工具包安装方法：
- 一定参考其GITHUB：https://github.com/pyg-team/pytorch_geometric
(千万不要pip直接安装，肯定不行的)
%matplotlib inline
import torch
import networkx as nx
import matplotlib.pyplot as plt
def visualize_graph(G, color):
plt.figure(figsize=(7,7))
plt.xticks([])
plt.yticks([])
nx.draw_networkx(G, pos=nx.spring_layout(G, seed=42), with_labels=False,
node_color=color, cmap="Set2")
plt.show()
def visualize_embedding(h, color, epoch=None, loss=None):
plt.figure(figsize=(7,7))
plt.xticks([])
plt.yticks([])
h = h.detach().cpu().numpy()
plt.scatter(h[:, 0], h[:, 1], s=140, c=color, cmap="Set2")
if epoch is not None and loss is not None:
plt.xlabel(f'Epoch: {epoch}, Loss: {loss.item():.4f}', fontsize=16)
plt.show()
D:\ProgramData\Anaconda3\lib\site-packages\numpy\_distributor_init.py:32: UserWarning: loaded more than 1 DLL from .libs:
D:\ProgramData\Anaconda3\lib\site-packages\numpy\.libs\libopenblas.IPBC74C7KURV7CB2PKT5Z5FNR3SIBV4J.gfortran-win_amd64.dll
D:\ProgramData\Anaconda3\lib\site-packages\numpy\.libs\libopenblas.NOIJJG62EMASZI6NYURL6JBKM4EVBGM7.gfortran-win_amd64.dll
stacklevel=1)
Graph Neural Networks
- 致力于解决不规则数据结构（图像和文本相对格式都固定，但是社交网络与化学分子等格式肯定不是固定的）
- GNN模型迭代更新主要基于图中每个节点及其邻居的信息，基本表示如下：
$$
\mathbf{x}v^{(\ell + 1)} = f^{(\ell + 1)} \left( \mathbf{x}_v^{(\ell)}, \left{ \mathbf{x}_w^{(\ell)} : w \in \mathcal{N}(v) \right} \right)
$$
节点的特征： $\mathbf{x}_v^{(\ell)}$ ， $v \in \mathcal{V}$ 在图中 $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ 根据其邻居信息进行更新 $\mathcal{N}(v)$:
数据集：Zachary's karate club network.
该图描述了一个空手道俱乐部会员的社交关系，以34名会员作为节点，如果两位会员在俱乐部之外仍保持社交关系，则在节点间增加一条边。
每个节点具有一个34维的特征向量，一共有78条边。
在收集数据的过程中，管理人员 John A 和 教练 Mr. Hi（化名）之间产生了冲突，会员们选择了站队，一半会员跟随 Mr. Hi 成立了新俱乐部，剩下一半会员找了新教练或退出了俱乐部。
PyTorch Geometric
- 这个就是咱们的核心了，说白了就是这里实现了各种图神经网络中的方法
- 咱们直接调用就可以了：PyTorch Geometric (PyG) library
数据集介绍
from torch_geometric.datasets import KarateClub
dataset = KarateClub()
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}')
Dataset: KarateClub():
======================
Number of graphs: 1
Number of features: 34
Number of classes: 4
data = dataset[0] # Get the first graph object.
print(data)
Data(x=[34, 34], edge_index=[2, 156], y=[34], train_mask=[34])
- 图的表示用
Data格式（说明可以点击）
edge_index
- edge_index：表示图的连接关系（start,end两个序列）
- node features：每个点的特征
- node labels：每个点的标签
- train_mask：有的节点木有标签（用来表示哪些节点要计算损失）
edge_index = data.edge_index
print(edge_index.t())
tensor([[ 0, 1],
[ 0, 2],
[ 0, 3],
[ 0, 4],
[ 0, 5],
[ 0, 6],
[ 0, 7],
[ 0, 8],
[ 0, 10],
[ 0, 11],
[ 0, 12],
[ 0, 13],
[ 0, 17],
[ 0, 19],
[ 0, 21],
[ 0, 31],
[ 1, 0],
[ 1, 2],
[ 1, 3],
[ 1, 7],
[ 1, 13],
[ 1, 17],
[ 1, 19],
[ 1, 21],
[ 1, 30],
[ 2, 0],
[ 2, 1],
[ 2, 3],
[ 2, 7],
[ 2, 8],
[ 2, 9],
[ 2, 13],
[ 2, 27],
[ 2, 28],
[ 2, 32],
[ 3, 0],
[ 3, 1],
[ 3, 2],
[ 3, 7],
[ 3, 12],
[ 3, 13],
[ 4, 0],
[ 4, 6],
[ 4, 10],
[ 5, 0],
[ 5, 6],
[ 5, 10],
[ 5, 16],
[ 6, 0],
[ 6, 4],
[ 6, 5],
[ 6, 16],
[ 7, 0],
[ 7, 1],
[ 7, 2],
[ 7, 3],
[ 8, 0],
[ 8, 2],
[ 8, 30],
[ 8, 32],
[ 8, 33],
[ 9, 2],
[ 9, 33],
[10, 0],
[10, 4],
[10, 5],
[11, 0],
[12, 0],
[12, 3],
[13, 0],
[13, 1],
[13, 2],
[13, 3],
[13, 33],
[14, 32],
[14, 33],
[15, 32],
[15, 33],
[16, 5],
[16, 6],
[17, 0],
[17, 1],
[18, 32],
[18, 33],
[19, 0],
[19, 1],
[19, 33],
[20, 32],
[20, 33],
[21, 0],
[21, 1],
[22, 32],
[22, 33],
[23, 25],
[23, 27],
[23, 29],
[23, 32],
[23, 33],
[24, 25],
[24, 27],
[24, 31],
[25, 23],
[25, 24],
[25, 31],
[26, 29],
[26, 33],
[27, 2],
[27, 23],
[27, 24],
[27, 33],
[28, 2],
[28, 31],
[28, 33],
[29, 23],
[29, 26],
[29, 32],
[29, 33],
[30, 1],
[30, 8],
[30, 32],
[30, 33],
[31, 0],
[31, 24],
[31, 25],
[31, 28],
[31, 32],
[31, 33],
[32, 2],
[32, 8],
[32, 14],
[32, 15],
[32, 18],
[32, 20],
[32, 22],
[32, 23],
[32, 29],
[32, 30],
[32, 31],
[32, 33],
[33, 8],
[33, 9],
[33, 13],
[33, 14],
[33, 15],
[33, 18],
[33, 19],
[33, 20],
[33, 22],
[33, 23],
[33, 26],
[33, 27],
[33, 28],
[33, 29],
[33, 30],
[33, 31],
[33, 32]])
inde是稀疏表示的，并不是n*n的邻接矩阵
使用networkx可视化展示
from torch_geometric.utils import to_networkx
G = to_networkx(data, to_undirected=True)
visualize_graph(G, color=data.y)
Graph Neural Networks 网络定义：
- GCN layer (Kipf et al. (2017)) 定义如下：
$$
\mathbf{x}v^{(\ell + 1)} = \mathbf{W}^{(\ell + 1)} \sum(v) , \cup , { v }} \frac{1}{c_{w,v}} \cdot \mathbf{x}_w^{(\ell)}
$$ - PyG 文档
GCNConv
import torch
from torch.nn import Linear
from torch_geometric.nn import GCNConv
class GCN(torch.nn.Module):
def __init__(self):
super().__init__()
torch.manual_seed(1234)
self.conv1 = GCNConv(dataset.num_features, 4) # 只需定义好输入特征和输出特征即可
self.conv2 = GCNConv(4, 4)
self.conv3 = GCNConv(4, 2)
self.classifier = Linear(2, dataset.num_classes)
def forward(self, x, edge_index):
h = self.conv1(x, edge_index) # 输入特征与邻接矩阵（注意格式，上面那种）
h = h.tanh()
h = self.conv2(h, edge_index)
h = h.tanh()
h = self.conv3(h, edge_index)
h = h.tanh()
# 分类层
out = self.classifier(h)
return out, h
model = GCN()
print(model)
GCN(
(conv1): GCNConv(34, 4)
(conv2): GCNConv(4, 4)
(conv3): GCNConv(4, 2)
(classifier): Linear(in_features=2, out_features=4, bias=True)
)
输出特征展示
- 最后不是输出了两维特征嘛，画出来看看长啥样
- 但是，但是，现在咱们的模型还木有开始训练。。。
model = GCN()
_, h = model(data.x, data.edge_index)
print(f'Embedding shape: {list(h.shape)}')
visualize_embedding(h, color=data.y)
Embedding shape: [34, 2]
训练模型(semi-supervised)
import time
model = GCN()
criterion = torch.nn.CrossEntropyLoss() # Define loss criterion.
optimizer = torch.optim.Adam(model.parameters(), lr=0.01) # Define optimizer.
def train(data):
optimizer.zero_grad()
out, h = model(data.x, data.edge_index) #h是两维向量，主要是为了咱们画个图
loss = criterion(out[data.train_mask], data.y[data.train_mask]) # semi-supervised
loss.backward()
optimizer.step()
return loss, h
for epoch in range(401):
loss, h = train(data)
if epoch % 10 == 0:
visualize_embedding(h, color=data.y, epoch=epoch, loss=loss)
time.sleep(0.3)
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