自编码器AutoEncoder

绝地灬酷狼 2021-10-15 10:29 751阅读 0赞

### 文章目录 ###

*   *  一. 什么是自编码器
     *  二. 有什么作用
     *   *  1) 图像去噪
         *  2) 可视化降维
     *  三. 如何实现
     *   *  1) 全连接层实现
         *  2) 测试: 对有噪声图像的自编码
         *  3) 卷积层实现
     *  四. 一些小细节

## 一. 什么是自编码器 ##

自动编码器 autoencoder, 简单表现编码器为将一组数据进行压缩编码(降维), 解码器将这组数据恢复成高维的数据. 这种编码和解码的过程不是无损的, 因此最终的输出和输入是有一些差异的, 且非常依赖于训练的数据集.

如图所示  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70]

如上面这张图所示, 对于一个简单的三层线性神经网络组成的自编码器, 我们在进行神经网络的搭建过程中, 将(input, hidden) 这个过程叫做编码器, 将(hidden, output) 这个过程叫做解码器. 对于mnist数据集而言, 它的维度变化是 784 -> x -> 784, 其中, x < 784, 是编码的维度.

--------------------

## 二. 有什么作用 ##

### 1) 图像去噪 ###

看上去很强啊  
![在这里插入图片描述][20190813222525217.png]

### 2) 可视化降维 ###

--------------------

## 三. 如何实现 ##

训练神经网络需要定义损失函数, 那么这个自编码器的损失衡量值是什么?

衡量损失的值是由网络的输出结果和输入决定的. 也就是说, 是由这两个784维数据的差别决定的.

### 1) 全连接层实现 ###

首先定义一个神经网络

class Autoencoder(nn.Module):
        def __init__(self, encoding_dim):
            super(Autoencoder, self).__init__()
            ## encoder ##
            self.encoder = nn.Linear(784, encoding_dim)
            
            ## decoder ##
            self.decoder = nn.Linear(encoding_dim, 784)
            
    
        def forward(self, x):
            # define feedforward behavior 
            # and scale the *output* layer with a sigmoid activation function
    # print(x.shape)
            x = x.view(-1, 784)
            x = F.relu(self.encoder(x))
            x = torch.sigmoid(self.decoder(x))
            return x
    
    # initialize the NN
    encoding_dim = 128
    model = Autoencoder(encoding_dim)

定义损失函数和优化器

# specify loss function
    criterion = nn.MSELoss()
    
    # specify loss function
    optimizer = torch.optim.Adam(model.parameters(), lr=0.001)

训练过程, 一共20个epochs, 话说pytorch还真慢, 这么简单的网络都要训练好一会

# number of epochs to train the model
    n_epochs = 20
    
    for epoch in range(1, n_epochs+1):
        # monitor training loss
        train_loss = 0.0
        
        ###################
        # train the model #
        ###################
        for data in train_loader:
            # _ stands in for labels, here
            images, _ = data
            # flatten images
            images = images.view(images.size(0), -1)
            # clear the gradients of all optimized variables
            optimizer.zero_grad()
            # forward pass: compute predicted outputs by passing inputs to the model
    # print(images.shape)
            outputs = model(images)
            # calculate the loss
            loss = criterion(outputs, images)
            # backward pass: compute gradient of the loss with respect to model parameters
            loss.backward()
            # perform a single optimization step (parameter update)
            optimizer.step()
            # update running training loss
            train_loss += loss.item()*images.size(0)
                
        # print avg training statistics 
        train_loss = train_loss/len(train_loader)
        print('Epoch: {} \tTraining Loss: {:.6f}'.format(
            epoch, 
            train_loss
            ))

训练过程的损失变化

Epoch: 1 	Training Loss: 0.342308
    Epoch: 2 	Training Loss: 0.081272
    Epoch: 3 	Training Loss: 0.058724
    Epoch: 4 	Training Loss: 0.051274
    Epoch: 5 	Training Loss: 0.047382
    Epoch: 6 	Training Loss: 0.044760
    Epoch: 7 	Training Loss: 0.043184
    Epoch: 8 	Training Loss: 0.042066
    Epoch: 9 	Training Loss: 0.041246
    Epoch: 10 	Training Loss: 0.040589
    Epoch: 11 	Training Loss: 0.040059
    Epoch: 12 	Training Loss: 0.039646
    Epoch: 13 	Training Loss: 0.039272
    Epoch: 14 	Training Loss: 0.038980
    Epoch: 15 	Training Loss: 0.038733
    Epoch: 16 	Training Loss: 0.038524
    Epoch: 17 	Training Loss: 0.038328
    Epoch: 18 	Training Loss: 0.038162
    Epoch: 19 	Training Loss: 0.038012
    Epoch: 20 	Training Loss: 0.037874

那么效果如何呢? 上面一排是输入图像, 下面一排是输出图像. 经过自编码器之后, 还原度还是很高的.

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 1]

### 2) 测试: 对有噪声图像的自编码 ###

首先查看一张图片

a_img = np.squeeze(images[0])
    print(a_img.shape)
    print(np.max(a_img))
    print(np.min(a_img))
    
    plt.imshow(a_img, cmap='gray')

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 2]  
然后向其中加入噪声

a_img_x = a_img + 0.08 * np.random.normal(loc=0.0, scale=1.0, size=a_img.shape)
    
    plt.imshow(a_img_x, cmap='gray')

这是加入噪声之后的图片, 可以看出差别还是很大的. 那么我们的编码器能还原出如何的效果呢?  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 3]

a_img_output = model(torch.Tensor(a_img_x).view(1, -1))
    print(a_img_output.shape)
    
    output_img = a_img_output.view(28, 28)
    output_img = output_img.detach().numpy()
    
    plt.imshow(output_img, cmap='gray')

这是还原后的, 说实话看到这个图片我心里也是很惊讶的. 就在于加入那么多噪声之后, 居然还可以还原的如此清晰. 当然这是对于MNIST数据集而言, 这个数据集比较简单.  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 4]

### 3) 卷积层实现 ###

不同之处在于定义自编码器的神经网络结构  
如图所示  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 5]  
可以看到在decoder中经过了两个反卷积层, 但是由于水平有限, 这个反卷积层看着好奇怪, 不知道是怎么反卷积的.

pytorch实现

import torch.nn as nn
    import torch.nn.functional as F
    
    # define the NN architecture
    class ConvAutoencoder(nn.Module):
        def __init__(self):
            super(ConvAutoencoder, self).__init__()
            ## encoder layers ##
            self.conv1 = nn.Conv2d(1, 16, 3, padding=1)
            self.conv2 = nn.Conv2d(16, 4, 3, padding=1)
            
            self.pool = nn.MaxPool2d(2, 2)        
            
            ## decoder layers ##
            ## a kernel of 2 and a stride of 2 will increase the spatial dims by 2
            self.t_conv1 = nn.ConvTranspose2d(4, 16, 2, stride=2)
            self.t_conv2 = nn.ConvTranspose2d(16, 1, 2, stride=2)
    
    
        def forward(self, x):
            ## encode ##
            
            ## decode ##
            ## apply ReLu to all hidden layers *except for the output layer
            ## apply a sigmoid to the output layer
            x = F.relu(self.conv1(x))
            x = self.pool(x)
            x = F.relu(self.conv2(x))
            x = self.pool(x)
            
            x = F.relu(self.t_conv1(x))
            x = torch.sigmoid(self.t_conv2(x))
                    
            return x
    
    # initialize the NN
    model = ConvAutoencoder()
    print(model)

训练起来比全连接层的网络还要慢很多, 而损失值的降低也慢很多, 不像之前从epoch 1 到 epoch 2 直接就断崖式下跌了. 下面是损失值的变化过程, 只训练了 15个epoch. 从损失之上看这个效果好像差很多?

Epoch: 1 	Training Loss: 0.448799
    Epoch: 2 	Training Loss: 0.266815
    Epoch: 3 	Training Loss: 0.251290
    Epoch: 4 	Training Loss: 0.240823
    Epoch: 5 	Training Loss: 0.231836
    Epoch: 6 	Training Loss: 0.220550
    Epoch: 7 	Training Loss: 0.210341
    Epoch: 8 	Training Loss: 0.202768
    Epoch: 9 	Training Loss: 0.197010
    Epoch: 10 	Training Loss: 0.193259
    Epoch: 11 	Training Loss: 0.190589
    Epoch: 12 	Training Loss: 0.188406
    Epoch: 13 	Training Loss: 0.186529
    Epoch: 14 	Training Loss: 0.184983
    Epoch: 15 	Training Loss: 0.183579

观察下图的数字9的话, 可以看到损失了不少.  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 6]

**再看看噪声图片的处理能力如何**

原图:  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 7]  
加入噪声:  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 8]  
经过自编码器  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 9]  
呃, 效果似乎有点不是很对, 可能是训练的epoch太少了, 毕竟我们可以前面看到训练15个epoch的损失值还是达到了0.18, 而在全连接层的简单自编码器上第二个epoch的损失值就达到了0.08

另一张图片

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 10]  
噪声  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 11]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 12]

--------------------

## 四. 一些小细节 ##

1.  numpy 的 squeeze 函数  
    [参考博客][Link 1]  
    作用：**从数组的形状中删除单维度条目，即把shape中为1的维度去掉**
2.  给MNIST图片加入噪声的方法

test_img_x = test_img + 0.08 * np.random.normal(loc=0.0, scale=1.0, size=test_img.shape)

就是加入一些随机值, 在原图的基础上进行小幅度修改.

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70]: /images/20211015/db325742f0564256930eca823e9226ee.png
[20190813222525217.png]: /images/20211015/f37d6495de9045ae80c1f28a63faba2c.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dqaDI2MjIwNzUxMjc_size_16_color_FFFFFF_t_70 1]: /images/20211015/18b3d4e970a44406a6cc04ad30b4c310.png
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[Link 1]: https://blog.csdn.net/zenghaitao0128/article/details/78512715