进入实战阶段~~~
数据准备
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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，那么认为对应的两个节点之间存在边，每个节点由一个1433维的词包特征向量描述。我们的任务是推断每个文档的类别（共7类）。 - 为了展现图神经网络的强大，我们通过节点分类任务来比较MLP和GCN, GAT（两个知名度很高的图神经网络）三者的节点表征学习能力。
dataset = Planetoid(root='./dataset/Cora', name='Cora', transform=NormalizeFeatures())
print()
print(f'Dataset:{dataset}:')
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]
print()
print(data)
print('===========')
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()}')
# result:
Number of graphs: 1
Number of features: 1433
Number of classes: 7
MLP模型
# MLP model
import torch
from torch.nn import Linear
import torch.nn.functional as F
class 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 x
model = MLP(hidden_channels=16)
print(model)
MLP的训练与测试
- MLP的模型还是比较简单，老少皆宜的
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[data.train_mask]) # Perform a single forward pass.
loss = criterion(out, 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.
model.eval()
val_out = model(data.x[data.val_mask])
val_loss = criterion(val_out, data.y[data.val_mask])
return loss, val_loss
for epoch in range(1, 201):
loss, val_loss = train()
print(f'Epoch: {epoch:03d}, Loss: {loss:.4f}, valid loss: {val_loss:.4f}')
def test():
model.eval()
out = model(data.x[data.test_mask])
pred = out.argmax(dim=1) # Use the class with highest probability.
test_correct = pred == 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_acc
test_acc = test()
print(f'Test Accuracy: {test_acc:.4f}')
# result: 59%
由此可以看出，MLP用于此任务的准确率很低，并且训练和评估损失差别较大。
推测是因为训练数据较少（5%左右）导致过拟合。
-
原始数据image.png
-
使用MLP：
image.png
GCN模型
- Paper：Semi-supervised Classification with Graph Convolutional Network
image.png -
卷积核在图像上对应位置相乘后累加求和,表达式为：
image.png - 其中I为图像，K为卷积核，σ 为激活函数。
# GCN图节点分类神经网络
from torch_geometric.nn import GCNConv
class 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
model = GCN(hidden_channels=16)
print(model)
# result：81.4%
-
原始数据：
-
使用GCN：
image.png
GAT模型
- Paper：Graph Attention Networks
-
数学表达式：
image.png - 实质上是加入attention的聚集。
# 构造GAT节点分类神经网络
import torch
from torch.nn import Linear
import torch.nn.functional as F
from torch_geometric.nn import GATConv
class 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
#result：73.8%
-
原始数据：
image.png -
使用GAT：
image.png
小结
- MLP：59.0% 可视化中聚集效果最差
- GCN：81.4% 可视化图聚集效果最好
- GAT：73.8%
- 作业后补~~~~
