PyTorch——从零实现图片分类（附完整代码）
参考链接
- https://tangshusen.me/Dive-into-DL-PyTorch/#/chapter03_DL-basics/3.4_softmax-regression
- https://tangshusen.me/Dive-into-DL-PyTorch/#/chapter03_DL-basics/3.5_fashion-mnist
- https://tangshusen.me/Dive-into-DL-PyTorch/#/chapter03_DL-basics/3.7_softmax-regression-pytorch
分类问题
和线性回归不同，softmax回归的输出单元从一个变成了多个，且引入了softmax运算使输出更适合离散值的预测和训练。
交叉熵损失函数
softmax运算将输出变成一个合法的类别预测分布，可以更方便地与离散标签计算误差。实际上，真实标签也可以用类别分布表达：对于样本 i i i，我们构造向量 y ( i ) ∈ R q \textbf{y}^{\left ( i\right )}\in R^{q} y(i)∈Rq，使得第 y ( i ) y^{\left ( i\right )} y(i)（样本 i i i类别的离散数值）个元素为1，其余为0.这样我们的训练目标就可以设为使预测概率分布 y ^ ( i ) \hat{\textbf{y}}^{\left ( i\right )} y^(i)尽可能接近真实的标签概率分布 y ( i ) \textbf{y}^{\left ( i\right )} y(i)。
我们可以像线性回归那样使用平方损失函数 ∥ y ^ ( i ) − y ( i ) ∥ 2 / 2 \left \| \hat{\textbf{y}}^{\left ( i\right )}-\textbf{y}^{\left ( i\right )}\right \|^{2}/2 ∥∥∥y^(i)−y(i)∥∥∥2/2。然而，平方损失过于严格，想要预测分类结果正确，我们其实并不需要预测概率完全等于标签概率。
改善上述问题的一个方法是使用更适合衡量两个概率分别差异的测量函数。其中，交叉熵（cross entropy）是一个常用的衡量方法：
H ( y ( i ) ， y ^ ( i ) ) = − ∑ j = 1 q y j ( i ) l o g y ^ j ( i ) H\left ( \textbf{y}^{\left ( i\right )}，\hat{\textbf{y}}^{\left ( i\right )}\right )=-\sum_{j=1}^{q}y_{j}^{\left ( i\right )}log\ \hat{y}_{j}^{\left ( i\right )} H(y(i)，y^(i))=−∑j=1qyj(i)log y^j(i)
其中，带下标的 y j ( i ) y_{j}^{\left ( i\right )} yj(i)是向量 y ( i ) \textbf{y}^{\left ( i\right )} y(i)中非0即1的元素。在上式中，我们知道向量 y ( i ) \textbf{y}^{\left ( i\right )} y(i)中只有第 y ( i ) y^{\left ( i\right )} y(i)个元素 y y ( i ) ( i ) y_{y\left ( i\right )}^{\left ( i\right )} yy(i)(i)为1，其余全为0，于是 H ( y ( i ) ， y ^ ( i ) ) = − l o g y ^ y ( i ) ( i ) H\left ( \textbf{y}^{\left ( i\right )}，\hat{\textbf{y}}^{\left ( i\right )}\right )=-log\ \hat{y}_{y\left ( i\right )}^{\left ( i\right )} H(y(i)，y^(i))=−log y^y(i)(i)。也就是说，交叉熵只关心对正确类别的预测概率，因为只要其值足够大，就可以确保分类结果正确。当然，遇到一个样本有多个标签时，例如图像里含有不止一个物体时，我们并不能做这一步简化。但即便对于这种情况，交叉熵同样只关心对图像中出现的物体类别的概率。
假设训练数据集的样本为 n n n，交叉熵损失函数定义为
l ( Θ ) = 1 n ∑ i = 1 n H ( y ( i ) ， y ^ ( i ) ) l\left ( \Theta \right )=\frac{1}{n}\sum_{i=1}^{n}H\left ( \textbf{y}^{\left ( i\right )}，\hat{\textbf{y}}^{\left ( i\right )}\right ) l(Θ)=n1∑i=1nH(y(i)，y^(i))
其中， Θ \Theta Θ代表模型参数，同样地，如果每个样本只有一个标签，那么交叉熵损失可以简写成 l ( Θ ) = − 1 n ∑ i = 1 n l o g y ^ y ( i ) ( i ) l\left ( \Theta \right )=-\frac{1}{n}\sum_{i=1}^{n}log\ \hat{y}_{y\left ( i\right )}^{\left ( i\right )} l(Θ)=−n1∑i=1nlog y^y(i)(i)，从另一个角度来看，我们知道最小化 l ( Θ ) l\left ( \Theta \right ) l(Θ)等价于最大化 e x p ( − n l ( Θ ) ) = ∏ i = 1 n y ^ y ( i ) ( i ) exp\left ( -nl\left ( \Theta \right )\right )=\prod_{i=1}^{n}\hat{y}_{y\left ( i\right )}^{\left ( i\right )} exp(−nl(Θ))=∏i=1ny^y(i)(i)，即最小化交叉熵函数函数等价于最大化训练数据集所有标签类别的联合预测概率。
加载数据
使用的是“Fashion-MNIST”数据集，运行后会自动下载。参数transform = transforms.ToTensor()使所有数据转换为Tensor，如果不进行转换则返回的是PIL图片。transforms.ToTensor()将尺寸为 (H x W x C) 且数据位于[0, 255]的PIL图片或者数据类型为np.uint8的NumPy数组转换为尺寸为(C x H x W)且数据类型为torch.float32且位于[0.0, 1.0]的Tensor。
mnist_train = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', train=True, download=True, transform=transforms.ToTensor())
mnist_test = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', train=False, download=True, transform=transforms.ToTensor())
def load_data_fashion_mnist(mnist_train, mnist_test, batch_size):
if sys.platform.startswith('win'):
num_workers = 0
else:
num_workers = 4
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)
return train_iter, test_iter
batch_size = 256
train_iter, test_iter = load_data_fashion_mnist(mnist_train, mnist_test, batch_size)
构建模型
简单地使用一层全连接层作为模型，接上softmax得到输出。
使用矩阵方式实现
num_inputs = 784
num_outputs = 10
W = torch.tensor(np.random.normal(0, 0.01, (num_inputs, num_outputs)), dtype=torch.float, requires_grad=True)
b = torch.zeros(num_outputs, dtype=torch.float, requires_grad=True)
def net(X):
return softmax(torch.mm(X.view((-1, num_inputs)), W) + b)
使用pytorch的全连接层实现
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)
init.normal_(net.linear.weight, mean=0, std=0.01)
init.constant_(net.linear.bias, val=0)
### softmax实现
def softmax(X):
X_exp = X.exp()
partition = X_exp.sum(dim=1, keepdim=True)
return X_exp / partition
定义损失函数
自定义实现交叉熵
def cross_entropy(y_hat, y):
return - torch.log(y_hat.gather(1, y.view(-1, 1)))
pytorch提供的交叉熵
这是一个包括softmax运算和交叉熵损失计算的函数
loss = nn.CrossEntropyLoss()
定义优化方法
自定义随机梯度下降
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
pytorch提供的优化器
optimizer = torch.optim.SGD(net.parameters(), lr=0.1)
开始训练
num_epochs, lr = 5, 0.1
def train(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()
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))
完整代码
使用autograd实现
import torch
import torchvision
import numpy as np
import torchvision.transforms as transforms
import sys
from matplotlib import pyplot as plt
mnist_train = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', train=True, download=True, transform=transforms.ToTensor())
mnist_test = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', train=False, download=True, transform=transforms.ToTensor())
def get_fashion_mnist_labels(labels):
text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
return [text_labels[int(i)] for i in labels]
def load_data_fashion_mnist(mnist_train, mnist_test, batch_size):
if sys.platform.startswith('win'):
num_workers = 0
else:
num_workers = 4
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)
return train_iter, test_iter
def show_fashion_mnist(images, labels):
_, 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()
batch_size = 256
train_iter, test_iter = load_data_fashion_mnist(mnist_train, mnist_test, batch_size)
num_inputs = 784
num_outputs = 10
W = torch.tensor(np.random.normal(0, 0.01, (num_inputs, num_outputs)), dtype=torch.float, requires_grad=True)
b = torch.zeros(num_outputs, dtype=torch.float, requires_grad=True)
def softmax(X):
X_exp = X.exp()
partition = X_exp.sum(dim=1, keepdim=True)
return X_exp / partition
def net(X):
return softmax(torch.mm(X.view((-1, num_inputs)), W) + b)
def cross_entropy(y_hat, y):
return - torch.log(y_hat.gather(1, y.view(-1, 1)))
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 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
num_epochs, lr = 5, 0.1
def train(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()
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(net, train_iter, test_iter, cross_entropy, num_epochs, batch_size, [W, b], lr)
X, y = iter(test_iter).next()
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[0:9], titles[0:9])
简洁实现
import torch
import torch.nn as nn
from torch.nn import init
import torchvision
import numpy as np
import torchvision.transforms as transforms
import sys
from matplotlib import pyplot as plt
mnist_train = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', train=True, download=True, transform=transforms.ToTensor())
mnist_test = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', train=False, download=True, transform=transforms.ToTensor())
def get_fashion_mnist_labels(labels):
text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
return [text_labels[int(i)] for i in labels]
def load_data_fashion_mnist(mnist_train, mnist_test, batch_size):
if sys.platform.startswith('win'):
num_workers = 0
else:
num_workers = 4
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)
return train_iter, test_iter
def show_fashion_mnist(images, labels):
_, 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()
batch_size = 256
train_iter, test_iter = load_data_fashion_mnist(mnist_train, mnist_test, batch_size)
num_inputs = 784
num_outputs = 10
class FlattenLayer(nn.Module):
def __init__(self):
super(FlattenLayer, self).__init__()
def forward(self, x): # x shape: (batch, *, *, ...)
return x.view(x.shape[0], -1)
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)
init.normal_(net.linear.weight, mean=0, std=0.01)
init.constant_(net.linear.bias, val=0)
loss = nn.CrossEntropyLoss()
optimizer = torch.optim.SGD(net.parameters(), lr=0.1)
num_epochs = 5
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(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()
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(net, train_iter, test_iter, loss, num_epochs, batch_size, None, None, optimizer)
X, y = iter(test_iter).next()
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[0:9], titles[0:9])