如何利用深度学习中的AutoEncoder进行特征降维和特征可视化，pytorch代码

我们将使用 Pytorch 中的 AutoEncoder(自动编码器架构)来减少特征维度和可视化。
北大出版社，人工智能原理与实践人工智能和数据科学从入门到精通详解机器学习深度学习算法原理

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首先，要安装 PyTorch，您可以使用以下 pip 命令，

$ pip install torch torchvision

torchvision 包含可在 PyTorch 中使用的图像数据集。

安装

导入相关依赖

import matplotlib.pyplot as plt
import numpy as np

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision

设置随机种子和其他配置以实现可重复性。

seed = 21
torch.manual_seed(seed)
torch.backends.cudnn.benchmark = False
torch.backends.cudnn.deterministic = True

设置batch大小、训练epoch数和学习率。

batch_size = 512
epochs = 50
learning_rate = 1e-3

获取数据

使用 torchvision 包加载 MNIST 数据集作为方便的示例。

transform = torchvision.transforms.Compose([torchvision.transforms.ToTensor()])

train_dataset = torchvision.datasets.MNIST(
    root="~/torch_datasets", train=True, transform=transform, download=True
)

train_loader = torch.utils.data.DataLoader(
    train_dataset, batch_size=batch_size, shuffle=True
)

检查其中一个数据点

examples = enumerate(train_loader)
batch_idx, (example_data, example_targets) = next(examples)

example_data[0][0].max()

tensor(1.)

Autoencoder

自动编码器是一种神经网络，它找到将特征 x 映射到自身的函数。这个目标被称为重建，自动编码器通过以下过程实现这一目标：
(1) 编码器学习低维空间中的数据表示，
(2) 解码器根据编码器学习到的表征学习重建原始数据。

在下文中，我们为其编码器和解码器组件定义了具有完全连接层和激活函数的自动编码器类。

from torch import Tensor

class AE(nn.Module):
    def __init__(self, **kwargs):
        super().__init__()
        self.encoder_hidden_layer = nn.Linear(
            in_features=kwargs["input_shape"], out_features=1000
        )
        self.encoder_output_layer = nn.Linear(
            in_features=1000, out_features=128
        )
        self.encoder_output_layer2 = nn.Linear(
            in_features=128, out_features=32
        )
        self.encoder_output_layer3 = nn.Linear(
            in_features=32, out_features=2
        )
        
        
            
        self.decoder_hidden_layer = nn.Linear(
            in_features=2, out_features=32
        )
        self.decoder_hidden_layer2 = nn.Linear(
            in_features=32, out_features=128
        )
        self.decoder_hidden_layer3 = nn.Linear(
            in_features=128, out_features=1000
        )
        
        
        self.decoder_output_layer = nn.Linear(
            in_features=1000, out_features=kwargs["input_shape"]
        )


    
    def encode(self, features: Tensor) -> Tensor:
        code = self.encoder_hidden_layer(features)
        code = torch.relu(code)
        code = self.encoder_output_layer(code)
        code = torch.relu(code)
        code = self.encoder_output_layer2(code)
        code = torch.relu(code)
        code = self.encoder_output_layer3(code)
        
        return code

    def decode(self, encoded: Tensor) -> Tensor:
        
        encode = self.decoder_hidden_layer(encoded)
        encode = torch.relu(encode)
        encode = self.decoder_hidden_layer2(encode)
        encode = torch.relu(encode)
        encode = self.decoder_hidden_layer3(encode)
        encode = torch.relu(encode)
        encode = self.decoder_output_layer(encode)
        reconstructed = torch.sigmoid(encode)
        
        return reconstructed   
    
    def forward(self, features: Tensor) -> Tensor:
        encoded = self.encode(features)
        return self.decode(encoded)

在使用我们定义的自动编码器类之前，我们需要做以下事情：
1. 我们配置要在哪个设备上运行。
2. 我们实例化一个 AE 对象。
3. 我们定义我们的优化器。
4. 我们定义重建损失。

#  use gpu if available
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

# create a model from `AE` autoencoder class
# load it to the specified device, either gpu or cpu
model = AE(input_shape=784).to(device)

# create an optimizer object
# Adam optimizer with learning rate 1e-3
optimizer = optim.Adam(model.parameters(), lr=learning_rate)

# mean-squared error loss
criterion = nn.MSELoss()

训练AutoEncoder模型

for epoch in range(epochs):
    loss = 0
    for batch_features, _ in train_loader:
        # reshape mini-batch data to [N, 784] matrix
        # load it to the active device
        batch_features = batch_features.view(-1, 784).to(device)
        
        # reset the gradients back to zero
        # PyTorch accumulates gradients on subsequent backward passes
        optimizer.zero_grad()
        
        # compute reconstructions
        outputs = model(batch_features)
        
        # compute training reconstruction loss
        train_loss = criterion(outputs, batch_features)
        
        # compute accumulated gradients
        train_loss.backward()
        
        # perform parameter update based on current gradients
        optimizer.step()
        
        # add the mini-batch training loss to epoch loss
        loss += train_loss.item()
    
    # compute the epoch training loss
    loss = loss / len(train_loader)
    
    # display the epoch training loss
    print("epoch : {}/{}, recon loss = {:.8f}".format(epoch + 1, epochs, loss))

epoch : 1/50, recon loss = 0.07389576
epoch : 2/50, recon loss = 0.05296296
epoch : 3/50, recon loss = 0.04810659
epoch : 4/50, recon loss = 0.04541392
epoch : 5/50, recon loss = 0.04336656
epoch : 6/50, recon loss = 0.04195889
epoch : 7/50, recon loss = 0.04092639
epoch : 8/50, recon loss = 0.04033839
epoch : 9/50, recon loss = 0.03984492
epoch : 10/50, recon loss = 0.03948938
epoch : 11/50, recon loss = 0.03939159
epoch : 12/50, recon loss = 0.03877884
epoch : 13/50, recon loss = 0.03859487
epoch : 14/50, recon loss = 0.03825530
epoch : 15/50, recon loss = 0.03797148
epoch : 16/50, recon loss = 0.03789599
epoch : 17/50, recon loss = 0.03754379
epoch : 18/50, recon loss = 0.03740290
epoch : 19/50, recon loss = 0.03735819
epoch : 20/50, recon loss = 0.03729593
epoch : 21/50, recon loss = 0.03699356
epoch : 22/50, recon loss = 0.03768872
epoch : 23/50, recon loss = 0.03694447
epoch : 24/50, recon loss = 0.03680794
epoch : 25/50, recon loss = 0.03654349
epoch : 26/50, recon loss = 0.03630730
epoch : 27/50, recon loss = 0.03620429
epoch : 28/50, recon loss = 0.03615394
epoch : 29/50, recon loss = 0.03615029
epoch : 30/50, recon loss = 0.03593704
epoch : 31/50, recon loss = 0.03589566
epoch : 32/50, recon loss = 0.03570651
epoch : 33/50, recon loss = 0.03599412
epoch : 34/50, recon loss = 0.03587519
epoch : 35/50, recon loss = 0.03641265
epoch : 36/50, recon loss = 0.03615064
epoch : 37/50, recon loss = 0.03541873
epoch : 38/50, recon loss = 0.03545310
epoch : 39/50, recon loss = 0.03534035
epoch : 40/50, recon loss = 0.03541123
epoch : 41/50, recon loss = 0.03511182
epoch : 42/50, recon loss = 0.03499481
epoch : 43/50, recon loss = 0.03487989
epoch : 44/50, recon loss = 0.03506399
epoch : 45/50, recon loss = 0.03487079
epoch : 46/50, recon loss = 0.03481269
epoch : 47/50, recon loss = 0.03454635
epoch : 48/50, recon loss = 0.03444027
epoch : 49/50, recon loss = 0.03448961
epoch : 50/50, recon loss = 0.03482613

让我们提取一些测试示例以使用我们训练有素的自动编码器进行重构。

test_dataset = torchvision.datasets.MNIST(
    root="~/torch_datasets", train=False, transform=transform, download=True
)

test_loader = torch.utils.data.DataLoader(
    test_dataset, batch_size=10, shuffle=False
)

test_examples = None

# loop the test data once to get the first batch of 10 datapoints for reconstruction quality check
with torch.no_grad():
    for batch_features in test_loader:
        batch_features = batch_features[0]
        test_examples = batch_features.view(-1, 784)
        reconstruction = model(test_examples)
        reconstruction_hidden = model.encode(test_examples)
        break

检查数据重建质量

让我们尝试使用我们训练有素的自动编码器重建一些测试图像。

with torch.no_grad():
    number = 10
    plt.figure(figsize=(20, 4))
    for index in range(number):
        # display original
        ax = plt.subplot(2, number, index + 1)
        plt.imshow(test_examples[index].numpy().reshape(28, 28))
        plt.gray()
        ax.get_xaxis().set_visible(False)
        ax.get_yaxis().set_visible(False)

        # display reconstruction
        ax = plt.subplot(2, number, index + 1 + number)
        plt.imshow(reconstruction[index].numpy().reshape(28, 28))
        plt.gray()
        ax.get_xaxis().set_visible(False)
        ax.get_yaxis().set_visible(False)
    plt.show()

在这里插入图片描述

结果分析

正如我们所看到的，重建是好的，但不是特别好；这主要是因为我们只使用 2 个节点中间隐藏层。仅使用 2 个节点很容易让我们看到减少的维度，但可能不够好捕捉所有重要特征。为了纯粹的特征减少目的，我们可以选择更多的节点
对于中间隐藏层。

可视化具有 2 个节点的中间隐藏层以降低维度

# reduce dimension example

results =[]
with torch.no_grad():
    for batch_features in test_loader:
        batch_features = batch_features[0]
        test_examples = batch_features.view(-1, 784)
        reconstruction_hidden = model.encode(test_examples)
        results.append(reconstruction_hidden.numpy())

import numpy as np
all_hidden = np.concatenate(results)
all_hidden

array([[-0.43485078,  0.31671965],
       [ 1.5935664 ,  4.4088674 ],
       [ 9.075943  ,  4.4781566 ],
       ...,
       [-0.90027434,  0.3994102 ],
       [-2.9567816 ,  2.2586362 ],
       [-4.884531  ,  1.9589175 ]], dtype=float32)

labels = test_dataset.targets.numpy()

import pandas as pd
rdf = pd.DataFrame(all_hidden)
rdf['lable'] = labels
rdf.columns = ['x','y','label']

from matplotlib import pyplot as plt
import seaborn as sns

plt.figure(figsize=(15,8))  
sns.scatterplot(data=rdf,x='x',y='y',hue='label')

<AxesSubplot:xlabel='x', ylabel='y'>

在这里插入图片描述

代码链接

文末有代码下载链接

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北大出版社，人工智能原理与实践人工智能和数据科学从入门到精通详解机器学习深度学习算法原理

人工智能原理与实践全面涵盖人工智能和数据科学各个重要体系经典