线性SVM分类器-PyTorch实现

之前使用Numpy实现了线性SVM分类器 - 线性SVM分类器。这一次使用PyTorch实现

简介

线性SVMsupport vector machine,支持向量机)分类器定义为特征空间上间隔最大的线性分类器模型,其学习策略是使得分类间隔最大化

其训练结果是使得正确类别的成绩至少比错误类别成绩高一个间隔$\triangle $

训练过程如下:

  • 首先对输入数据进行线性映射,得到分类成绩;
  • 然后,使用折页损失(hinge loss)函数计算损失值
  • 最后根据损失值进行梯度求导,反向传播

Hinge Loss

完整的损失值包括折页损失+正则化项

折页损失(hinge loss)计算表达式如下:

其中$i$表示批量数据中第$i$个样本,$y_{i}$表示第$i$个样本的正确类别,$j$表示不正确类别

正则化项使用L2范数:

前向计算

输入参数:

前向计算如下:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
def hinge_loss(outputs, labels):
"""
折页损失计算
:param outputs: 大小为(N, num_classes)
:param labels: 大小为(N)
:return: 损失值
"""
num_labels = len(labels)
corrects = outputs[range(num_labels), labels].unsqueeze(0).T

# 最大间隔
margin = 1.0
margins = outputs - corrects + margin
loss = torch.sum(torch.max(margins, 1)[0]) / len(labels)

# # 正则化强度
# reg = 1e-3
# loss += reg * torch.sum(weight ** 2)

return loss

MNIST训练

使用线性SVM训练MNIST数据集,训练参数如下:

  1. 学习率:1e-3
  2. 动量因子:0.9
  3. 批量大小:128
  4. 最大间隔:1.0

完整代码如下:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
# -*- coding: utf-8 -*-

"""
@date: 2020/3/1 下午2:38
@file: svm.py
@author: zj
@description:
"""

import time
import copy
import torch
import torch.nn as nn
import torch.optim as optim
from torch.utils.data import DataLoader
import torchvision.transforms as transforms
from torchvision.datasets import MNIST


def load_data():
transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.5,), (0.5,))
])

data_loaders = {}
data_sizes = {}
for name in ['train', 'val']:
data_set = MNIST('./data', download=True, transform=transform)
# 测试
# img, target = data_set.__getitem__(0)
# print(img.shape)
# print(target)
# exit(0)

data_loader = DataLoader(data_set, shuffle=True, batch_size=128, num_workers=8)
data_loaders[name] = data_loader
data_sizes[name] = len(data_set)
return data_loaders, data_sizes


def hinge_loss(outputs, labels):
"""
折页损失计算
:param outputs: 大小为(N, num_classes)
:param labels: 大小为(N)
:return: 损失值
"""
num_labels = len(labels)
corrects = outputs[range(num_labels), labels].unsqueeze(0).T

# 最大间隔
margin = 1.0
margins = outputs - corrects + margin
loss = torch.sum(torch.max(margins, 1)[0]) / len(labels)

# # 正则化强度
# reg = 1e-3
# loss += reg * torch.sum(weight ** 2)

return loss


def train_model(data_loaders, model, criterion, optimizer, lr_scheduler, num_epochs=25, device=None):
since = time.time()

best_model_weights = copy.deepcopy(model.state_dict())
best_acc = 0.0

for epoch in range(num_epochs):
print('Epoch {}/{}'.format(epoch, num_epochs - 1))
print('-' * 10)

# Each epoch has a training and validation phase
for phase in ['train', 'val']:
if phase == 'train':
model.train() # Set model to training mode
else:
model.eval() # Set model to evaluate mode

running_loss = 0.0
running_corrects = 0

# Iterate over data.
for inputs, labels in data_loaders[phase]:
# print(inputs.shape)
# print(labels.shape)
inputs = inputs.reshape(-1, 28 * 28)
inputs = inputs.to(device)
labels = labels.to(device)

# zero the parameter gradients
optimizer.zero_grad()

# forward
# track history if only in train
with torch.set_grad_enabled(phase == 'train'):
outputs = model(inputs)
# print(outputs.shape)
_, preds = torch.max(outputs, 1)
loss = criterion(outputs, labels)

# backward + optimize only if in training phase
if phase == 'train':
loss.backward()
optimizer.step()

# statistics
running_loss += loss.item() * inputs.size(0)
running_corrects += torch.sum(preds == labels.data)
if phase == 'train':
lr_scheduler.step()

epoch_loss = running_loss / data_sizes[phase]
epoch_acc = running_corrects.double() / data_sizes[phase]

print('{} Loss: {:.4f} Acc: {:.4f}'.format(
phase, epoch_loss, epoch_acc))

# deep copy the model
if phase == 'val' and epoch_acc > best_acc:
best_acc = epoch_acc
best_model_weights = copy.deepcopy(model.state_dict())

print()

time_elapsed = time.time() - since
print('Training complete in {:.0f}m {:.0f}s'.format(
time_elapsed // 60, time_elapsed % 60))
print('Best val Acc: {:4f}'.format(best_acc))

# load best model weights
model.load_state_dict(best_model_weights)
return model


if __name__ == '__main__':
device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')

data_loaders, data_sizes = load_data()
# print(data_loaders)
# print(data_sizes)

model = nn.Linear(28 * 28, 10).to(device)
# criterion = nn.CrossEntropyLoss()
criterion = hinge_loss
optimizer = optim.SGD(model.parameters(), lr=1e-3, momentum=0.9)
lr_schduler = optim.lr_scheduler.StepLR(optimizer, step_size=7, gamma=0.1)

train_model(data_loaders, model, criterion, optimizer, lr_schduler, num_epochs=25, device=device)

25轮迭代训练结果如下:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Epoch 0/24
----------
train Loss: 1.0502 Acc: 0.7911
val Loss: 1.0268 Acc: 0.8372

Epoch 1/24
----------
train Loss: 1.0214 Acc: 0.8622
val Loss: 1.0238 Acc: 0.8432

Epoch 2/24
----------
train Loss: 1.0180 Acc: 0.8713
val Loss: 1.0150 Acc: 0.8852
...
...
Epoch 24/24
----------
train Loss: 1.0075 Acc: 0.9049
val Loss: 1.0075 Acc: 0.9047

Training complete in 2m 52s
Best val Acc: 0.910633
坚持原创技术分享,您的支持将鼓励我继续创作!