图神经网络_03-基于图神经网络的节点表征学习

基于图神经网络的节点表征学习

图节点预测或边预测任务过程：使用图神经网络来生成节点表征，并通过基于监督学习的对图神经网络的训练，使得图神经网络学会产生高质量的节点表征。
高质量的节点表征能够用于衡量节点的相似性，同时高质量的节点表征也是准确分类节点的前提。

`Cora`数据集

Cora是一个论文引用网络，节点代表论文，如果两篇论文存在引用关系，则对应的两个节点之间存在边，各节点的属性都是一个1433维的词包特征向量。

获取并分析数据集

from torch_geometric.datasets import Planetoid
from torch_geometric.transforms import NormalizeFeaturesdataset = Planetoid(root='dataset', name='Cora', transform=NormalizeFeatures())print()
print(f'Dataset: {dataset}:')
print('======================')
print(f'Number of graphs: {len(dataset)}')
print(f'Number of features: {dataset.num_features}')
print(f'Number of classes: {dataset.num_classes}')data = dataset[0]  # Get the first graph object.print()
print(data)
print('======================')# Gather some statistics about the graph.
print(f'Number of nodes: {data.num_nodes}')
print(f'Number of edges: {data.num_edges}')
print(f'Average node degree: {data.num_edges / data.num_nodes:.2f}')
print(f'Number of training nodes: {data.train_mask.sum()}')
print(f'Training node label rate: {int(data.train_mask.sum()) / data.num_nodes:.2f}')
print(f'Contains isolated nodes: {data.contains_isolated_nodes()}')
print(f'Contains self-loops: {data.contains_self_loops()}')
print(f'Is undirected: {data.is_undirected()}')

运行结果：

Dataset: Cora():
======================
Number of graphs: 1
Number of features: 1433
Number of classes: 7Data(edge_index=[2, 10556], test_mask=[2708], train_mask=[2708], val_mask=[2708], x=[2708, 1433], y=[2708])
======================
Number of nodes: 2708
Number of edges: 10556
Average node degree: 3.90
Number of training nodes: 140
Training node label rate: 0.05
Contains isolated nodes: False
Contains self-loops: False
Is undirected: True

从结果得出，Cora图是无向图，拥有2708个节点，无孤立节点，10556条边，平均节点度为3.9，训练集使用了140个节点，占整体的5%。

可视化节点表征分布

利用TSNE方法将高维的节点表征映射到二维平面空间，然后在二维平面画出节点来实现节点表征分布的可视化。

import matplotlib.pyplot as plt
from sklearn.manifold import TSNEdef visualize(x, y):z = TSNE(n_components=2).fit_transform(x.detach().cpu().numpy())plt.figure(figsize=(10,10))plt.xticks([])plt.yticks([])plt.scatter(z[:, 0], z[:, 1], s=70, c=y, cmap="Set2")plt.show()visualize(data.x, data.y)

使用MLP神经网络进行节点分类

下面构建了一个简单的MLP神经网络,只对输入节点的表征做变换，在所有节点之间共享权重。
第一个线程层将1433维的节点表征嵌入（embedding）到低维空间中（hidden_channels=16），第二个线性层将节点表征嵌入到类别空间中（num_classes=7）。

MLP神经网络

模型

import torch
from torch.nn import Linear
import torch.nn.functional as Fclass MLP(torch.nn.Module):def __init__(self, hidden_channels):super(MLP, self).__init__()torch.manual_seed(12345)self.lin1 = Linear(dataset.num_features, hidden_channels)self.lin2 = Linear(hidden_channels, dataset.num_classes)def forward(self, x):x = self.lin1(x)x = x.relu()x = F.dropout(x, p=0.5, training=self.training)x = self.lin2(x)return xmodel = MLP(hidden_channels=16)
print(model)

MLP((lin1): Linear(in_features=1433, out_features=16, bias=True)(lin2): Linear(in_features=16, out_features=7, bias=True)
)

训练

model = MLP(hidden_channels=16)
criterion = torch.nn.CrossEntropyLoss()  # Define loss criterion.
optimizer = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4)  # Define optimizer.def train():model.train()optimizer.zero_grad()  # Clear gradients.out = model(data.x)  # Perform a single forward pass.loss = criterion(out[data.train_mask], data.y[data.train_mask])  # Compute the loss solely based on the training nodes.loss.backward()  # Derive gradients.optimizer.step()  # Update parameters based on gradients.return lossfor epoch in range(1, 201):loss = train()print(f'Epoch: {epoch:03d}, Loss: {loss:.4f}')

Epoch: 001, Loss: 1.9615
Epoch: 002, Loss: 1.9557
Epoch: 003, Loss: 1.9505
Epoch: 004, Loss: 1.9423
Epoch: 005, Loss: 1.9327
...
Epoch: 196, Loss: 0.3615
Epoch: 197, Loss: 0.3985
Epoch: 198, Loss: 0.4664
Epoch: 199, Loss: 0.3714
Epoch: 200, Loss: 0.3810

3.测试

def test():model.eval()out = model(data.x)pred = out.argmax(dim=1)  # Use the class with highest probability.test_correct = pred[data.test_mask] == data.y[data.test_mask]  # Check against ground-truth labels.test_acc = int(test_correct.sum()) / int(data.test_mask.sum())  # Derive ratio of correct predictions.return test_acctest_acc = test()
print(f'Test Accuracy: {test_acc:.4f}')

Test Accuracy: 0.5900

MLP只有大约59%的测试准确性，该模型表现不佳。

MLP表现不佳其中一个重要原因是，用于训练此神经网络的有标签节点数量过少，产生了过拟合，所以泛化能力较差。

卷积图神经网络（GCN）

PyG中GCNConv 模块说明

GCNConv函数：

GCNConv(in_channels: int, out_channels: int, improved: bool = False, cached: bool = False, add_self_loops: bool = True, normalize: bool = True, bias: bool = True, **kwargs)

in_channels：输入数据维度；
out_channels：输出数据维度；
improved：如果为true， $\mathbf{\hat{A}} = \mathbf{A} + 2\mathbf{I}$ ，其目的在于增强中心节点自身信息；
cached：是否存储 $\mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2}$ 的计算结果以便后续使用，这个参数只应在归纳学习（transductive learning）的场景中设置为true（归纳学习可以简单理解为在训练、验证、测试、推理（inference）四个阶段都只使用一个数据集）；
add_self_loops：是否在邻接矩阵中增加自环边；
normalize：是否添加自环边并在运行中计算对称归一化系数；
bias：是否包含偏置项。

GCNConv官方文档。

模型
将MLP中的torch.nn.Linear替换成torch_geometric.nn.GCNConv，就可以得到一个GCN图神经网络

from torch_geometric.nn import GCNConvclass GCN(torch.nn.Module):def __init__(self, hidden_channels):super(GCN, self).__init__()torch.manual_seed(12345)self.conv1 = GCNConv(dataset.num_features, hidden_channels)self.conv2 = GCNConv(hidden_channels, dataset.num_classes)def forward(self, x, edge_index):x = self.conv1(x, edge_index)x = x.relu()x = F.dropout(x, p=0.5, training=self.training)x = self.conv2(x, edge_index)return x

未经训练的GCN图神经网络生成的节点表征可视化

model = GCN(hidden_channels=16)
model.eval()out = model(data.x, data.edge_index)
visualize(out, color=data.y)

通过visualize函数的可视化处理，7维特征的节点被映射到2维的平面上，能看到“同类节点群聚”的现象。
在这里插入图片描述

训练

model = GCN(hidden_channels=16)
optimizer = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4)
criterion = torch.nn.CrossEntropyLoss()def train():      model.train()      optimizer.zero_grad()  # Clear gradients.      out = model(data.x, data.edge_index)  # Perform a single forward pass.      loss = criterion(out[data.train_mask], 		data.y[data.train_mask])  # Compute the loss solely based on the training nodes.      loss.backward()  # Derive gradients.      optimizer.step()  # Update parameters based on gradients.      return lossfor epoch in range(1, 201):    loss = train()    print(f'Epoch: {epoch:03d}, Loss: {loss:.4f}')

测试

def test():model.eval()out = model(data.x, data.edge_index)pred = out.argmax(dim=1)  # Use the class with highest probability.test_correct = pred[data.test_mask] == data.y[data.test_mask]  # Check against ground-truth labels.test_acc = int(test_correct.sum()) / int(data.test_mask.sum())  # Derive ratio of correct predictions.return test_acctest_acc = test()
print(f'Test Accuracy: {test_acc:.4f}')

Test Accuracy: 0.8140

仅仅将torch.nn.Linear替换成torch_geometric.nn.GCNConv，我们获得了81.4%的测试准确率！与MLP图神经网络相比，GCN图神经网络准确性要高很多。这表明节点的邻接信息在取得更好的准确率方面起着关键作用。

训练后的GCN图神经网络生成的节点表征可视化
再来执行一遍可视化代码

model.eval()
out = model(data.x, data.edge_index)
visualize(out, color=data.y)

在这里插入图片描述
由可视化训练后的GCN图神经网络生成的节点表征，我们会发现“同类节点群聚”的现象更加明显了。说明GCN图神经网络生成的节点表征质量更高了。

图注意力神经网络（GAT）

PyG中GATConv 模块说明

GATConv构造函数接口：

GATConv(in_channels: Union[int, Tuple[int, int]], out_channels: int, heads: int = 1, concat: bool = True, negative_slope: float = 0.2, dropout: float = 0.0, add_self_loops: bool = True, bias: bool = True, **kwargs)

in_channels：输入数据维度；
out_channels：输出数据维度；
heads：在GATConv使用多少个注意力模型（Number of multi-head-attentions）；
concat：如为true，不同注意力模型得到的节点表征被拼接到一起（表征维度翻倍），否则对不同注意力模型得到的节点表征求均值；

GATConv官方文档

GAT图神经网络的构造

将MLP神经网络例子中的torch.nn.Linear替换成torch_geometric.nn.GATConv，来实现GAT图神经网络的构造

import torch
import torch.nn.functional as Ffrom torch_geometric.nn import GATConvclass GAT(torch.nn.Module):def __init__(self, hidden_channels):super(GAT, self).__init__()torch.manual_seed(12345)self.conv1 = GATConv(dataset.num_features, hidden_channels)self.conv2 = GATConv(hidden_channels, dataset.num_classes)def forward(self, x, edge_index):x = self.conv1(x, edge_index)x = x.relu()x = F.dropout(x, p=0.5, training=self.training)x = self.conv2(x, edge_index)return x