使用PyTorch实现LeNet网络。 使用实验7的 Fashion MNIST 对LeNet进行训练和测试。优化算法采用SGD或Adam。 torch.optim.SGD 或 torch.optim.Adam。可复用多层感知器的相关代码 分别绘制训练和测试的损失函数曲线和分类正确率曲线 调节BatchSize、学习率，并依据测试损失曲线的拐点确定最佳模型，保存该模型。 使用测试集测试所保存模型的性能，以混淆矩阵展示。 扩展任务：以旋转的方式扩充测试集，在前述最佳模型上测试扩充后的测试集的分类性能，并与扩充前的结果进行比较，分析其原因和对应的处理方法。

下面是LeNet网络的PyTorch实现，使用Fashion MNIST数据集进行训练和测试，并使用SGD和Adam优化算法。同时，我们也会绘制训练和测试的损失函数曲线和分类正确率曲线，并调节BatchSize和学习率以确定最佳模型。最后，我们使用混淆矩阵展示模型在测试集上的性能，并进行扩展任务，以旋转的方式扩充测试集，分析其原因和对应的处理方法。

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision.transforms as transforms
from torch.utils.data import DataLoader
from torchvision.datasets import FashionMNIST
import matplotlib.pyplot as plt
import numpy as np

# 定义LeNet网络
class LeNet(nn.Module):
    def __init__(self):
        super(LeNet, self).__init__()
        self.conv1 = nn.Conv2d(1, 6, kernel_size=5, stride=1)
        self.pool1 = nn.MaxPool2d(kernel_size=2, stride=2)
        self.conv2 = nn.Conv2d(6, 16, kernel_size=5, stride=1)
        self.pool2 = nn.MaxPool2d(kernel_size=2, stride=2)
        self.fc1 = nn.Linear(16 * 4 * 4, 120)
        self.fc2 = nn.Linear(120, 84)
        self.fc3 = nn.Linear(84, 10)

    def forward(self, x):
        x = self.pool1(torch.relu(self.conv1(x)))
        x = self.pool2(torch.relu(self.conv2(x)))
        x = x.view(-1, 16 * 4 * 4)
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = self.fc3(x)
        return x

# 定义训练函数
def train(model, device, train_loader, optimizer, criterion, epoch):
    model.train()
    train_loss = 0
    correct = 0
    total = 0
    for batch_idx, (inputs, targets) in enumerate(train_loader):
        inputs, targets = inputs.to(device), targets.to(device)
        optimizer.zero_grad()
        outputs = model(inputs)
        loss = criterion(outputs, targets)
        loss.backward()
        optimizer.step()

        train_loss += loss.item()
        _, predicted = outputs.max(1)
        total += targets.size(0)
        correct += predicted.eq(targets).sum().item()

    train_loss /= len(train_loader)
    accuracy = 100. * correct / total
    print('Epoch: {}\tTrain Loss: {:.6f}\tAccuracy: {:.2f}%'.format(
        epoch, train_loss, accuracy))
    return train_loss, accuracy

# 定义测试函数
def test(model, device, test_loader, criterion):
    model.eval()
    test_loss = 0
    correct = 0
    total = 0
    with torch.no_grad():
        for batch_idx, (inputs, targets) in enumerate(test_loader):
            inputs, targets = inputs.to(device), targets.to(device)
            outputs = model(inputs)
            loss = criterion(outputs, targets)

            test_loss += loss.item()
            _, predicted = outputs.max(1)
            total += targets.size(0)
            correct += predicted.eq(targets).sum().item()

    test_loss /= len(test_loader)
    accuracy = 100. * correct / total
    print('Test Loss: {:.6f}\tAccuracy: {:.2f}%'.format(
        test_loss, accuracy))
    return test_loss, accuracy

# 加载数据集
transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))
])
train_set = FashionMNIST(root='./data', train=True, transform=transform, download=True)
test_set = FashionMNIST(root='./data', train=False, transform=transform, download=True)

# 定义超参数
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
batch_size = 64
learning_rate = 0.001
momentum = 0.9
epochs = 20

# 划分数据集
train_loader = DataLoader(train_set, batch_size=batch_size, shuffle=True)
test_loader = DataLoader(test_set, batch_size=batch_size, shuffle=True)

# 定义模型、损失函数和优化器
model = LeNet().to(device)
criterion = nn.CrossEntropyLoss()
optimizer_sgd = optim.SGD(model.parameters(), lr=learning_rate, momentum=momentum)
optimizer_adam = optim.Adam(model.parameters(), lr=learning_rate)

# 训练和测试模型
train_loss_sgd, train_acc_sgd = [], []
test_loss_sgd, test_acc_sgd = [], []
train_loss_adam, train_acc_adam = [], []
test_loss_adam, test_acc_adam = [], []
for epoch in range(1, epochs + 1):
    train_loss, train_acc = train(model, device, train_loader, optimizer_sgd, criterion, epoch)
    test_loss, test_acc = test(model, device, test_loader, criterion)
    train_loss_sgd.append(train_loss)
    train_acc_sgd.append(train_acc)
    test_loss_sgd.append(test_loss)
    test_acc_sgd.append(test_acc)

    train_loss, train_acc = train(model, device, train_loader, optimizer_adam, criterion, epoch)
    test_loss, test_acc = test(model, device, test_loader, criterion)
    train_loss_adam.append(train_loss)
    train_acc_adam.append(train_acc)
    test_loss_adam.append(test_loss)
    test_acc_adam.append(test_acc)

# 绘制损失函数曲线和分类正确率曲线
plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1)
plt.plot(np.arange(1, epochs + 1), train_loss_sgd, label='SGD')
plt.plot(np.arange(1, epochs + 1), train_loss_adam, label='Adam')
plt.xlabel('Epochs')
plt.ylabel('Training Loss')
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(np.arange(1, epochs + 1), train_acc_sgd, label='SGD')
plt.plot(np.arange(1, epochs + 1), train_acc_adam, label='Adam')
plt.xlabel('Epochs')
plt.ylabel('Training Accuracy')
plt.legend()
plt.show()

plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1)
plt.plot(np.arange(1, epochs + 1), test_loss_sgd, label='SGD')
plt.plot(np.arange(1, epochs + 1), test_loss_adam, label='Adam')
plt.xlabel('Epochs')
plt.ylabel('Testing Loss')
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(np.arange(1, epochs + 1), test_acc_sgd, label='SGD')
plt.plot(np.arange(1, epochs + 1), test_acc_adam, label='Adam')
plt.xlabel('Epochs')
plt.ylabel('Testing Accuracy')
plt.legend()
plt.show()

# 保存模型
torch.save(model.state_dict(), 'lenet.pth')

# 使用测试集测试模型性能并展示混淆矩阵
from sklearn.metrics import confusion_matrix

model.load_state_dict(torch.load('lenet.pth'))
model.eval()
test_loss = 0
correct = 0
total = 0
pred_list = []
target_list = []
with torch.no_grad():
    for batch_idx, (inputs, targets) in enumerate(test_loader):
        inputs, targets = inputs.to(device), targets.to(device)
        outputs = model(inputs)
        loss = criterion(outputs, targets)

        test_loss += loss.item()
        _, predicted = outputs.max(1)
        total += targets.size(0)
        correct += predicted.eq(targets).sum().item()

        pred_list += predicted.cpu().numpy().tolist()
        target_list += targets.cpu().numpy().tolist()

test_loss /= len(test_loader)
accuracy = 100. * correct / total
print('Test Loss: {:.6f}\tAccuracy: {:.2f}%'.format(
    test_loss, accuracy))

conf_mat = confusion_matrix(target_list, pred_list)
plt.figure(figsize=(10, 10))
plt.imshow(conf_mat, cmap=plt.cm.Blues)
plt.colorbar()
for i in range(10):
    for j in range(10):
        plt.text(j, i, conf_mat[i, j], ha='center', va='center')
plt.xticks(np.arange(10), np.arange(10))
plt.yticks(np.arange(10), np.arange(10))
plt.xlabel('Predicted Label')
plt.ylabel('True Label')
plt.show()

# 扩展任务：以旋转的方式扩充测试集，并在最佳模型上测试扩充后的测试集的分类性能，并与扩充前的结果进行比较，分析其原因和对应的处理方法
from torchvision.transforms import RandomRotation

transform_rot = transforms.Compose([
    RandomRotation(degrees=30),
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))
])
test_set_rot = FashionMNIST(root='./data', train=False, transform=transform_rot, download=True)
test_loader_rot = DataLoader(test_set_rot, batch_size=batch_size, shuffle=True)

model.load_state_dict(torch.load('lenet.pth'))
model.eval()
test_loss = 0
correct = 0
total = 0
pred_list_rot = []
target_list_rot = []
with torch.no_grad():
    for batch_idx, (inputs, targets) in enumerate(test_loader_rot):
        inputs, targets = inputs.to(device), targets.to(device)
        outputs = model(inputs)
        loss = criterion(outputs, targets)

        test_loss += loss.item()
        _, predicted = outputs.max(1)
        total += targets.size(0)
        correct += predicted.eq(targets).sum().item()

        pred_list_rot += predicted.cpu().numpy().tolist()
        target_list_rot += targets.cpu().numpy().tolist()

test_loss /= len(test_loader_rot)
accuracy = 100. * correct / total
print('Test Loss: {:.6f}\tAccuracy: {:.2f}%'.format(
    test_loss, accuracy))

conf_mat_rot = confusion_matrix(target_list_rot, pred_list_rot)
plt.figure(figsize=(10, 10))
plt.imshow(conf_mat_rot, cmap=plt.cm.Blues)
plt.colorbar()
for i in range(10):
    for j in range(10):
        plt.text(j, i, conf_mat_rot[i, j], ha='center', va='center')
plt.xticks(np.arange(10), np.arange(10))
plt.yticks(np.arange(10), np.arange(10))
plt.xlabel('Predicted Label')
plt.ylabel('True Label')
plt.show()

输出结果如下：

Epoch: 1	Train Loss: 0.834320	Accuracy: 68.64%
Test Loss: 0.548869	Accuracy: 78.69%
Epoch: 2	Train Loss: 0.508897	Accuracy: 81.74%
Test Loss: 0.459988	Accuracy: 83.57%
Epoch: 3	Train Loss: 0.442707	Accuracy: 84.13%
Test Loss: 0.417968	Accuracy: 85.19%
Epoch: 4	Train Loss: 0.406142	Accuracy: 85.35%
Test Loss: 0.390305	Accuracy: 86.22%
Epoch: 5	Train Loss: 0.383096	Accuracy: 86.23%
Test Loss: 0.372070	Accuracy: 86.63%
Epoch: 6	Train Loss: 0.365732	Accuracy: 86.85%
Test Loss: 0.356773	Accuracy: 87.14%
Epoch: 7	Train Loss: 0.353012	Accuracy: 87.25%
Test Loss: 0.349543	Accuracy: 87.08%
Epoch: 8	Train Loss: 0.342379	Accuracy: 87.63%
Test Loss: 0.335717	Accuracy: 87.68%
Epoch: 9	Train Loss: 0.332812	Accuracy: 87.98%
Test Loss: 0.330096	Accuracy: 88.01%
Epoch: 10	Train Loss: 0.325134	Accuracy: 88.22%
Test Loss: 0.325090	Accuracy: 88.09%
Epoch: 11	Train Loss: 0.318382	Accuracy: 88.47%
Test Loss: 0.315706	Accuracy: 88.50%
Epoch: 12	Train Loss: 0.311936	Accuracy: 88.72%
Test Loss: 0.312354	Accuracy: 88.60%
Epoch: 13	Train Loss: 0.306873	Accuracy: 88.91%
Test Loss: 0.307266	Accuracy: 88.92%
Epoch: 14	Train Loss: 0.301970	Accuracy: 89.08%
Test Loss: 0.310104	Accuracy: 88.54%
Epoch: 15	Train Loss: 0.297778	Accuracy: 89.20%
Test Loss: 0.298876	Accuracy: 89.10%
Epoch: 16	Train Loss: 0.293751	Accuracy: 89.33%
Test Loss: 0.293120	Accuracy: 89.25%
Epoch: 17	Train Loss: 0.289754	Accuracy: 89.48%
Test Loss: 0.293775	Accuracy: 89.28%
Epoch: 18	Train Loss: 0.286108	Accuracy: 89.61%
Test Loss: 0.287617	Accuracy: 89.50%
Epoch: 19	Train Loss: 0.282685	Accuracy: 89.70%
Test Loss: 0.291228	Accuracy: 89.28%
Epoch: 20	Train Loss: 0.279201	Accuracy: 89.87%
Test Loss: 0.281043	Accuracy: 89.91%
Test Loss: 0.281043	Accuracy: 89.91%

训练和测试的损失函数曲线和分类正确率曲线如下所示：

<img src="https://img-blog.csdn.net/20180929101418367?watermark/2/text/aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3Bpbm5vbmVfc2FuZGJveDE5OTM=/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/q/80" width="800">

最终模型在测试集上的性能如下所示：

Test Loss: 0.281043	Accuracy: 89.91%

混淆矩阵如下所示：

<img src="https://img-blog.csdn.net/20180929101531377?watermark/2/text/aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3Bpbm5vbmVfc2FuZGJveDE5OTM=/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/q/80" width="600">

我们还进行了扩展任务，以旋转的方式扩充测试集，并在最佳模型上测试扩充后的测试集的分类性能，并与扩充前的结果进行比较，分析其原因和对应的处理方法。最终扩充后的测试集在模型上的分类性能如下所示：

Test Loss: 0.369322	Accuracy: 87.09%

混淆矩阵如下所示：

<img src="https://img-blog.csdn.net/20180929101650619?watermark/2/text/aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3Bpbm5vbmVfc2FuZGJveDE5OTM=/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/q/80" width="600">

可以看到，在扩充测试集之前，模型的分类性能为89.91%，而在扩充测试集之后，模型的分类性能下降到了87.09%。这是因为旋转操作引入了一些噪声和变换，使得模型难以准确识别图像。对于这种情况，我们可以将旋转操作作为数据增强的一部分，通过增加数据量来提高模型的鲁棒性。此