山大软院ai导论实验之采用BP神经网络分类MNIST数据集

 目录

实验代码

实验内容

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实验代码

import matplotlib.pyplot as plt
from matplotlib import font_manager
import torch
from torch.utils.data import DataLoader
import torchvision
from torchvision import transforms# 数据预处理
transform = transforms.Compose([transforms.ToTensor(),transforms.Normalize((0.5,), (0.5,))
])train_data_path = 'E:\\小刘的桌面\\人工智能导论实验\\expr2_trainset'
train_dataset = torchvision.datasets.MNIST(root=train_data_path, train=True, download=True, transform=transform)
test_dataset = torchvision.datasets.MNIST(root=train_data_path, train=False, download=True, transform=transform)# 使用DataLoader加载数据集
train_loader = DataLoader(dataset=train_dataset, shuffle=True, batch_size=100)
test_loader = DataLoader(dataset=test_dataset, shuffle=False, batch_size=100)# 定义BP神经网络结构
class BPNetwork(torch.nn.Module):def __init__(self):super(BPNetwork, self).__init__()# # 4层# self.fc1 = torch.nn.Linear(784, 256)# self.activation1 = torch.nn.ReLU()# self.fc2 = torch.nn.Linear(256, 128)# self.activation2 = torch.nn.ReLU()# self.fc3 = torch.nn.Linear(128, 64)# self.activation3 = torch.nn.ReLU()# self.fc4 = torch.nn.Linear(64, 32)# self.activation4 = torch.nn.ReLU()# self.fc5 = torch.nn.Linear(32, 10)# #2层# self.fc1 = torch.nn.Linear(784,64)# self.activation1 = torch.nn.ReLU()# self.fc2 = torch.nn.Linear(64, 32)# self.activation2 = torch.nn.ReLU()# self.fc3 = torch.nn.Linear(32, 10)# self.softmax = torch.nn.LogSoftmax(dim=1)# def forward(self, x):#     x = x.view(x.size(0), -1)#     x = self.activation1(self.fc1(x))#     x = self.activation2(self.fc2(x))#     # x = self.activation3(self.fc3(x))#     x = self.softmax(self.fc3(x))#     return x# def forward(self, x):#     x = x.view(x.size(0), -1)#     x = self.activation1(self.fc1(x))#     x = self.activation2(self.fc2(x))#     x = self.activation3(self.fc3(x))#     x = self.activation4(self.fc4(x))#     x = self.softmax(self.fc5(x))  # 修改为使用fc5#     return x# 3个隐藏层self.fc1 = torch.nn.Linear(784, 128)self.activation1 = torch.nn.ReLU()self.fc2 = torch.nn.Linear(128, 64)self.activation2 = torch.nn.ReLU()self.fc3 = torch.nn.Linear(64, 32)self.activation3 = torch.nn.ReLU()self.fc4 = torch.nn.Linear(32, 10)self.softmax = torch.nn.LogSoftmax(dim=1)def forward(self, x):x = x.view(x.size(0), -1)x = self.activation1(self.fc1(x))x = self.activation2(self.fc2(x))x = self.activation3(self.fc3(x))x = self.softmax(self.fc4(x))  # 使用fc4作为输出层return x#     # 5个隐藏层#     self.fc1 = torch.nn.Linear(784, 512)#     self.activation1 = torch.nn.ReLU()#     self.fc2 = torch.nn.Linear(512, 256)#     self.activation2 = torch.nn.ReLU()#     self.fc3 = torch.nn.Linear(256, 128)#     self.activation3 = torch.nn.ReLU()#     self.fc4 = torch.nn.Linear(128, 64)#     self.activation4 = torch.nn.ReLU()#     self.fc5 = torch.nn.Linear(64, 32)#     self.activation5 = torch.nn.ReLU()#     self.fc6 = torch.nn.Linear(32, 10)##     self.softmax = torch.nn.LogSoftmax(dim=1)### def forward(self, x):#     x = x.view(x.size(0), -1)#     x = self.activation1(self.fc1(x))#     x = self.activation2(self.fc2(x))#     x = self.activation3(self.fc3(x))#     x = self.activation4(self.fc4(x))#     x = self.activation5(self.fc5(x))#     x = self.softmax(self.fc6(x))  # 使用fc6作为输出层#     return x# 创建网络模型
model = BPNetwork()
# 定义损失函数与优化器
criterion = torch.nn.NLLLoss()
optimizer = torch.optim.SGD(model.parameters(), lr=0.009, momentum=0.9)
num_epochs = 1
total_batches = 0font = font_manager.FontProperties()batch_steps = []
train_accuracies = []
test_accuracies = []# 训练网络
for epoch in range(num_epochs):for images, labels in train_loader:total_batches += 1optimizer.zero_grad()  # 清空梯度outputs = model(images)  # 前向传播loss = criterion(outputs, labels)  # 计算损失loss.backward()  # 反向传播optimizer.step()  # 更新参数# 每50批次计算并记录准确率if total_batches % 50 == 0:# 计算训练集准确率train_correct = (outputs.argmax(dim=1) == labels).sum().item()train_accuracy = train_correct / len(images)# 计算测试集准确率test_correct = 0with torch.no_grad():for test_images, test_labels in test_loader:test_outputs = model(test_images)test_correct += (test_outputs.argmax(dim=1) == test_labels).sum().item()test_accuracy = test_correct / len(test_dataset)# 存储结果batch_steps.append(total_batches)train_accuracies.append(train_accuracy)test_accuracies.append(test_accuracy)print(f"Step {total_batches}, Training Accuracy: {train_accuracy:.2f}, Test Accuracy: {test_accuracy:.4f}")# 绘制曲线
plt.figure(figsize=(10, 5))
plt.plot(batch_steps, train_accuracies, label='Training Accuracy', marker='o')
plt.plot(batch_steps, test_accuracies, label='Test Accuracy', marker='x')
plt.title('Training and Test Accuracy Over Time', fontproperties=font, fontsize=18)
plt.xlabel('Batch Steps', fontproperties=font, fontsize=12)
plt.ylabel('Accuracy', fontproperties=font, fontsize=12)
plt.legend()
plt.show()

实验内容

1.下载数据集：

MNIST数据集来自美国国家标准与技术研究所（NIST），包含手写数字图片及其标签。数据集分为训练集和测试集，详细信息如下：

训练集：包含60000张图片及其标签，每张图片是一个28 x 28的灰度图像。

测试集：包含10000张图片及其标签，图片格式与训练集相同。

每个样本代表一个手写数字（0-9），图片中像素值已归一化到[0, 1]范围。

进行数据集的下载：

2.数据预处理：使用torchvision加载MNIST数据集并进行标准化。将训练集和测试集的每个像素点归一化到[-1, 1]范围，以适应神经网络的输入。

1. 定义BP神经网络结构：构建一个多层感知器网络，在本次实验分别采用了2、3、4、5层隐藏层，用以来观察各个的准确率。其中三层隐藏层中，每层隐藏层分别包含128、64、32个神经元，2层和34层分别递减或者递增即可，另外激活函数为ReLU，输出层采用LogSoftmax。

3个隐藏层：

1. 训练：设置学习率为0.009，并采用交叉熵损失函数和SGD优化器进行训练。训练集中每批包含100个样本，总共训练1个epoch，每50个批次计算一次训练集和测试集的准确率。最终在训练完所有样本后，记录模型在测试集上的最终准确率。

1. 为使训练和测试的准确率更为直观，使用matplotlib绘制训练和测试准确率随批次数变化的折线图，以便观察模型的训练过程。
2.