上一节介绍了处理cora数据集，以及返回的结果：

• features：论文的属性特征，维度$2708\times 1433$，并且做了归一化，即每一篇论文属性值的和为1.
• labels：每一篇论文对应的分类编号：0-6
• adj：邻接矩阵，维度$2708\times 2708$
• idx_train：0-139
• idx_val：200-499
• idx_test：500-1499

这一节介绍GCN的模型。

GCN 模型

model:

import torch.nn as nn
import torch.nn.functional as F
from pygcn.layers import GraphConvolutionclass GCN(nn.Module):def __init__(self, nfeat, nhid, nclass, dropout):super(GCN, self).__init__()self.gc1 = GraphConvolution(nfeat, nhid)  # 构建第一层 GCNself.gc2 = GraphConvolution(nhid, nclass)  # 构建第二层 GCNself.dropout = dropoutdef forward(self, x, adj):x = F.relu(self.gc1(x, adj))x = F.dropout(x, self.dropout, training=self.training)x = self.gc2(x, adj)return F.log_softmax(x, dim=1)

layers:

import mathimport torchfrom torch.nn.parameter import Parameter
from torch.nn.modules.module import Moduleclass GraphConvolution(Module):"""Simple GCN layer, similar to https://arxiv.org/abs/1609.02907"""def __init__(self, in_features, out_features, bias=True):super(GraphConvolution, self).__init__()self.in_features = in_featuresself.out_features = out_featuresself.weight = Parameter(torch.FloatTensor(in_features, out_features))  # input_features, out_featuresif bias:self.bias = Parameter(torch.FloatTensor(out_features))else:self.register_parameter('bias', None)self.reset_parameters()def reset_parameters(self):stdv = 1. / math.sqrt(self.weight.size(1))self.weight.data.uniform_(-stdv, stdv)  # 随机化参数if self.bias is not None:self.bias.data.uniform_(-stdv, stdv)def forward(self, input, adj):support = torch.mm(input, self.weight)  # GraphConvolution forward。input*weightoutput = torch.spmm(adj, support)  # 稀疏矩阵的相乘，和mm一样的效果if self.bias is not None:return output + self.biaselse:return outputdef __repr__(self):return self.__class__.__name__ + ' (' \+ str(self.in_features) + ' -> ' \+ str(self.out_features) + ')'

初始化模型

调用模型：

model = GCN(nfeat=features.shape[1],nhid=args.hidden,nclass=labels.max().item() + 1,dropout=args.dropout)

具体参数：

model = GCN(nfeat=1433,nhid=16,nclass=7,dropout=0.5)

初始化模型两层GCN:

self.gc1 = GraphConvolution(nfeat=1433, nhid=16)  # 构建第一层 GCN
self.gc2 = GraphConvolution(nhid=16, nclass=7)  # 构建第二层 GCN
self.dropout = 0.5

初始化具体layer:
第一层：gc1

def __init__(self, in_features, out_features, bias=True):super(GraphConvolution, self).__init__()self.in_features = 1433self.out_features = 16self.weight = Parameter(torch.FloatTensor(1433, 16))  # input_features, out_featuresself.bias = Parameter(torch.FloatTensor(16))self.reset_parameters() # 初始化w和b

参数$w$的维度：W1433×16W_{1433 \times 16}W1433×16​
参数$b$的维度：b1×16b_{1 \times 16}b1×16​
第二层：gc2

def __init__(self, in_features, out_features, bias=True):super(GraphConvolution, self).__init__()self.in_features = 16self.out_features = 7self.weight = Parameter(torch.FloatTensor(16, 7))  # input_features, out_featuresself.bias = Parameter(torch.FloatTensor(7))self.reset_parameters() # 初始化w和b

参数$w$的维度：W1433×16W_{1433 \times 16}W1433×16​
参数$b$的维度： b1×7b_{1 \times 7}b1×7​

forward执行模型

1. 首先执行model:

def forward(self, x, adj):x = F.relu(self.gc1(x, adj))x = F.dropout(x, self.dropout, training=self.training)x = self.gc2(x, adj)return F.log_softmax(x, dim=1)

2. 执行self.gc1(x, adj)，x表示输入特征，维度$2708\times 1433$，adj表示邻接矩阵，维度$2708\times 2708$

3. 执行GCN layer gc1层，

        support = torch.mm(input, self.weight)  # GraphConvolution forward。input*weightoutput = torch.spmm(adj, support)

计算output，output2708×16=adj2708×2708×input2708×1433×W1433×16output_{2708 \times 16} = adj_{2708 \times 2708} \times input_{2708 \times 1433} \times W_{1433 \times 16}output2708×16​=adj2708×2708​×input2708×1433​×W1433×16​，然后返回output=output2708×16+bias1×16output = output_{2708 \times 16} + bias_{1 \times 16}output=output2708×16​+bias1×16​

output[0]=
tensor([ 0.0201, -0.0242,  0.0608,  0.0272,  0.0133,  0.0085,  0.0084, -0.0265,0.0149, -0.0100,  0.0077,  0.0029,  0.0145, -0.0181, -0.0021, -0.0183],grad_fn=<SelectBackward>)
self.bias=
Parameter containing:
tensor([-0.2232, -0.0295, -0.1387,  0.2170, -0.1749, -0.1551,  0.1056, -0.1860,-0.0666, -0.1327,  0.0212,  0.1587,  0.2496, -0.0154, -0.1683,  0.0151],requires_grad=True)
(output + self.bias)[0]=
tensor([-0.2030, -0.0537, -0.0779,  0.2442, -0.1616, -0.1466,  0.1140, -0.2125,-0.0516, -0.1427,  0.0289,  0.1615,  0.2641, -0.0336, -0.1704, -0.0032],grad_fn=<SelectBackward>)

4. 使用$Relu$激活函数，

x = F.relu(self.gc1(x, adj))
x[0]=
tensor([0.0000, 0.0000, 0.0000, 0.2442, 0.0000, 0.0000, 0.1140, 0.0000, 0.0000,0.0000, 0.0289, 0.1615, 0.2641, 0.0000, 0.0000, 0.0000],grad_fn=<SelectBackward>)

5. 在training阶段，使用$dropout$， 执行x=x1−0.5x=\frac{x}{1-0.5}x=1−0.5x​，并以0.5的概率去除:

x = F.dropout(x, self.dropout, training=self.training)
x[0]=
tensor([0.0000, 0.0000, 0.0000, 0.4884, 0.0000, 0.0000, 0.2280, 0.0000, 0.0000,0.0000, 0.0000, 0.3230, 0.5282, 0.0000, 0.0000, 0.0000],grad_fn=<SelectBackward>)

6. 执行第二层 gc2

        support = torch.mm(input, self.weight)  # GraphConvolution forward。input*weightoutput = torch.spmm(adj, support)

计算output，output2708×7=adj2708×2708×input2708×16×W16×7output_{2708 \times 7} = adj_{2708 \times 2708} \times input_{2708 \times 16} \times W_{16 \times 7}output2708×7​=adj2708×2708​×input2708×16​×W16×7​，然后返回output=output2708×7+bias1×7output = output_{2708 \times 7} + bias_{1 \times 7}output=output2708×7​+bias1×7​

output[0]=
tensor([-0.1928,  0.1723,  0.1689, -0.0516,  0.0387, -0.0276, -0.1027],grad_fn=<SelectBackward>)

7. 将返回结果x，直接吐给$F.log\_softmax(x,dim=1)$，$dim=1$表示对7维度进行log_softmax

x[0]=
tensor([-2.1474, -1.7823, -1.7856, -2.0062, -1.9158, -1.9822, -2.0573],grad_fn=<SelectBackward>)

8. 将output与label进行计算loss 与 acc_train
   loss=tensor(1.9186, grad_fn=<NllLossBackward>) acc_train=tensor(0.1357, dtype=torch.float64)
9. 最后进行反向传播，更新梯度W和b
10. 完成一次train的过程