深度学习基础--SOFTMAX回归（单层神经网络）

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，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 npdef 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_iterbatch_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 ynet = 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 = 10def 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.datadef evaluate_accuracy(data_iter, net):acc_sum, n = 0.0, 0for X, y in data_iter:acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()n += y.shape[0]return acc_sum / ndef 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, 0for 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）

END！