上一節介紹了處理cora數據集，以及返回的結果：

• features：論文的屬性特征，維度$2708\times 1433$，并且做了歸一化，即每一篇論文屬性值的和為1.
• labels：每一篇論文對應的分類編號：0-6
• adj：鄰接矩陣，維度$2708\times 2708$
• idx_train：0-139
• idx_val：200-499
• idx_test：500-1499

這一節介紹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) # 構建第一層 GCNself.gc2 = GraphConvolution(nhid, nclass) # 構建第二層 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) # 隨機化參數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) # 稀疏矩陣的相乘，和mm一樣的效果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

調用模型：

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

具體參數：

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

初始化模型兩層GCN:

self.gc1 = GraphConvolution(nfeat=1433, nhid=16) # 構建第一層 GCN self.gc2 = GraphConvolution(nhid=16, nclass=7) # 構建第二層 GCN self.dropout = 0.5

初始化具體layer:
第一層：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

參數$w$的維度：$W_{1433\times 16}$
參數$b$的維度：$b_{1\times 16}$
第二層：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

參數$w$的維度：$W_{1433\times 16}$
參數$b$的維度： $b_{1\times 7}$

forward執行模型

首先執行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)

執行self.gc1(x, adj)，x表示輸入特征，維度$2708\times 1433$，adj表示鄰接矩陣，維度$2708\times 2708$

執行GCN layer gc1層，

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

計算output，$outpu{t}_{2708\times 16}=ad{j}_{2708\times 2708}\times inpu{t}_{2708\times 1433}\times W_{1433\times 16}$，然后返回$output=outpu{t}_{2708\times 16}+bia{s}_{1\times 16}$

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>)

使用$Relu$激活函數，

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>)

在training階段，使用$dropout$， 執行$x=\frac{x}{1?0.5}$，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>)

執行第二層 gc2

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

計算output，$outpu{t}_{2708\times 7}=ad{j}_{2708\times 2708}\times inpu{t}_{2708\times 16}\times W_{16\times 7}$，然后返回$output=outpu{t}_{2708\times 7}+bia{s}_{1\times 7}$

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

將返回結果x，直接吐給$F.log\_softmax(x,dim=1)$，$dim=1$表示對7維度進行log_softmax

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

將output與label進行計算loss 與 acc_train
loss=tensor(1.9186, grad_fn=<NllLossBackward>) acc_train=tensor(0.1357, dtype=torch.float64)

最后進行反向傳播，更新梯度W和b

完成一次train的過程

總結

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