利用卷积神经网络实现手写字识别

本文我们介绍一下卷积(convolution)神经网络(CNN网络)，然后基于pytorch实现一个卷积(convolution)神经网络(CNN网络)，并实现手写字识别

卷积(convolution)神经网络(CNN网络)介绍

传统神经网络处理图片问题的不足

让我们先复习一下神经网络的工作流(stream)程：

1. 搭建一个神经网络
2. 将要训练的数据(如图片)转换为神经网络能够识别的向量
3. 训练神经网络并实现预测

然而，以上过程中，如果训练的是图片，而图片非常大(像素)，则将图片转换成向量后的向量的维度将会非常大，这样会导致在训练网络的时候所需的神经元非常多，需要涉及到非常多参数的更新，也就导致了训练效果不好。

计算机中，图片是以矩阵(matrix)的形式存的，以我们实验数据集(Dataset)mnist中的手写字为例：
一张手写字 0 的图片为：

0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	0	11	150	253	202	31	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	0	37	251	251	253	107	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	21	197	251	251	253	107	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	110	190	251	251	251	253	169	109	62	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	253	251	251	251	251	253	251	251	220	51	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	182	255	253	253	253	253	234	222	253	253	253	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	63	221	253	251	251	251	147	77	62	128	251	251	105	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	32	231	251	253	251	220	137	10	0	0	31	230	251	243	113	5	0	0	0	0	0	
0	0	0	0	0	0	0	37	251	251	253	188	20	0	0	0	0	0	109	251	253	251	35	0	0	0	0	0	
0	0	0	0	0	0	0	37	251	251	201	30	0	0	0	0	0	0	31	200	253	251	35	0	0	0	0	0	
0	0	0	0	0	0	0	37	253	253	0	0	0	0	0	0	0	0	32	202	255	253	164	0	0	0	0	0	
0	0	0	0	0	0	0	140	251	251	0	0	0	0	0	0	0	0	109	251	253	251	35	0	0	0	0	0	
0	0	0	0	0	0	0	217	251	251	0	0	0	0	0	0	21	63	231	251	253	230	30	0	0	0	0	0	
0	0	0	0	0	0	0	217	251	251	0	0	0	0	0	0	144	251	251	251	221	61	0	0	0	0	0	0	
0	0	0	0	0	0	0	217	251	251	0	0	0	0	0	182	221	251	251	251	180	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	218	253	253	73	73	228	253	253	255	253	253	253	253	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	113	251	251	253	251	251	251	251	253	251	251	251	147	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	31	230	251	253	251	251	251	251	253	230	189	35	10	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	62	142	253	251	251	251	251	253	107	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	72	174	251	173	71	72	30	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	

mnist数据集(Dataset)是一个非常小的数据集(Dataset)，每个图片的像素仅有28*28维，而我们经常遇到的图片比这个可大了多了。

同时，还有一个问题不容忽视：一张图片中的像素并不是每个像素点都是一样的，以我们图中的手写体0为例，仅仅黑的有手写的部分是有用的，而别的白的地方是没有用的。

给一张高清图，即使把它压缩到非常小也不影响我们对图中信息的判断。

因此，我们可否让计算机像人一样，只去处理一些关键的信息，而不用把所有的信息全处理了呢。

答案当然是肯定的，不过我们先不着急去想怎么做，而是看一下下一部分的趣图 —— 矩阵(matrix)运算。

卷积(convolution)神经网络(CNN网络)

矩阵(matrix)运算 —— 卷积(convolution)运算

我们都知道矩阵(matrix)可以相乘，给定一个大矩阵(matrix)，我们可以用其中的子矩阵(matrix)与给定的矩阵(matrix)做内积(inner product)(矩阵(matrix)相乘后相加)，将会得到一个较小的矩阵(matrix)，如下图所示：

我们可以将这种操作操作叫卷积(convolution)或特征提取

数据降维(dimensionality reduction)—— 池化(Pooling)操作

虽然经过以上的操作，原始较大的矩阵(matrix)被处理为了较小的矩阵(matrix)，但还是相对比较大，毫无疑问，我们可以将其继续进行卷积(convolution)操作以得到维度更小的矩阵(matrix)。但这样显得太麻烦了，我们可以采取更简单的方法：

将矩阵(matrix)分成几大块，取其中大块中小块值中的最大值或所有小块值的平均值作为更小矩阵(matrix)的值：

• 取最大值的叫最大池化(Pooling)(Max-Pooling)
• 取平均值的叫平均池化(Pooling)(Average-Pooling)

其实，就是在做降维(dimensionality reduction)操作，也许子采样(Sampling)(Subsampling)的名字更适合

输入(input)神经网络 —— flatten

经过以上两步的处理，原始高维度数据的信息将会得到降低，实在不行，多进行以上两种操作就行了。

但还有一个事实，处理后我们的数据还是图片或者其他维的矩阵(matrix)，并不能直接输入(input)到神经网络中加以运算。

一个可以的操作：将最终的低维矩阵(matrix)转换成一维的数据(掰平 – flatten)。

然后就可以输入(input)到神经网络中进行运算运算了。关于神经网络的运算，不懂得可以看博主之前得博客。

所以，总结一下：

• 卷积(convolution)神经网络(CNN网络)是卷积(convolution)加神经网络的结合，卷积(convolution)部分主要包括卷积(convolution)、池化(Pooling)、flatten等操作 —— 提取特征，然后供神经网络进行运算

关于神经网络部分，这里不再赘述，不懂的可以看机器学习(machine learning)专栏关于神经网络的文章

卷积(convolution)神经网络(CNN网络)实现及手写字识别

• 从http://yann.lecun.com/exdb/mnist/下载，下载后将文件解压
• 将main函数中的path改为下载文件的存储路径即可

如果对数据集(Dataset)有问题，可以私信博主

关于实现：

• 使用经典的LeNet-5结构(激活函数(Activation Function)等有所不同)：
  

  

• 基于pytorch实现，包括神经网络的构建，激活函数(Activation Function)的选择
• 归一化(Normalization)使用了像素值/255的方式实现，可以尝试用别的方式进行归一化(Normalization)处理

import numpy as np
import torch
import torch.optim as optim
from torch import nn
class Data:
    '''
    this class is about data module
    '''
    def __init__(self):
        self.start_loc_image=16 # the start location of image data
        self.start_loc_label=8 # the start location of label data
        self.num_pixel=28*28 # the number of pixels
        self.choice={'train-image':'train-images.idx3-ubyte','train-label':'train-labels.idx1-ubyte',
                'test-image':'t10k-images.idx3-ubyte','test-label':'t10k-labels.idx1-ubyte'} # the specific file name
    def get(self,path,train_test='',image_label=''):
        '''
        get the data from the file whose path is "path"
        :param path: the saving path of given files, default is "./file/"
        :param train_test: the data category("train" or "test")
        :param image_label: the data information("image" or "label")
        :return: the data you want
        '''
        if train_test not in ['train','test'] or image_label not in ['image','label']:raise NameError(
            'please check you spelling,"train_test" can be "train/test", "image_label" can be "image/label"')
        ch=train_test+'-'+image_label
        data=[]
        if image_label=='image':
            print('loading images ...')
            with open(path+self.choice[ch],'rb',) as f:
                file=f.read()
                for i in range(self.start_loc_image,file.__len__(),self.num_pixel):
                    item=[]
                    pixel=file[i:i+self.num_pixel].hex()
                    for p in range(0,pixel.__len__(),2):
                        item.append(int(pixel[p:p+2],16)) # decode -> get the pixel information from original file
                    data.append(self.transform2image(item))
            f.close()
        elif image_label=='label':
            print('load labels ...')
            with open(path+self.choice[ch],'rb',) as f:
                file=f.read()
                for i in range(self.start_loc_label,file.__len__()):
                    data.append(file[i]) # decode -> get the label from original file
            f.close()
        return data
    def transform2image(self,data:list):
        '''
        transform pixel point to image
        :param data: the original 1D pixel points
        :return: transformed image(28*28)
        '''
        assert data.__len__()==784
        import numpy as np
        return [np.reshape(data,(28,-1))]
    def transfer_tensor(self,data):
        '''
        transfer data to tensor format
        :param data: the original input data
        :return: transferred data
        '''
        return torch.tensor(data)
    def normalize(self,data,maximum=255):
        '''
        normalize the data with maximum
        :param data: the input data
        :param maximum: the maximum of pixel(is 255)
        :return: normalized data
        '''
        return torch.div(data,maximum)
class Network(nn.Module):
    def __init__(self):
        '''
        the corresponding parameters
        '''
        self.channel_input = 1  # the channel of input data
        self.size_kernel=5 # the size of kernel
        self.len_padding=2 # the length of kernel
        self.channel_c1=6 # the channel of convolution1
        self.channel_c2=16 # the channel of convolution2
        self.len_flatten=120 # the length of flatten data
        self.len_hidden=84 # the length of hidden layer
        self.len_out=10 # the length of final output
        super(Network, self).__init__()
        self.c1=nn.Conv2d(self.channel_input,self.channel_c1,kernel_size=self.size_kernel,padding=self.len_padding)
        self.c2=nn.Conv2d(self.channel_c1,self.channel_c2,kernel_size=self.size_kernel)
        self.fc1=nn.Linear(self.channel_c2*5*5,self.len_flatten)
        self.fc2=nn.Linear(self.len_flatten,self.len_hidden)
        self.fc3=nn.Linear(self.len_hidden,self.len_out)
        ### other parameters
        self.learning_rate=0.01 # learning rate
        self.optimizer=optim.SGD(self.parameters(),lr=self.learning_rate)
    def forward(self,x):
        '''
        calculate the output
        :param x: input vector
        :return: output
        '''
        out_c1=self.c1(x)
        out_sub1=nn.MaxPool2d(2)(out_c1)
        out_c2=self.c2(out_sub1)
        out_sub2=nn.MaxPool2d(2)(out_c2)
        out_flatten=out_sub2.view(x.size(0), -1)
        out_full_con1=self.fc1(out_flatten)
        out_full_con2=self.fc2(out_full_con1)
        out=self.fc3(out_full_con2)
        return out
    def accuracy(self,act,pre):
        '''
        calculate the accuracy
        :param act: actual value
        :param pre: predicted value
        :return: accuracy
        '''
        assert act.__len__()==pre.__len__()
        return round((act==pre).sum().item()/act.__len__(),3)
    def pre_process(self,feature,label):
        '''
        pre processing
        :param feature: feature
        :param label: label
        :return: preprocessed feature and label
        '''
        ### transform to the format of tensor
        feature=dat.transfer_tensor(feature)
        feature=dat.normalize(feature)
        label=dat.transfer_tensor(label)
        return feature,torch.tensor(label,dtype=torch.int64)
    def per_train(self,epoch,feature,label,validation=0.2,batch=50,verbose=True,num_view=5):
        '''
        train neural network
        :param epoch: training times
        :param feature: feature
        :param label: label
        :param validation: for using evaluation
        :param batch: batch size
        :param verbose: whether view the training process or not
        :param num_view: view via training "num_view" times
        :return: none
        '''
        assert feature.__len__()==label.__len__()
        print('training neural network ...')
        fea,lab=self.pre_process(feature,label)
        len_train=int(feature.__len__()*(1-validation))
        data_train,label_train=fea[:len_train+1],lab[:len_train+1]
        data_train=[data_train[i:i+batch]for i in range(0,len_train,batch)]
        label_train=[label_train[i:i+batch]for i in range(0,len_train,batch)]
        data_val,label_val=fea[len_train:],lab[len_train:]
        for e in range(epoch+1):
            self.train()
            loss_tmp=[]
            for img,lab in zip(data_train,label_train):
                pre=self(img)
                loss_train=nn.CrossEntropyLoss()(pre,lab)
                loss_tmp.append(loss_train)
                loss_train.backward()
                self.optimizer.step()
                self.optimizer.zero_grad()
            if verbose and e>0 and e%num_view==0:
                self.eval()
                pre=self(data_val)
                loss_val=nn.CrossEntropyLoss()(pre,label_val)
                _,pre_view=pre.max(1)
                acc=self.accuracy(label_val,pre_view)
                print('epoch: '+str(e)+'/'+str(epoch)+' --> training loss:',loss_train.item(),'validation loss:',
                      loss_val.item(),'validation accuracy:',acc)
def set_seed(seed):
    '''
    set random seed in order that result can be replayed
    :param seed: random seed
    :return: none
    '''
    import random
    torch.manual_seed(seed)
    torch.cuda.manual_seed(seed)
    torch.backends.cudnn.deterministic = True
    np.random.seed(seed)
    random.seed(seed)
Seed=0
Size_pixel= 28*28
Hidden=200
Output=10
set_seed(Seed)
if __name__ == '__main__':
    ### set some necessary parameters
    path='./file/' # the path of saved file
    ### initialize necessary class
    dat=Data() # for data related
    net=Network() # build network
    ### load image and label of training data and testing data
    # train_image=dat.get(path,'train','image')
    # train_label=dat.get(path,'train','label')
    test_image=dat.get(path,'test','image')
    test_label=dat.get(path,'test','label')
    ### train network
    epoch=100 # training times
    net.per_train(epoch,test_image,test_label)

结果展示

运行结果

loading images ...
load labels ...
training neural network ...
epoch: 5/100 --> training loss: 0.20060116052627563 validation loss: 0.3406471908092499 validation accuracy: 0.896
epoch: 10/100 --> training loss: 0.07570216804742813 validation loss: 0.226552814245224 validation accuracy: 0.929
epoch: 15/100 --> training loss: 0.043092332780361176 validation loss: 0.17325899004936218 validation accuracy: 0.948
epoch: 20/100 --> training loss: 0.026798103004693985 validation loss: 0.13407514989376068 validation accuracy: 0.957
epoch: 25/100 --> training loss: 0.018509650602936745 validation loss: 0.11087674647569656 validation accuracy: 0.963
epoch: 30/100 --> training loss: 0.012325393036007881 validation loss: 0.09859741479158401 validation accuracy: 0.971
epoch: 35/100 --> training loss: 0.0074988435953855515 validation loss: 0.09093887358903885 validation accuracy: 0.972
epoch: 40/100 --> training loss: 0.004394318908452988 validation loss: 0.08551845699548721 validation accuracy: 0.974
epoch: 45/100 --> training loss: 0.0024089752696454525 validation loss: 0.08029623329639435 validation accuracy: 0.975
epoch: 50/100 --> training loss: 0.0013418461894616485 validation loss: 0.0761108547449112 validation accuracy: 0.976
epoch: 55/100 --> training loss: 0.0008003945695236325 validation loss: 0.07389482110738754 validation accuracy: 0.978
epoch: 60/100 --> training loss: 0.0004860269255004823 validation loss: 0.07341232150793076 validation accuracy: 0.977
epoch: 65/100 --> training loss: 0.00030446669552475214 validation loss: 0.0740547850728035 validation accuracy: 0.977
epoch: 70/100 --> training loss: 0.00019296690879855305 validation loss: 0.07532798498868942 validation accuracy: 0.978
epoch: 75/100 --> training loss: 0.00012676884944085032 validation loss: 0.07695875316858292 validation accuracy: 0.978
epoch: 80/100 --> training loss: 8.715855801710859e-05 validation loss: 0.07869979739189148 validation accuracy: 0.978
epoch: 85/100 --> training loss: 6.354562356136739e-05 validation loss: 0.08037523180246353 validation accuracy: 0.979
epoch: 90/100 --> training loss: 4.849363540415652e-05 validation loss: 0.08200100064277649 validation accuracy: 0.978
epoch: 95/100 --> training loss: 3.824889790848829e-05 validation loss: 0.08359858393669128 validation accuracy: 0.978
epoch: 100/100 --> training loss: 3.062502946704626e-05 validation loss: 0.08513176441192627 validation accuracy: 0.979

效果展示