P9 多分类问题

    softmax的输入不需要再做非线性变换，即softmax之前不再需要激活函数(relu)。
softmax两个作用：
1、如果在进行softmax前的input有负数，通过指数变换，得到正数。
2、使所有类的概率求和为1。

    在多分类问题中，标签y的类型是LongTensor。比如说手写字符0-9分类问题，如果y = torch.LongTensor([3])，对应的one-hot是[0,0,0,1,0,0,0,0,0,0].(这里要注意，如果使用了one-hot，标签y的类型是LongTensor，糖尿病数据集中的target的类型是FloatTensor)

softmax的数学表达

交叉熵损失

''' 手写字符识别pytorch实现 '''
import torch
from torchvision import transforms, datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
from tqdm import tqdm

#定义一个cpu
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")

# prepare dataset
batch_size = 64
# 图像预处理
transform = transforms.Compose([transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))]) #归一化，两个值是均值和方差

train_dataset = datasets.MNIST(root = 'dataset/mnist/', train = True, download = True, transform = transform)
train_loader = DataLoader(train_dataset, shuffle = True, batch_size = batch_size)
test_dataset = datasets.MNIST(root = 'dataset/mnist/', train = False, download = True, transform = transform)
test_loader = DataLoader(test_dataset, shuffle = False, batch_size = batch_size)

# design model using class
class Net(torch.nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.l1 = torch.nn.Linear(28*28, 512)
        self.l2 = torch.nn.Linear(512, 256)
        self.l3 = torch.nn.Linear(256, 128)
        self.l4 = torch.nn.Linear(128, 64)
        self.l5 = torch.nn.Linear(64, 10)

    def forward(self, x):
        x = x.view(-1, 784) #将N*1*28*28的图片转换成N*1*784，-1代表N的值，即自动获取mini_batch
        x = F.relu(self.l1(x))
        x = F.relu(self.l2(x))
        x = F.relu(self.l3(x))
        x = F.relu(self.l4(x))
        return self.l5(x)  # 最后一层不做激活,直接接到softmax

model = Net()
model.to(device)

# construct loss and optimizer
criterion = torch.nn.CrossEntropyLoss()
optimizer = torch.optim.SGD(model.parameters(), lr = 0.01, momentum = 0.5)

# training cycle forward, backward, update
def train(epoch):
    running_loss = 0.0
    for batch_idx, data in enumerate(tqdm(train_loader), 0):
        inputs, labels = data[0].to(device), data[1].to(device) # 使用gpu训练
        optimizer.zero_grad()

        #forward + backward + optimize
        # 获得模型预测结果(64, 10)
        outputs = model(inputs)
        # 交叉熵代价函数outputs(64,10),target（64）
        loss = criterion(outputs, labels)
        loss.backward()
        optimizer.step()

        running_loss += loss.item()
        if batch_idx % 300 == 299: # 输出每次的平均loss
            print('\n [%d, %5d] loss: %.3f' % (epoch+1, batch_idx+1, running_loss/300))
            running_loss = 0.0

def test():
    correct = 0
    total = 0
    with torch.no_grad():
        for data in test_loader:
            images, labels = data[0].to(device), data[1].to(device)
            outputs = model(images)
            _, predicted = torch.max(outputs.data, dim = 1) #并不关心最大值是多少，用下划线来存，需要在意的是index，
            #dim=1表示输出所在行的最大值，若改写成dim=0则输出所在列的最大值。
            total += labels.size(0) # N*1
            correct += (predicted == labels).sum().item() # 张量之间的比较运算
        print('accuracy on test set: %d %% ' % (100*correct/total))

if __name__ == '__main__':
    for epoch in range(10):
        train(epoch)
        test()

参考博客https://blog.csdn.net/bit452/article/details/109686936