0)
plt.legend(loc='lower right')
plt.show()

运行结果：

如上运行结果：

如果使用MNIST数据集训练SimpleConvNet，则训练数据的识别率为99.82%，测试数据的识别率为98.91%（会有一些误差）。测试数据的识别率大约为99%，就小型网络来说，这是一个非常高的识别率。

6、卷积神经网络（CNN）的可视化

6.1、第1层（卷积层）权重的可视化

将卷积层（第1层）的滤波器显示为图像，然后来比较一下学习前和学习后的权重：

代码：

# 卷积层权重的可视化
import numpy as np
import matplotlib.pyplot as plt
from ch07.simple_convnet import SimpleConvNetdef filter_show(filters, nx=8, margin=3, scale=10):"""c.f. https://gist.github.com/aidiary/07d530d5e08011832b12#file-draw_weight-py"""FN, C, FH, FW = filters.shapeny = int(np.ceil(FN / nx))fig = plt.figure()fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)for i in range(FN):ax = fig.add_subplot(ny, nx, i+1, xticks=[], yticks=[])ax.imshow(filters[i, 0], cmap=plt.cm.gray_r, interpolation='nearest')plt.show()network = SimpleConvNet()
# 随机进行初始化后的权重
filter_show(network.params['W1'])# 学习后的权重
network.load_params("params.pkl")
filter_show(network.params['W1'])

运行结果：

学习前：