| |
| """Generate GCN notebook.""" |
|
|
| import nbformat as nbf |
|
|
| nb = nbf.v4.new_notebook() |
| nb.metadata = {"kernelspec": {"display_name": "Python 3", "language": "python", "name": "python3"},"language_info": {"name": "python", "version": "3.12.0"}} |
|
|
| cells = [] |
| def md(s): cells.append(nbf.v4.new_markdown_cell(s)) |
| def code(s): cells.append(nbf.v4.new_code_cell(s)) |
|
|
| md("# GCN: Graph Convolutional Network\n\nNode classification on citation graphs using spectral graph convolution.\n") |
|
|
| md("""## 背景 |
| |
| GCN（Kipf & Welling, 2017）将卷积操作推广到图结构数据。核心思想： |
| 每个节点的特征由其邻居节点加权聚合而来。 |
| |
| 与图像 CNN 的区别： |
| - CNN：固定网格结构，卷积核在空间上滑动 |
| - GCN：任意图结构，卷积由邻接矩阵定义的消息传递实现 |
| |
| 数据集：**Cora** — 2708 篇论文，每篇用 1433 维词袋向量表示，分为 7 类。边表示引用关系。 |
| """) |
|
|
| md("""## 数学原理 |
| |
| ### 图卷积层 |
| |
| $$H^{(l+1)} = \\sigma\\left(\\hat{A} H^{(l)} W^{(l)}\\right)$$ |
| |
| 其中 $\\hat{A} = D^{-1/2} A D^{-1/2}$ 是归一化邻接矩阵。 |
| |
| - $A$: 邻接矩阵（加自环后） |
| - $D$: 度矩阵 $D_{ii} = \\sum_j A_{ij}$ |
| - $H^{(l)}$: 第 $l$ 层的节点表示 |
| - $W^{(l)}$: 可学习的权重矩阵 |
| |
| ### 2 层 GCN |
| |
| $$Z = \\text{softmax}\\left(\\hat{A}\\ \\text{ReLU}\\left(\\hat{A} X W^{(0)}\\right) W^{(1)}\\right)$$ |
| |
| 半监督学习：只用少量标注节点（每类 20 个）训练，模型通过图结构传播标签信息到未标注节点。 |
| """) |
|
|
| code("""\ |
| import torch |
| import torch.nn as nn |
| import torch.optim as optim |
| |
| from graph.gcn.model import GCN |
| from graph.gcn.data import load_cora |
| from utils.config import load_config |
| from utils.seed import set_seed |
| from utils.device import get_device |
| |
| device = get_device() |
| print(f"Device: {device}") |
| |
| features, adj_norm, labels, train_mask, val_mask, test_mask, classes = load_cora() |
| features = features.to(device) |
| adj_norm = adj_norm.to(device) |
| labels = labels.to(device) |
| train_mask = train_mask.to(device) |
| val_mask = val_mask.to(device) |
| """) |
|
|
| code("""\ |
| model = GCN( |
| in_features=features.size(1), |
| hidden_dim=16, |
| num_classes=labels.max().item() + 1, |
| dropout=0.5, |
| ).to(device) |
| print(f"Parameters: {model.num_params():,}") |
| """) |
|
|
| md("""## 训练 |
| |
| > ⏱ 预估耗时：**200 epoch × ~0.1s/epoch ≈ 20 秒**（CPU 即可完成） |
| """) |
|
|
| code("""\ |
| NUM_EPOCHS = 200 |
| LR = 0.01 |
| WEIGHT_DECAY = 5e-4 |
| |
| criterion = nn.CrossEntropyLoss() |
| optimizer = optim.Adam(model.parameters(), lr=LR, weight_decay=WEIGHT_DECAY) |
| |
| loss_hist, acc_hist = [], [] |
| |
| for epoch in range(1, NUM_EPOCHS + 1): |
| model.train() |
| optimizer.zero_grad() |
| output = model(features, adj_norm) |
| loss = criterion(output[train_mask], labels[train_mask]) |
| loss.backward() |
| optimizer.step() |
| |
| model.eval() |
| with torch.no_grad(): |
| output = model(features, adj_norm) |
| val_acc = (output[val_mask].argmax(dim=1) == labels[val_mask]).float().mean().item() |
| loss_hist.append(loss.item()) |
| acc_hist.append(val_acc) |
| |
| if epoch % 20 == 0 or epoch == 1: |
| print(f"Epoch [{epoch:3d}/{NUM_EPOCHS}] Loss: {loss.item():.4f} Val Acc: {val_acc:.2%}") |
| """) |
|
|
| md("""## Loss 曲线""") |
|
|
| code("""\ |
| import matplotlib.pyplot as plt |
| |
| fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4)) |
| ax1.plot(loss_hist); ax1.set_xlabel("Epoch"); ax1.set_ylabel("Loss"); ax1.set_title("Training Loss"); ax1.grid(True) |
| ax2.plot(acc_hist, color='green'); ax2.set_xlabel("Epoch"); ax2.set_ylabel("Val Acc"); ax2.set_title("Validation Accuracy"); ax2.grid(True) |
| plt.tight_layout(); plt.show() |
| """) |
|
|
| md("""## 测试准确率""") |
|
|
| code("""\ |
| model.eval() |
| with torch.no_grad(): |
| output = model(features, adj_norm) |
| pred = output[test_mask].argmax(dim=1) |
| test_acc = (pred == labels[test_mask]).float().mean().item() |
| print(f"Test Accuracy: {test_acc:.2%}") |
| """) |
|
|
| md("""\ |
| ## 思考题 |
| |
| 1. 为什么 GCN 的归一化用 $D^{-1/2} A D^{-1/2}$ 而不是 $D^{-1} A$？ |
| 2. GCN 能处理归纳式（inductive）任务吗？还是只能直推式（transductive）？ |
| 3. 如果不用邻接矩阵只用节点特征，准确率会降到多少？ |
| 4. GCN 层数加深为什么会导致性能下降？（提示：过平滑问题） |
| """) |
|
|
| nb.cells = cells |
| with open("graph/gcn/gcn.ipynb", "w") as f: |
| nbf.write(nb, f) |
| print("Generated graph/gcn/gcn.ipynb") |
|
|
