Graph Convolution Network图卷积网络（三）嵌入其他网络结构

Bertha 。 2022-04-25 08:42 191阅读 0赞

背景：实现GCN，并且于resnet输出端的score level实现。

**目录**

一、GCN理论基础

二、邻接矩阵正则化

2.1 矩阵A的正则化

2.2 运算与存储

三、torch实现

3.1 init中的super

3.2 矩阵的读取与运算

3.2 图卷积层的实现

3.3 GCN实现

3.4 cuda的实现

--------------------

相关内容

[GCN (Graph Convolutional Network) 图卷积网络解析 ][GCN _Graph Convolutional Network_ _]

# 一、GCN理论基础 #

[GCN (Graph Convolutional Network) 图卷积网络解析 ][GCN _Graph Convolutional Network_ _]

![20190418213747896.png][]![wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==][wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zNjQ3NDgwOQ_size_16_color_FFFFFF_t_70][]![wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==][wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw]

*  隐层的feature maps的数量为H，输入层数量为C，输出层为F
 *  其中A为下面3.4中提到的symmetric adjacency matrix，![20190418214023658.png][]![wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==][wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw]
 *  权重![20190418214811651.png][]![wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==][wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw]为输入层到隐层的权值矩阵
 *  同理，权重![20190418214936166.png][]![wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==][wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw]为隐层到输出层的权值矩阵

这个公式跟BP有点像，只不过比BP多了一个稀疏的adj matrix A

# 二、邻接矩阵正则化 #

## 2.1 矩阵A的正则化 ##

运行过程中，需要对邻接矩阵A进行正则化：

例如：

def normalize_adj(self, adj, threshold):
            adj = (adj > threshold)*adj
            # adj[adj>0.4]=1
            D = np.power(np.sum(adj, axis=1), -0.5)
            D = np.diag(D)
            adj = np.matmul(np.matmul(D, adj), D)
            return adj

公式为symmetric adjacency matrix，![20190418214023658.png][]![wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==][wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw]

或者

def gen_adj(A):
        D = torch.pow(A.sum(1).float(), -0.5)
        D = torch.diag(D)
        adj = torch.matmul(torch.matmul(A, D).t(), D)
        return adj

如果A非对称的结构，经历此步可能并不能使A变成对称的。

## 2.2 运算与存储 ##

直接嵌套入程序运算略显麻烦，不如直接运算好存起来再用。

import pickle
    import matplotlib.pyplot as plt
    import seaborn as sns
    import numpy as np
    import pandas as pd
    import json
    import os
    
    from sklearn import datasets
    from sklearn.cluster import SpectralClustering
    from sklearn import metrics
    
    
    class adj_matrix_gen():
    
        def __init__(self):
            self.load_dir='/Users/baidu/Desktop/code/ML_GAT-master/'
            self.save_dir='/Users/baidu/Desktop/code/ML_GAT-master/'
            self.load_corelation_filename='coco_correlations.pkl'
            self.load_names_filename='coco_names.pkl'
            self.save_filename='coco_normalized_adj.pkl'
    
            self.load_correlation_file_path=self.load_dir+self.load_corelation_filename
            self.load_names_file_path=self.load_dir+self.load_names_filename
            self.save_file_path=self.save_dir+self.save_filename
            self.un_normalized_fig_path=self.save_dir+'un_normalized_adj.jpg'
            self.normalized_fig_path=self.save_dir+'normalized_adj.jpg'
    
        def run_adj_matrix_gen(self):
    
            # plot heatmap of matrix
            def plot_cor(mat, names,save_fig_name):
                fig, ax = plt.subplots()
                # 二维的数组的热力图，横轴和数轴的ticklabels要加上去的话，既可以通过将array转换成有column
                # 和index的DataFrame直接绘图生成，也可以后续再加上去。后面加上去的话，更灵活，包括可设置labels大小方向等。
                sns.heatmap(
                    pd.DataFrame(mat * (mat >= 0), columns=names,
                                 index=names),
                    xticklabels=True,
                    yticklabels=True,cmap="YlGnBu") # cmap="YlGnBu"  'RdYlBu'
                # sns.heatmap(np.round(a,2), annot=True, vmax=1,vmin = 0, xticklabels= True, yticklabels= True,
                #            square=True, cmap="YlGnBu")
                ax.set_title('Correlation', fontsize=18)
                # ax.set_ylabel('Attribute', fontsize=18)
                # ax.set_xlabel('Attribute', fontsize=18)  # 横变成y轴，跟矩阵原始的布局情况是一样的
                plt.savefig(save_fig_name)
                plt.close('all')
    
            def normalize_adj_gen(un_normalized_adj,threshold):
                un_normalized_adj = (un_normalized_adj > threshold) * un_normalized_adj
                # adj[adj>0.4]=1
                D = np.power(np.sum(un_normalized_adj, axis=1), -0.5)
                D = np.diag(D)
                normalized_adj = np.matmul(np.matmul(D, un_normalized_adj), D)
                return normalized_adj
    
    
            # load correlation matrix and names
            with open(self.load_correlation_file_path, 'rb') as f:
                print("loading ",self.load_correlation_file_path," from local...")
                correlations = pickle.load(f)
            unnormalized_adj = correlations['pp']
            with open(self.load_names_file_path,'rb') as f:
                print("loading ",self.load_names_file_path," from local...")
                names=pickle.load(f)
    
    
            plot_cor(mat=unnormalized_adj,names=names,save_fig_name=self.un_normalized_fig_path)
    
            normalized_adj=normalize_adj_gen(un_normalized_adj=unnormalized_adj,threshold=0.1)
    
            plot_cor(mat=normalized_adj, names=names, save_fig_name=self.normalized_fig_path)
    
    
    if __name__ == '__main__':
        adj_matrix_gen().run_adj_matrix_gen()
        print('finished....')

# 三、torch实现 #

## 3.1 init中的super ##

不加super会报错

class Graph_convolution_network(nn.Module):
        def __init__(self, in_features,hidden_features, out_features):
            # super(Graph_convolution_network, self).__init__()

File "/Users/baidu/Desktop/code/ML_GAT-master/models/resnet_gcn.py", line 50, in __init__
        self.graph_convolution_layer1=Graph_convolution_Layer(in_features=in_features, out_features=hidden_features)
      File "/Users/baidu/anaconda3/envs/torch041/lib/python3.5/site-packages/torch/nn/modules/module.py", line 565, in __setattr__
        "cannot assign module before Module.__init__() call")
    AttributeError: cannot assign module before Module.__init__() call

## 3.2 矩阵的读取与运算 ##

这篇文章中有相关于 np变量与cuda变量的实现。[Graph Attention Network 图注意力网络 (三) 更改邻接masked attention ][Graph Attention Network _ _ _masked attention]

# torch.floatTensor format
            mask = torch.FloatTensor(np.where(unnormalized_adj > self.probability_filter_threshold, 1, 0))
            unnormalized_adj=torch.FloatTensor(unnormalized_adj).mul(mask)
            # numpy format
            mask=np.where(unnormalized_adj > self.probability_filter_threshold, 1, 0)
            unnormalized_adj=np.multiply(unnormalized_adj,mask)
            D = np.power(np.sum(unnormalized_adj, axis=1), -0.5)
            D = np.diag(D)
            normalized_adj=np.matmul(np.matmul(D, unnormalized_adj), D)
            print()
    
            # def normalize_adj(adj, threshold):
            #     # adj=np.array(adj.data())
            #     adj = (adj > threshold) * adj
            #     # adj[adj>0.4]=1
            #     D = np.power(np.sum(adj, axis=1), -0.5)
            #     D = np.diag(D)
            #     adj = np.matmul(np.matmul(D, adj), D)
            #     return adj
            self.normalized_adj=torch.FloatTensor(normalized_adj)

注意torch与np格式的数据均可实现。

## 3.2 图卷积层的实现 ##

class Graph_convolution_Layer(nn.Module):
        def __init__(self, in_features, out_features, bias=False):
            super(Graph_convolution_Layer, self).__init__()
            self.in_features = in_features
            self.out_features = out_features
            self.weight = Parameter(torch.Tensor(in_features, out_features))
            if bias:
                self.bias = Parameter(torch.Tensor(1, 1, 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)
            if self.bias is not None:
                self.bias.data.uniform_(-stdv, stdv)
    
        def forward(self, input, adj):
            # adj=torch.FloatTensor(adj).cuda()
            # adj = torch.FloatTensor(adj)
            support = torch.matmul(input, self.weight)
            output = torch.matmul(adj, support)
            if self.bias is not None:
                return output + self.bias
            else:
                return output
    
        def __repr__(self):
            return self.__class__.__name__ + ' (' \
                   + str(self.in_features) + ' -> ' \
                   + str(self.out_features) + ')'

## 3.3 GCN实现 ##

class Graph_convolution_network(nn.Module):
        def __init__(self, in_features,hidden_features, out_features):
            super(Graph_convolution_network, self).__init__()
            self.graph_convolution_layer1=Graph_convolution_Layer(in_features=in_features, out_features=hidden_features)
            self.graph_convolution_layer2=Graph_convolution_Layer(in_features=hidden_features, out_features=out_features)
            self.relu = nn.LeakyReLU(0.2)
    
            with open('coco_correlations.pkl', 'rb') as f:
                print("loading coco_correlations.pkl from local...")
                correlations = pickle.load(f)
            unnormalized_adj = correlations['pp']
            self.probability_filter_threshold = 0.1
            # torch.floatTensor format
            mask = torch.FloatTensor(np.where(unnormalized_adj > self.probability_filter_threshold, 1, 0))
            self.unnormalized_adj=torch.FloatTensor(unnormalized_adj).mul(mask)
    
        def forward(self,input):
            # normalized_adj=self.unnormalized_adj.cuda()
            x=self.graph_convolution_layer1(input=input,adj=self.unnormalized_adj)
            x=self.relu(x)
            x=self.graph_convolution_layer2(input=x,adj=self.unnormalized_adj)
            return x

## 3.4 cuda的实现 ##

adj矩阵读入为numpy，所以需要将其改为torch.FloatTensor.cuda

floatTensor可以直接转，cuda需要在forward中转换。否则会有报错：

File "/home/ssd1/slurm_submit/6submit_ML_GAT/torch/lib/python3.5/site-packages/torch/nn/modules/module.py", line 477, in __call__
        result = self.forward(*input, **kwargs)
      File "/home/ssd1/slurm_submit/6submit_ML_GAT/models/resnet_gcn.py", line 67, in forward
        x=self.graph_convolution_layer1(input=input,adj=self.unnormalized_adj)
      File "/home/ssd1/slurm_submit/6submit_ML_GAT/torch/lib/python3.5/site-packages/torch/nn/modules/module.py", line 477, in __call__
        result = self.forward(*input, **kwargs)
      File "/home/ssd1/slurm_submit/6submit_ML_GAT/models/resnet_gcn.py", line 38, in forward
        output = torch.matmul(adj, support)
    RuntimeError: Expected object of type torch.FloatTensor but found type torch.cuda.FloatTensor for argument #2 'mat2'

读入转为FloatTensor，

with open('coco_correlations.pkl', 'rb') as f:
                print("loading coco_correlations.pkl from local...")
                correlations = pickle.load(f)
            unnormalized_adj = correlations['pp']
            self.probability_filter_threshold = 0.1
            # torch.floatTensor format
            mask = torch.FloatTensor(np.where(unnormalized_adj > self.probability_filter_threshold, 1, 0))
            self.unnormalized_adj=torch.FloatTensor(unnormalized_adj).mul(mask)
    
        def forward(self,input):
            # normalized_adj=self.unnormalized_adj.cuda()
            x=self.graph_convolution_layer1(input=input,adj=self.unnormalized_adj)
            x=self.relu(x)
            x=self.graph_convolution_layer2(input=x,adj=self.unnormalized_adj)
            return x

layer之中转为cuda

def forward(self, input, adj):
            # adj=torch.FloatTensor(adj).cuda()
            # adj = torch.FloatTensor(adj)
            adj=adj.cuda()
            support = torch.matmul(input, self.weight)
            output = torch.matmul(adj, support)
            if self.bias is not None:
                return output + self.bias
            else:
                return output

[GCN _Graph Convolutional Network_ _]: https://blog.csdn.net/weixin_36474809/article/details/89316439
[20190418213747896.png]: https://img-blog.csdnimg.cn/20190418213747896.png
[wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw]: 
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zNjQ3NDgwOQ_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20190418215120422.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl8zNjQ3NDgwOQ==,size_16,color_FFFFFF,t_70
[20190418214023658.png]: https://img-blog.csdnimg.cn/20190418214023658.png
[20190418214811651.png]: https://img-blog.csdnimg.cn/20190418214811651.png
[20190418214936166.png]: https://img-blog.csdnimg.cn/20190418214936166.png
[Graph Attention Network _ _ _masked attention]: https://blog.csdn.net/weixin_36474809/article/details/90693821