一、卷積神經(jīng)網(wǎng)絡(luò)
卷積神經(jīng)網(wǎng)絡(luò)（ConvolutionalNeuralNetwork，CNN）最初是為解決圖像識(shí)別等問(wèn)題設(shè)計(jì)的，CNN現(xiàn)在的應(yīng)用已經(jīng)不限于圖像和視頻，也可用于時(shí)間序列信號(hào)，比如音頻信號(hào)和文本數(shù)據(jù)等。CNN作為一個(gè)深度學(xué)習(xí)架構(gòu)被提出的最初訴求是降低對(duì)圖像數(shù)據(jù)預(yù)處理的要求，避免復(fù)雜的特征工程。在卷積神經(jīng)網(wǎng)絡(luò)中，第一個(gè)卷積層會(huì)直接接受圖像像素級(jí)的輸入，每一層卷積（濾波器）都會(huì)提取數(shù)據(jù)中最有效的特征，這種方法可以提取到圖像中最基礎(chǔ)的特征，而后再進(jìn)行組合和抽象形成更高階的特征，因此CNN在理論上具有對(duì)圖像縮放、平移和旋轉(zhuǎn)的不變性。
卷積神經(jīng)網(wǎng)絡(luò)CNN的要點(diǎn)就是局部連接（LocalConnection）、權(quán)值共享（WeightsSharing）和池化層（Pooling）中的降采樣（Down-Sampling）。其中，局部連接和權(quán)值共享降低了參數(shù)量，使訓(xùn)練復(fù)雜度大大下降并減輕了過(guò)擬合。同時(shí)權(quán)值共享還賦予了卷積網(wǎng)絡(luò)對(duì)平移的容忍性，池化層降采樣則進(jìn)一步降低了輸出參數(shù)量并賦予模型對(duì)輕度形變的容忍性，提高了模型的泛化能力?？梢园丫矸e層卷積操作理解為用少量參數(shù)在圖像的多個(gè)位置上提取相似特征的過(guò)程。
二、代碼實(shí)現(xiàn)
import torch import torch.nn as nn from torch.autograd import Variable import torch.utils.data as Data import torchvision import matplotlib.pyplot as plt torch.manual_seed(1) EPOCH = 1 BATCH_SIZE = 50 LR = 0.001 DOWNLOAD_MNIST = True # 獲取訓(xùn)練集dataset training_data = torchvision.datasets.MNIST( root='./mnist/', # dataset存儲(chǔ)路徑 train=True, # True表示是train訓(xùn)練集，F(xiàn)alse表示test測(cè)試集 transform=torchvision.transforms.ToTensor(), # 將原數(shù)據(jù)規(guī)范化到（0,1）區(qū)間 download=DOWNLOAD_MNIST, ) # 打印MNIST數(shù)據(jù)集的訓(xùn)練集及測(cè)試集的尺寸 print(training_data.train_data.size()) print(training_data.train_labels.size()) # torch.Size([60000, 28, 28]) # torch.Size([60000]) plt.imshow(training_data.train_data[0].numpy(), cmap='gray') plt.title('%i' % training_data.train_labels[0]) plt.show() # 通過(guò)torchvision.datasets獲取的dataset格式可直接可置于DataLoader train_loader = Data.DataLoader(dataset=training_data, batch_size=BATCH_SIZE, shuffle=True) # 獲取測(cè)試集dataset test_data = torchvision.datasets.MNIST(root='./mnist/', train=False) # 取前2000個(gè)測(cè)試集樣本 test_x = Variable(torch.unsqueeze(test_data.test_data, dim=1), volatile=True).type(torch.FloatTensor)[:2000]/255 # (2000, 28, 28) to (2000, 1, 28, 28), in range(0,1) test_y = test_data.test_labels[:2000] class CNN(nn.Module): def __init__(self): super(CNN, self).__init__() self.conv1 = nn.Sequential( # (1,28,28) nn.Conv2d(in_channels=1, out_channels=16, kernel_size=5, stride=1, padding=2), # (16,28,28) # 想要con2d卷積出來(lái)的圖片尺寸沒(méi)有變化, padding=(kernel_size-1)/2 nn.ReLU(), nn.MaxPool2d(kernel_size=2) # (16,14,14) ) self.conv2 = nn.Sequential( # (16,14,14) nn.Conv2d(16, 32, 5, 1, 2), # (32,14,14) nn.ReLU(), nn.MaxPool2d(2) # (32,7,7) ) self.out = nn.Linear(32*7*7, 10) def forward(self, x): x = self.conv1(x) x = self.conv2(x) x = x.view(x.size(0), -1) # 將（batch，32,7,7）展平為（batch，32*7*7） output = self.out(x) return output cnn = CNN() print(cnn) ''''' CNN ( (conv1): Sequential ( (0): Conv2d(1, 16, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2)) (1): ReLU () (2): MaxPool2d (size=(2, 2), stride=(2, 2), dilation=(1, 1)) ) (conv2): Sequential ( (0): Conv2d(16, 32, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2)) (1): ReLU () (2): MaxPool2d (size=(2, 2), stride=(2, 2), dilation=(1, 1)) ) (out): Linear (1568 -> 10) ) ''' optimizer = torch.optim.Adam(cnn.parameters(), lr=LR) loss_function = nn.CrossEntropyLoss() for epoch in range(EPOCH): for step, (x, y) in enumerate(train_loader): b_x = Variable(x) b_y = Variable(y) output = cnn(b_x) loss = loss_function(output, b_y) optimizer.zero_grad() loss.backward() optimizer.step() if step % 100 == 0: test_output = cnn(test_x) pred_y = torch.max(test_output, 1)[1].data.squeeze() accuracy = sum(pred_y == test_y) / test_y.size(0) print('Epoch:', epoch, '|Step:', step, '|train loss:%.4f'%loss.data[0], '|test accuracy:%.4f'%accuracy) test_output = cnn(test_x[:10]) pred_y = torch.max(test_output, 1)[1].data.numpy().squeeze() print(pred_y, 'prediction number') print(test_y[:10].numpy(), 'real number') ''''' Epoch: 0 |Step: 0 |train loss:2.3145 |test accuracy:0.1040 Epoch: 0 |Step: 100 |train loss:0.5857 |test accuracy:0.8865 Epoch: 0 |Step: 200 |train loss:0.0600 |test accuracy:0.9380 Epoch: 0 |Step: 300 |train loss:0.0996 |test accuracy:0.9345 Epoch: 0 |Step: 400 |train loss:0.0381 |test accuracy:0.9645 Epoch: 0 |Step: 500 |train loss:0.0266 |test accuracy:0.9620 Epoch: 0 |Step: 600 |train loss:0.0973 |test accuracy:0.9685 Epoch: 0 |Step: 700 |train loss:0.0421 |test accuracy:0.9725 Epoch: 0 |Step: 800 |train loss:0.0654 |test accuracy:0.9710 Epoch: 0 |Step: 900 |train loss:0.1333 |test accuracy:0.9740 Epoch: 0 |Step: 1000 |train loss:0.0289 |test accuracy:0.9720 Epoch: 0 |Step: 1100 |train loss:0.0429 |test accuracy:0.9770 [7 2 1 0 4 1 4 9 5 9] prediction number [7 2 1 0 4 1 4 9 5 9] real number ''' 三、分析解讀
通過(guò)利用torchvision.datasets可以快速獲取可以直接置于DataLoader中的dataset格式的數(shù)據(jù)，通過(guò)train參數(shù)控制是獲取訓(xùn)練數(shù)據(jù)集還是測(cè)試數(shù)據(jù)集，也可以在獲取的時(shí)候便直接轉(zhuǎn)換成訓(xùn)練所需的數(shù)據(jù)格式。
卷積神經(jīng)網(wǎng)絡(luò)的搭建通過(guò)定義一個(gè)CNN類來(lái)實(shí)現(xiàn)，卷積層conv1，conv2及out層以類屬性的形式定義，各層之間的銜接信息在forward中定義，定義的時(shí)候要留意各層的神經(jīng)元數(shù)量。
CNN的網(wǎng)絡(luò)結(jié)構(gòu)如下：
CNN ( (conv1): Sequential ( (0): Conv2d(1, 16,kernel_size=(5, 5), stride=(1, 1), padding=(2, 2)) (1): ReLU () (2): MaxPool2d (size=(2,2), stride=(2, 2), dilation=(1, 1)) ) (conv2): Sequential ( (0): Conv2d(16, 32,kernel_size=(5, 5), stride=(1, 1), padding=(2, 2)) (1): ReLU () (2): MaxPool2d (size=(2,2), stride=(2, 2), dilation=(1, 1)) ) (out): Linear (1568 ->10))
經(jīng)過(guò)實(shí)驗(yàn)可見(jiàn)，在EPOCH=1的訓(xùn)練結(jié)果中，測(cè)試集準(zhǔn)確率可達(dá)到97.7%。
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