接觸過深度學習的朋友對MNIST資料集肯定不陌生。基本上算是玩神經網路裡的“hello,world！”

本節基於MNIST資料集，實現CNN學習過程。

下面是一個 CNN 最後一層的學習過程, 我們先視覺化看看:

MNIST手寫資料 

首先是資料集下載，為了看看資料集裡究竟是長什麼樣子的，我也作了展示：

# library
# standard library
import os

# third-party library
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)    # reproducible

# Hyper Parameters
EPOCH = 1               # train the training data n times, to save time, we just train 1 epoch
BATCH_SIZE = 50
LR = 0.001              # learning rate
DOWNLOAD_MNIST = False


# Mnist digits dataset
if not(os.path.exists('./mnist/')) or not os.listdir('./mnist/'):
    # not mnist dir or mnist is empyt dir
    DOWNLOAD_MNIST = True

train_data = torchvision.datasets.MNIST(
    root='./mnist/',
    train=True,                                     # this is training data
    transform=torchvision.transforms.ToTensor(),    # Converts a PIL.Image or numpy.ndarray to
                                                    # torch.FloatTensor of shape (C x H x W) and normalize in the range [0.0, 1.0]
    download=DOWNLOAD_MNIST,
)

# plot one example
print(train_data.train_data.size())                 # (60000, 28, 28)
print(train_data.train_labels.size())               # (60000)
plt.imshow(train_data.train_data[0].numpy(), cmap='gray')
plt.title('%i' % train_data.train_labels[0])
plt.show()
 

結果如下：

首先看下載後的資料集目錄

展示example

黑色的地方的值都是0, 白色的地方值大於0.

同樣, 我們除了訓練資料, 還給一些測試資料, 測試看看它有沒有訓練好

CNN模型 ¶

和以前一樣, 我們用一個 class 來建立 CNN 模型. 這個 CNN 整體流程是 卷積(Conv2d) -> 激勵函式(ReLU) -> 池化, 向下取樣 (MaxPooling) -> 再來一遍 -> 展平多維的卷積成的特徵圖 -> 接入全連線層 (Linear) -> 輸出

# Data Loader for easy mini-batch return in training, the image batch shape will be (50, 1, 28, 28)
train_loader = Data.DataLoader(dataset=train_data, batch_size=BATCH_SIZE, shuffle=True)

# convert test data into Variable, pick 2000 samples to speed up testing
# # 為了節約時間, 我們測試時只測試前2000個
test_data = torchvision.datasets.MNIST(root='./mnist/', train=False)
test_x = Variable(torch.unsqueeze(test_data.test_data, dim=1), volatile=True).type(torch.FloatTensor)[:2000]/255.   # shape from (2000, 28, 28) to (2000, 1, 28, 28), value 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(         # input shape (1, 28, 28)
            nn.Conv2d(
                in_channels=1,              # input height
                out_channels=16,            # n_filters
                kernel_size=5,              # filter size
                stride=1,                   # filter movement/step
                padding=2,                  # if want same width and length of this image after con2d, padding=(kernel_size-1)/2 if stride=1
            ),                              # output shape (16, 28, 28)
            nn.ReLU(),                      # activation
            nn.MaxPool2d(kernel_size=2),    # choose max value in 2x2 area, output shape (16, 14, 14)
        )
        self.conv2 = nn.Sequential(         # input shape (16, 14, 14)
            nn.Conv2d(16, 32, 5, 1, 2),     # output shape (32, 14, 14)
            nn.ReLU(),                      # activation
            nn.MaxPool2d(2),                # output shape (32, 7, 7)
        )
        self.out = nn.Linear(32 * 7 * 7, 10)   # fully connected layer, output 10 classes

    def forward(self, x):
        x = self.conv1(x)
        x = self.conv2(x)
        x = x.view(x.size(0), -1)           # flatten the output of conv2 to (batch_size, 32 * 7 * 7)
        output = self.out(x)
        return output, x    # return x for visualization


cnn = CNN()
print(cnn)  # net architecture
 

結構列印如下：

訓練 

下面我們開始訓練, 將 x y 都用 Variable 包起來, 然後放入 cnn 中計算 output, 最後再計算誤差. 

optimizer = torch.optim.Adam(cnn.parameters(), lr=LR)   # optimize all cnn parameters
loss_func = nn.CrossEntropyLoss()                       # the target label is not one-hotted

# following function (plot_with_labels) is for visualization, can be ignored if not interested
from matplotlib import cm
try: from sklearn.manifold import TSNE; HAS_SK = True
except: HAS_SK = False; print('Please install sklearn for layer visualization')
def plot_with_labels(lowDWeights, labels):
    plt.cla()
    X, Y = lowDWeights[:, 0], lowDWeights[:, 1]
    for x, y, s in zip(X, Y, labels):
        c = cm.rainbow(int(255 * s / 9)); plt.text(x, y, s, backgroundcolor=c, fontsize=9)
    plt.xlim(X.min(), X.max()); plt.ylim(Y.min(), Y.max()); plt.title('Visualize last layer'); plt.show(); plt.pause(0.01)

plt.ion()
# training and testing
for epoch in range(EPOCH):
    for step, (x, y) in enumerate(train_loader):   # gives batch data, normalize x when iterate train_loader
        b_x = Variable(x)   # batch x
        b_y = Variable(y)   # batch y

        output = cnn(b_x)[0]               # cnn output
        loss = loss_func(output, b_y)   # cross entropy loss
        optimizer.zero_grad()           # clear gradients for this training step
        loss.backward()                 # backpropagation, compute gradients
        optimizer.step()                # apply gradients

        if step % 50 == 0:
            test_output, last_layer = cnn(test_x)
            pred_y = torch.max(test_output, 1)[1].data.squeeze()
            accuracy = sum(pred_y == test_y) / float(test_y.size(0))
            print('Epoch: ', epoch, '| train loss: %.4f' % loss.data[0], '| test accuracy: %.2f' % accuracy)
            if HAS_SK:
                # Visualization of trained flatten layer (T-SNE)
                tsne = TSNE(perplexity=30, n_components=2, init='pca', n_iter=5000)
                plot_only = 500
                low_dim_embs = tsne.fit_transform(last_layer.data.numpy()[:plot_only, :])
                labels = test_y.numpy()[:plot_only]
                plot_with_labels(low_dim_embs, labels)
plt.ioff()
 

訓練過程展示：

最後我們再來取10個數據, 看看預測的值到底對不對:

預測結果

視覺化訓練

     因為視覺化可以幫助理解, 所以還是有必要提一下. 視覺化的程式碼主要是用 matplotlib 和 sklearn 來完成的, 因為其中我們用到了 T-SNE 的降維手段, 將高維的 CNN 最後一層輸出結果視覺化, 也就是 CNN forward 程式碼中的 x = x.view(x.size(0), -1) 這一個結果.