CNN学习MNIST实现手写数字识别

CNN的实现

我们之前已经实现了卷积层和池化层，现在来组合这些层，搭建进行手写数字识别的CNN。

# 初始化权重
self.params = {'W1': weight_init_std * np.random.randn(filter_num, input_dim[0], filter_size, filter_size),'b1': np.zeros(filter_num),'W2': weight_init_std * np.random.randn(pool_output_size, hidden_size),'b2': np.zeros(hidden_size),'W3': weight_init_std * np.random.randn(hidden_size, output_size),'b3': np.zeros(output_size)}# 生成层
self.layers = OrderedDict()
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'])self.last_layer = SoftmaxWithLoss()

SimpleConvNet类实现如下：

# coding: utf-8
import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
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）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 : 指定权重的标准差（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”"""def __init__(self, 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):""":param input_dim:输入数据的维度：（通道，高，长）:param 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filter_size―滤波器的大小stride―步幅pad―填充:param hidden_size:隐藏层（全连接）的神经元数量:param output_size:输出层（全连接）的神经元数量:param weight_init_std:初始化时权重的标准差"""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]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self.params = {'W1': weight_init_std * np.random.randn(filter_num, input_dim[0], filter_size, filter_size),'b1': np.zeros(filter_num),'W2': weight_init_std * np.random.randn(pool_output_size, hidden_size),'b2': np.zeros(hidden_size),'W3': weight_init_std * np.random.randn(hidden_size, output_size),'b3': np.zeros(output_size)}# 生成层self.layers = OrderedDict()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'])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是教师标签"""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 = {'W1': self.layers['Conv1'].dW,'b1': self.layers['Conv1'].db,'W2': self.layers['Affine1'].dW,'b2': self.layers['Affine1'].db,'W3': self.layers['Affine2'].dW,'b3': self.layers['Affine2'].db}return 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)]

现在，使用这个SimpleConvNet学习MNIST数据集。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98.96%（每次学习的识别精度都会发生一些误差）。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。

学习MNIST数据集：

# coding: utf-8
import sys, ossys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
import matplotlib.pyplot as plt
from dataset.mnist import load_mnist
from 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()

测试泛化能力

训练好的参数总得拿出来用一用吧，对于mnist测试数据和训练数据直接导入参数文件，推理(识别)就行了。要注意的是格式NCHW，N张C通道高为H宽为W的图片，我们各取10张。

def train_img():(x_train, t_train), (x_test, t_test) = load_mnist(flatten=False)t = 10x_train_sample, t_train_sample = x_train[:t], t_train[:t]network = 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)network.load_params("params.pkl")a = network.predict(x_train_sample)for i in range(0, 10):print("测试集第", i, "张图片预测值：", np.argmax(a[i]), "标签值：", t_train_sample[i])def test_img():(x_train, t_train), (x_test, t_test) = load_mnist(flatten=False)t = 10x_test_sample, t_test_sample = x_test[:t], t_test[:t]network = 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)network.load_params("params.pkl")a = network.predict(x_test_sample)for i in range(0, 10):print("测试集第", i, "张图片预测值：", np.argmax(a[i]), "标签值：", t_test_sample[i])

为什么不测试一下自己手写的呢？还是手写的那10个数字。

这里顺便直接把图像处理封装成一个函数：

def deal_img(filename):kernel_size = (3, 3)img = cv2.imread(filename)img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)  # 从RBG和BGR颜色空间转换到灰度空间ret, thresh2 = cv2.threshold(img_gray, 127, 255, cv2.THRESH_BINARY)  # 像素值>threshold设为255 其他0kernel = np.ones(kernel_size, np.uint8)thresh2 = cv2.erode(thresh2, kernel, iterations=1)ret, thresh2 = cv2.threshold(thresh2, 127, 255, cv2.THRESH_BINARY_INV)  # 像素值>threshold设为0 其他255thresh2 = cv2.resize(thresh2, (28, 28), fx=1, fy=1)  # 图片缩放 1：1缩放image_out = thresh2.reshape(1, 1, thresh2.shape[0], thresh2.shape[1])return image_outdef else_img():network = 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)network.load_params("params.pkl")network.load_params("params.pkl")x = ["0.png", "1.png", "2.png", "3.png", "4.png", "5.png", "6.png", "7.png", "8.png", "9.png"]t = np.arange(10)for i in range(10):image_out = deal_img(x[i])a = network.predict(image_out)print("手写集第", i, "张图片预测值：", np.argmax(a), "标签值：", t[i])

最后的识别结果如下，手写的10个数字还是错了3个，这里图像处理的问题应该占了很大一部分原因了。到这里我猛然醒悟，如果我在黑色背景下写白字不就直接略过图像处理这一步了吗？

重新写了10个数字：

果然，全部识别出来。图像并不是不用处理了，只是不那么麻烦了，图像还是要处理成1通道：

def deal_img2(filename):img = cv2.imread(filename)img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)  # 从RBG和BGR颜色空间转换到灰度空间thresh2 = cv2.resize(img_gray, (28, 28), fx=1, fy=1)  # 图片缩放 1：1缩放image_out = thresh2.reshape(1, 1, thresh2.shape[0], thresh2.shape[1])return image_out

完整程序如下：

# coding: utf-8
import sys, osimport cv2sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
import matplotlib.pyplot as plt
from dataset.mnist import load_mnist
from simple_convnet import SimpleConvNet
from common.trainer import Trainer
from PIL import Imagedef img_show(img):pil_img = Image.fromarray(np.uint8(img))pil_img.show()def train_img():(x_train, t_train), (x_test, t_test) = load_mnist(flatten=False)t = 10x_train_sample, t_train_sample = x_train[:t], t_train[:t]network = 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)network.load_params("params.pkl")a = network.predict(x_train_sample)for i in range(0, 10):print("训练集第", i, "张图片预测值：", np.argmax(a[i]), "标签值：", t_train_sample[i])def test_img():(x_train, t_train), (x_test, t_test) = load_mnist(flatten=False)t = 10x_test_sample, t_test_sample = x_test[:t], t_test[:t]network = 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)network.load_params("params.pkl")a = network.predict(x_test_sample)for i in range(0, 10):print("测试集第", i, "张图片预测值：", np.argmax(a[i]), "标签值：", t_test_sample[i])def deal_img(filename):kernel_size = (3, 3)img = cv2.imread(filename)img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)  # 从RBG和BGR颜色空间转换到灰度空间ret, thresh2 = cv2.threshold(img_gray, 127, 255, cv2.THRESH_BINARY)  # 像素值>threshold设为255 其他0kernel = np.ones(kernel_size, np.uint8)thresh2 = cv2.erode(thresh2, kernel, iterations=1)ret, thresh2 = cv2.threshold(thresh2, 127, 255, cv2.THRESH_BINARY_INV)  # 像素值>threshold设为0 其他255thresh2 = cv2.resize(thresh2, (28, 28), fx=1, fy=1)  # 图片缩放 1：1缩放image_out = thresh2.reshape(1, 1, thresh2.shape[0], thresh2.shape[1])return image_outdef deal_img2(filename):img = cv2.imread(filename)img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)  # 从RBG和BGR颜色空间转换到灰度空间thresh2 = cv2.resize(img_gray, (28, 28), fx=1, fy=1)  # 图片缩放 1：1缩放image_out = thresh2.reshape(1, 1, thresh2.shape[0], thresh2.shape[1])return image_outdef else_img():network = 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)network.load_params("params.pkl")network.load_params("params.pkl")x = ["0.png", "1.png", "2.png", "3.png", "4.png", "5.png", "6.png", "7.png", "8.png", "9.png"]x1 = ["10.png", "11.png", "12.png", "13.png", "14.png", "15.png", "16.png", "17.png", "18.png", "19.png"]t = np.arange(10)for i in range(10):image_out = deal_img2(x1[i])a = network.predict(image_out)print("手写集第", i, "张图片预测值：", np.argmax(a), "标签值：", t[i])train_img()
test_img()
else_img()

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CNN学习MNIST实现手写数字识别

CNN的实现

测试泛化能力

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