深度学习中降维的几种方法

笔者在搞网络的时候碰到个问题，就是将特征维度从1024降维到268，那么可以通过哪些深度学习方法来实现呢？

1. 卷积层降维

可以使用1x1卷积层（也叫pointwise卷积）来减少通道数。这种方法保留了特征图的空间维度（宽度和高度），同时减少了通道数。

import torch
import torch.nn as nn

class ReduceDim(nn.Module):
    def __init__(self, in_channels, out_channels):
        super(ReduceDim, self).__init__()
        self.conv1x1 = nn.Conv2d(in_channels, out_channels, kernel_size=1)

    def forward(self, x):
        return self.conv1x1(x)

# 假设输入的特征图为 (bs, 1024, 28, 28)
x = torch.randn(56, 1024, 28, 28)
model = ReduceDim(1024, 268)
output = model(x)
print(output.shape)  # 输出形状应为 (56, 268, 28, 28)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

2. 全连接层降维

可以将特征图展平为一个向量，然后使用全连接层（线性层）来降维。这种方法适用于特征图的全局降维。

class ReduceDimFC(nn.Module):
    def __init__(self, in_channels, out_channels, width, height):
        super(ReduceDimFC, self).__init__()
        self.fc = nn.Linear(in_channels * width * height, out_channels * width * height)
        self.width = width
        self.height = height

    def forward(self, x):
        bs, c, w, h = x.shape
        x = x.view(bs, -1)
        x = self.fc(x)
        x = x.view(bs, out_channels, self.width, self.height)
        return x

# 假设输入的特征图为 (bs, 1024, 28, 28)
x = torch.randn(56, 1024, 28, 28)
model = ReduceDimFC(1024, 268, 28, 28)
output = model(x)
print(output.shape)  # 输出形状应为 (56, 268, 28, 28)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

3. 使用注意力机制

可以使用基于注意力机制的方法来降维。例如，可以使用Transformer编码器或自注意力机制来实现降维。

import torch
import torch.nn as nn

class ReduceDimAttention(nn.Module):
    def __init__(self, in_channels, out_channels):
        super(ReduceDimAttention, self).__init__()
        self.attention = nn.MultiheadAttention(embed_dim=in_channels, num_heads=8)
        self.fc = nn.Linear(in_channels, out_channels)

    def forward(self, x):
        bs, c, w, h = x.shape
        x = x.view(bs, c, -1).permute(2, 0, 1)  # (w*h, bs, c)
        x, _ = self.attention(x, x, x)
        x = x.permute(1, 2, 0).view(bs, c, w, h)
        x = self.fc(x.permute(0, 2, 3, 1)).permute(0, 3, 1, 2)
        return x

# 假设输入的特征图为 (bs, 1024, 28, 28)
x = torch.randn(56, 1024, 28, 28)
model = ReduceDimAttention(1024, 268)
output = model(x)
print(output.shape)  # 输出形状应为 (56, 268, 28, 28)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22

4. 使用自编码器

可以训练一个自编码器网络来学习降维。自编码器由编码器和解码器组成，通过最小化重建误差来学习紧凑的表示。

class Encoder(nn.Module):
    def __init__(self, in_channels, out_channels):
        super(Encoder, self).__init__()
        self.conv1 = nn.Conv2d(in_channels, 512, kernel_size=3, padding=1)
        self.conv2 = nn.Conv2d(512, out_channels, kernel_size=3, padding=1)

    def forward(self, x):
        x = torch.relu(self.conv1(x))
        x = torch.relu(self.conv2(x))
        return x

class Decoder(nn.Module):
    def __init__(self, in_channels, out_channels):
        super(Decoder, self).__init__()
        self.conv1 = nn.Conv2d(in_channels, 512, kernel_size=3, padding=1)
        self.conv2 = nn.Conv2d(512, out_channels, kernel_size=3, padding=1)

    def forward(self, x):
        x = torch.relu(self.conv1(x))
        x = torch.relu(self.conv2(x))
        return x

class Autoencoder(nn.Module):
    def __init__(self, in_channels, bottleneck_channels, out_channels):
        super(Autoencoder, self).__init__()
        self.encoder = Encoder(in_channels, bottleneck_channels)
        self.decoder = Decoder(bottleneck_channels, out_channels)

    def forward(self, x):
        x = self.encoder(x)
        x = self.decoder(x)
        return x

# 假设输入的特征图为 (bs, 1024, 28, 28)
x = torch.randn(56, 1024, 28, 28)
model = Autoencoder(1024, 268, 1024)
encoded = model.encoder(x)
print(encoded.shape)  # 输出形状应为 (56, 268, 28, 28)
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

以上方法都是有效的深度学习降维技术，可以根据具体的需求和应用场景选择合适的方法。Enjoy~

$${\sim }_{Onepersongofaster,agroupofpeoplecangofurther}\sim$$