多分类问题

多分类问题

Softmax

二分类问题

给定一系列特征，输出为0或1，表示是否满足某个条件。具体做法是输出一个概率，表示给定特征满足这个条件的概率，或者不满足这个条件的概率。

多分类问题

给定一系列特征，预测是多个类别中的哪一类，比如手写数组识别、物体识别等。

如果在多分类问题中仍采用二分类问题的解决方法，即输出可能属于每个类别的概率，会出现的问题有

1. 输出的概率可能为负数
2. 所有类别概率之和不为1，即不是一个分布

提出Softmax Classifier解决上述问题，最后一个线性层输出的结果是z，包括预测属于k个类别的概率，公式如下

1. 通过计算指数保证了最终输出结果必为正数
2. 通过归一化保证了最终输出所有类别概率之和为1

举例如下

多分类损失函数

二分类损失函数cross-entropy（交叉熵）

本质还是损失函数，描述预测结果和真实结果之间的差异程度

y：真实值，y_head：预测值

• y = 1

  • y_head = 1

    预测值和真实值之间吻合，loss会很小

  • y_head = 0

    预测值和真实值之间差异较大，loss会很大，注意看-log(y_head)

• y = 0

  • y_head = 1

    预测值和真实值之间差异较大，loss会很大，注意看-log(1-y_head)

  • y_head = 0

    预测值和真实值之间吻合，loss会很小

多分类损失函数

没太明白，看弹幕有什么独热编码，记住公式吧？

pytorch提供的交叉熵损失函数直接包括计算log(y_head)、softmax和损失函数计算

注意：最后一层不做激活，直接使用交叉熵损失函数，传入softmax

手写数字识别（全连接网络）

import torch
from torch import nn
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch.optim as optim

# --------------------------------------- 数据准备 ----------------------------------------
batch_size = 64
transform = transforms.Compose([
   transforms.ToTensor(),
   transforms.Normalize((0.1307,), (0.3081,))
])

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)


# --------------------------------------- 定义网络模型 ----------------------------------------
class Net(nn.Module):
   def __init__(self):
       super(Net, self).__init__()
       self.linear1 = nn.Linear(784, 512)
       self.linear2 = nn.Linear(512, 256)
       self.linear3 = nn.Linear(256, 128)
       self.linear4 = nn.Linear(128, 64)
       self.linear5 = nn.Linear(64, 10)

   def forward(self, x):
       x = x.view(-1, 784)
       x = F.relu(self.linear1(x))
       x = F.relu(self.linear2(x))
       x = F.relu(self.linear3(x))
       x = F.relu(self.linear4(x))
       x = self.linear5(x)         # 注意最后一层不加激活函数
       return x


# -------------------------- 实例化网络模型 定义损失函数和优化器 --------------------------------

device = torch.device("cuda")   # 定义gpu设备
model = Net()
model = model.to(device)

criterion = nn.CrossEntropyLoss()   # 交叉熵损失函数
criterion = criterion.to(device)
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)


# --------------------------------------- 定义训练过程 ----------------------------------------

def train(epoch):
   running_loss = 0.0
   for batch_idx, data in enumerate(train_loader, 0):
       inputs, targets = data
       inputs = inputs.to(device)
       targets = targets.to(device)
       optimizer.zero_grad()
       outputs = model(inputs)  # forward
       loss = criterion(outputs, targets)  # get loss
       loss.backward()  # backward
       optimizer.step()  # update

       running_loss += loss.item()
       if batch_idx % 300 == 299:  # 每300次输出
           print('[%d, %5d] loss: %3f' % (epoch + 1, batch_idx + 1, running_loss / 300))
           running_loss = 0.0


# --------------------------------------- 定义测试过程 ----------------------------------------
def test():
   correct = 0
   total = 0
   with torch.no_grad():
       for data in test_loader:
           images, labels = data
           images = images.to(device)
           labels = labels.to(device)
           outputs = model(images)
           _, predicted = torch.max(outputs.data, dim=1)
           total += labels.size(0)
           correct += (predicted == labels).sum().item()
   print('Accuracy on test set: %d %%' % (100 * correct / total))


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

手写数字识别（CNN）

卷积神经网络模型如下

实现代码如下

import torch
from torch import nn, optim
from torch.utils.data import DataLoader
from torchvision import transforms, datasets
import torch.nn.functional as F

# --------------------------------------- 数据准备 ----------------------------------------
batch_size = 64
transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
])

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)


# --------------------------------------- 定义网络模型 ----------------------------------------
class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, 5)
        self.conv2 = nn.Conv2d(10, 20, 5)
        self.maxPool = nn.MaxPool2d(2)
        self.linear1 = nn.Linear(320, 10)

    def forward(self, x):
        batch_size = x.size(0)
        x = F.relu(self.maxPool(self.conv1(x)))
        x = F.relu(self.maxPool(self.conv2(x)))
        x = x.view(batch_size, -1)
        x = self.linear1(x)
        return x


device = torch.device("cuda")
model = Net()
model = model.to(device)

criterion = nn.CrossEntropyLoss()  # 交叉熵损失函数
criterion = criterion.to(device)
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)


def train(epoch):
    running_loss = 0.0
    for batch_idx, data in enumerate(train_loader, 0):
        inputs, targets = data
        inputs, targets = inputs.to(device), targets.to(device)
        optimizer.zero_grad()

        outputs = model(inputs)
        loss = criterion(outputs, targets)
        loss.backward()
        optimizer.step()

        running_loss += loss.item()
        if batch_idx % 300 == 299:  # 每300次输出
            print('[%d, %5d] loss: %3f' % (epoch + 1, batch_idx + 1, running_loss / 2000))
            running_loss = 0.0


def test():
    correct = 0
    total = 0
    with torch.no_grad():
        for data in test_loader:
            images, labels = data
            images = images.to(device)
            labels = labels.to(device)
            outputs = model(images)
            _, predicted = torch.max(outputs.data, dim=1)
            total += labels.size(0)
            correct += (predicted == labels).sum().item()
    print('Accuracy on test set: %d %% [%d/%d]' % (100 * correct / total, correct, total))


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

训练10轮结果如下

修改神经网络模型，增加一层卷积和池化，增加两层线性层

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, 3, padding=1)
        self.conv2 = nn.Conv2d(10, 20, 3)
        self.conv3 = nn.Conv2d(20, 30, 3)
        self.maxPool = nn.MaxPool2d(2)
        self.linear1 = nn.Linear(120, 60)
        self.linear2 = nn.Linear(60, 30)
        self.linear3 = nn.Linear(30, 10)



    def forward(self, x):
        batch_size = x.size(0)
        x = F.relu(self.maxPool(self.conv1(x)))
        x = F.relu(self.maxPool(self.conv2(x)))
        x = F.relu(self.maxPool(self.conv3(x)))
        x = x.view(batch_size, -1)
        x = self.linear1(x)
        x = self.linear2(x)
        x = self.linear3(x)
        return x

训练结果如下