深度学习基础--SOFTMAX回归（单层神经网络）

刺骨的言语ヽ痛彻心扉 2022-08-28 07:42 261阅读 0赞

## 深度学习基础–SOFTMAX回归（单层神经网络） ##

最近在阅读一本书籍–Dive-into-DL-Pytorch（动手学深度学习），链接：[https://github.com/newmonkey/Dive-into-DL-PyTorch][https_github.com_newmonkey_Dive-into-DL-PyTorch]，自身觉得受益匪浅，在此记录下自己的学习历程。

本篇主要记录关于SOFTMAX回归的知识。softmax回归和线性回归一样都属于单层神经网络；线性回归主要适用于回归问题，而softmax回归主要使用于分类问题。本文主要尝试对手写数字进行识别。sofemax函数又叫归一化指数函数。

#### 1 收集数据集 ####

我们通过torchvision的 torchvision.datasets 来下载这个手写数字识别数据集MNIST。可以获得60000个训练集样本数与10000个测试集样本数。

import torch
    import torchvision
    import numpy as np
    
    def load_data_fashion_mnist(batch_size, root='本地地址url'):
        transform = torchvision.transforms.ToTensor()
        mnist_train = torchvision.datasets.MNIST(root=root, train=True, download=True, transform=transform)
        mnist_test = torchvision.datasets.MNIST(root=root, train=False, download=True, transform=transform)
        train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True)
        test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False)
        return train_iter,test_iter
    
    batch_size=256
    train_iter,test_iter=load_data_fashion_mnist(batch_size)

#### 2 定义和初始化模型 ####

每个样本的shape为\[1,28,28\],即通道数为1，高和宽都为为28像素的图像。故模型的输入向量的长度是784。softmax回归的输出层是⼀个全连接层，所以我们⽤⼀个线性模块就可以了。

import torch.nn as nn
    num_inputs = 784
    num_outputs = 10
    class LinearNet(nn.Module):
        def __init__(self, num_inputs, num_outputs):
            super(LinearNet, self).__init__()
            self.linear = nn.Linear(num_inputs, num_outputs)
        def forward(self, x): # x shape: (batch, 1, 28, 28)
            y = self.linear(x.view(x.shape[0], -1))
            return y
     
    net = LinearNet(num_inputs, num_outputs)
    print(net)
    
    init.normal_(net.linear.weight, mean=0, std=0.01)
    init.constant_(net.linear.bias, val=0)

#### 3 sofemax和交叉熵损失函数 ####

PyTorch提供了⼀个包括softmax运算和交叉熵损失计算的函数。

loss=nn.CrossEntropyLoss()

#### 4 定义优化算法 ####

采用学习率为0.005的⼩批量随机梯度下降（SGD）为优化算法。

optimizer = torch.optim.SGD(net.parameters(), lr=0.005)

#### 5 训练模型 ####

迭代周期设置为10，模型训练。

num_epochs = 10
    
    def sgd(params, lr, batch_size):
        for param in params:
            param.data -= lr * param.grad / batch_size # 注意这里更改param时用的param.data
    
    def evaluate_accuracy(data_iter, net):
        acc_sum, n = 0.0, 0
        for X, y in data_iter:
            acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()
            n += y.shape[0]
        return acc_sum / n
    
    def train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size,params=None, lr=None, optimizer=None):
        for epoch in range(num_epochs):
            train_l_sum, train_acc_sum, n = 0.0, 0.0, 0
            for X, y in train_iter:
                y_hat = net(X)
                l = loss(y_hat, y).sum()
                
                # 梯度清零
                if optimizer is not None:
                    optimizer.zero_grad()
                elif params is not None and params[0].grad is not None:
                    for param in params:
                        param.grad.data.zero_()
                
                l.backward()
                if optimizer is None:
                    sgd(params, lr, batch_size)
                else:
                    optimizer.step()  # “softmax回归的简洁实现”一节将用到
                
                train_l_sum += l.item()
                train_acc_sum += (y_hat.argmax(dim=1) == y).sum().item()
                n += y.shape[0]
            test_acc = evaluate_accuracy(test_iter, net)
            print('epoch %d, loss %.4f, train acc %.3f, test acc %.3f'% (epoch + 1, train_l_sum / n, train_acc_sum / n, test_acc))
    
    train_ch3(net, train_iter, test_iter, loss, num_epochs,batch_size, None, None, optimizer)
    #结果
    #epoch 1, loss 0.0071, train acc 0.675, test acc 0.788
    #epoch 2, loss 0.0050, train acc 0.795, test acc 0.821
    #epoch 3, loss 0.0040, train acc 0.819, test acc 0.837
    #epoch 4, loss 0.0034, train acc 0.832, test acc 0.846
    #epoch 5, loss 0.0031, train acc 0.841, test acc 0.855
    #epoch 6, loss 0.0028, train acc 0.848, test acc 0.860
    #epoch 7, loss 0.0026, train acc 0.853, test acc 0.865
    #epoch 8, loss 0.0025, train acc 0.857, test acc 0.868
    #epoch 9, loss 0.0024, train acc 0.860, test acc 0.871
    #epoch 10, loss 0.0023, train acc 0.863, test acc 0.874

#### 6 预测 ####

训练完成后，现在就可以演示如何对图像进⾏分类了。第⼀⾏为真实标签，第⼆⾏为预测标签，第三行为图像。

from IPython import display
    import matplotlib.pyplot as plt
    X, y = iter(test_iter).next()
    def get_fashion_mnist_labels(labels):
        text_labels = ['0', '1', '2', '3', '4','5', '6', '7', '8', '9']
        return [text_labels[int(i)] for i in labels]
    
    def show_fashion_mnist(images, labels):
        #use_svg_display()
        display.display_svg()
        # 这⾥的_表示我们忽略（不使⽤）的变量
        _, figs = plt.subplots(1, len(images), figsize=(12, 12))
        for f, img, lbl in zip(figs, images, labels):
            f.imshow(img.view((28, 28)).numpy())
            f.set_title(lbl)
            f.axes.get_xaxis().set_visible(False)
            f.axes.get_yaxis().set_visible(False)
        plt.show()
    
    true_labels = get_fashion_mnist_labels(y.numpy())
    pred_labels =get_fashion_mnist_labels(net(X).argmax(dim=1).numpy())
    titles = [true + '\n' + pred for true, pred in zip(true_labels,pred_labels)]
    show_fashion_mnist(X[0:20], titles[0:20])

预测结果展示：（第⼀⾏为真实标签，第⼆⾏为预测标签，第三行为图像）  
![在这里插入图片描述][be996b07e76845fe86a16b7c89a2c7d5.png]  
END！

[https_github.com_newmonkey_Dive-into-DL-PyTorch]: https://github.com/newmonkey/Dive-into-DL-PyTorch
[be996b07e76845fe86a16b7c89a2c7d5.png]: /images/20220828/e7ab9871f4734bcba82a8a9e94ad84cb.png