参考：[DataWhale GNN 学习资料]，torch_geometric.nn — pytorch_geometric 1.7.1 documentation (pytorch-geometric.readthedocs.io)、

from torch_geometric.datasets import Planetoid from torch_geometric.transforms import NormalizeFeatures  dataset = Planetoid(root='data/Planetoid', 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()}') 

Dataset: Cora():
======================
Number of graphs: 1
Number of features: 1433
Number of classes: 7

Data(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

​ 由结果可以看出 Cora 图拥有：

​ 利用 **TSNE **将对高维节点[模型的输出的结果]表征嵌入到二维平面空间，然后在二维平面空间画出节点

import matplotlib.pyplot as plt
from sklearn.manifold import TSNE

def visualize(out, color):
    z = TSNE(n_components=2).fit_transform(out.detach().cpu().numpy())
    plt.figure(figsize=(10,10))
    plt.xticks([])
    plt.yticks([])

    plt.scatter(z[:, 0], z[:, 1], s=70, c=color, cmap="Set2")
    plt.show()

​ MLP 只对输入节点的特征进行操作，它在所有节点之间共享权重

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)	# 为 CPU 设置种子用于生成随机数，以使得结果是确定的
        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( (lin1): Linear(in_features=1433, out_features=16, bias=True) (lin2): Linear(in_features=16, out_features=7, bias=True) ) """

利用交叉熵损失和 Adam 优化器进行训练：

model = MLP(hidden_channels=16)
criterion = torch.nn.CrossEntropyLoss()  # 定义损失标准
optimizer = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4)  # 定义优化函数

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])  # 只根据训练节点计算损失
    loss.backward()  		# Derive gradients.
    optimizer.step()  		# 根据梯度更新参数
    return loss

for epoch in range(1, 51):
    loss = train()
    print(f'Epoch: {epoch:03d}, Loss: {loss:.4f}')
    """ Epoch: 046, Loss: 1.1284 Epoch: 047, Loss: 1.1229 Epoch: 048, Loss: 1.0383 Epoch: 049, Loss: 1.0439 Epoch: 050, Loss: 1.0563 """

def test():
    model.eval()
    out = model(data.x)
    pred = out.argmax(dim=1)  # 选取概率最高的一类
    test_correct = pred[data.test_mask] == data.y[data.test_mask]	# 预测与真实对比
    test_acc = int(test_correct.sum()) / int(data.test_mask.sum())  # 准确率
    return test_acc

test_acc = test()
print(f'Test Accuracy: {test_acc:.4f}')

​ 用于训练 MLP 的有标签节点数量过少，此神经网络被过拟合，它对未见过的节点泛化性很差

X ′ = D ^ − 1 / 2 A ^ D ^ − 1 / 2 X Θ , \mathbf{X}^{\prime} = \mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2} \mathbf{X} \mathbf{\Theta}, X′=D^−1/2A^D^−1/2XΘ,

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)

其中：

• in_channels：输入数据维度
• out_channels：输出数据维度
• improved：如果为 true， A ^ = A + 2 I \mathbf{\hat{A}} = \mathbf{A} + 2\mathbf{I} A^=A+2I，其目的在于增强中心节点自身信息
• cached：是否存储 D ^ − 1 / 2 A ^ D ^ − 1 / 2 \mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2} D^−1/2A^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的景中设置为true
• 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

​ 与 MLP 图节点分类器模型的不同在于：将线性层（torch.nn.Linear）改为了图卷积层（torch_geometric.nn.GCNConv）

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)
""" GCN( (conv1): GCNConv(1433, 16) (conv2): GCNConv(16, 7) ) """

model.eval()

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

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])  # 只根据训练节点计算损失
      loss.backward()  # Derive gradients.
      optimizer.step()  # 根据梯度更新参数
      return loss

for epoch in range(1, 51):
    loss = train()
    print(f'Epoch: {epoch:03d}, Loss: {loss:.4f}')
    """ Epoch: 046, Loss: 1.2266 Epoch: 047, Loss: 1.2149 Epoch: 048, Loss: 1.1631 Epoch: 049, Loss: 1.1756 Epoch: 050, Loss: 1.1714 """