基于多通道的边学习图卷积网络

doi:10.11959/j.issn.1000-0801.2022250

电信科学 ›› 2022, Vol. 38 ›› Issue (9): 95-104.doi: 10.11959/j.issn.1000-0801.2022250

基于多通道的边学习图卷积网络

杨帅, 王瑞琴, 马辉

湖州师范学院信息工程学院，浙江湖州 313000

修回日期:2022-08-22 出版日期:2022-09-20 发布日期:2022-09-01
作者简介:杨帅（1996- ），男，湖州师范学院信息工程学院硕士生，主要研究方向为机器学习、个性化推荐等
王瑞琴（1979- ），女，博士，湖州师范学院信息工程学院教授，主要研究方向为机器学习、数据挖掘、社交网络分析以及个性化推荐等
马辉（1997- ），男，湖州师范学院信息工程学院硕士生，主要研究方向为聚类、神经网络等
基金资助:
国家社会科学基金资助项目(20BTQ093);浙江省自然科学基金资助项目(LY20F020006)

Multi-channel based edge-learning graph convolutional network

Shuai YANG, Ruiqin WANG, Hui MA

School of Information Engineering, Huzhou University, Huzhou 313000, China

Revised:2022-08-22 Online:2022-09-20 Published:2022-09-01
Supported by:
The National Social Science Foundation of China(20BTQ093);The Natural Science Foundation of Zhejiang Province(LY20F020006)

摘要/Abstract

摘要：

通常图的边包含了图的重要信息，然而目前大多数用于图学习的深度学习模型（如图卷积网络（graph convolutional network，GCN）和图注意力网络（graph attention network，GAT））没有充分利用多维边特征的特性；另一个问题是图中可能存在噪声，影响图学习的性能。使用多层感知机对图数据进行去噪优化处理，在GCN的基础上引入了多通道学习边特征的方法，对图的多维边属性进行编码，按原始图所包含的属性分别建模为多通道，每个通道对应一种边特征属性对图节点进行约束训练，可以让算法更合理地学习图中多维边特征，在Cora、Tox21、Freesolv等数据集上的实验证明了去噪方法与多通道方法的有效性。

关键词: 图卷积网络, 边特征, 图去噪, 多通道, 边学习

Abstract:

Usually the edges of the graph contain important information of the graph.However, most of deep learning models for graph learning, such as graph convolutional network (GCN) and graph attention network (GAT), do not fully utilize the characteristics of multi-dimensional edge features.Another problem is that there may be noise in the graph that affects the performance of graph learning.Multilayer perceptron (MLP) was used to denoise and optimize the graph data, and a multi-channel learning edge feature method was introduced on the basis of GCN.The multi-dimensional edge attributes of the graph were encoded, and the attributes contained in the original graph were modeled as multi-channel.Each channel corresponds to an edge feature attribute to constrain the training of graph nodes, which allows the algorithm to learn multi-dimensional edge features in the graph more reasonably.Experiments based on Cora, Tox21, Freesolv and other datasets had proved the effectiveness of denoising methods and multi-channel methods.

Key words: graph convolutional network, edge feature, graph denoising, multi-channel, edge-learning

中图分类号:

TP391

杨帅, 王瑞琴, 马辉. 基于多通道的边学习图卷积网络[J]. 电信科学, 2022, 38(9): 95-104.

Shuai YANG, Ruiqin WANG, Hui MA. Multi-channel based edge-learning graph convolutional network[J]. Telecommunications Science, 2022, 38(9): 95-104.

图/表 9

图1

表1

GCN、GAT与EGCN的时间复杂度与内存复杂度对比"

模型	GCN	GAT	EGCN
时间复杂度	$O (K m d + K n d^{2})$	$O (K m d + K n d^{2})$	$O (c K m d + c K n d^{2})$
内存复杂度	$O (K n d + K d^{2})$	$O (K n d + K d^{2})$	$O (c K n d + c K d^{2})$

表1

表2

表3

各模型基于引文网络数据集的结果"

模型	Cora		Citeseer
模型	Sparse	Dense	Sparse	Dense
GCN	0.729±0.008	0.720±1.002	0.692±0.007	0.753±0.004
GAT	0.755±1.001	0.790±1.000	0.695±0.005	0.749±0.005
EGNN	0.834±0.003	$0 . 888 \pm 0 . 003$	0.706±0.003	0.771±0.004
EGCN	$0 . 849 \pm 0 . 005$	0.883±0.005	$0 . 747 \pm 0 . 009$	$0 . 791 \pm 0 . 004$

表3

表4

EGCN模型在引文网络数据集上消融实验的结果"

模型	Cora		Citeseer
模型	Sparse	Dense	Sparse	Dense
EGCN(N)	0.827±0.004	0.861±0.005	0.725±0.002	0.74.9±0.005
EGCN(M)	0.781±0.004	0.802±0.004	0.698±0.004	0.78.7±0.003
EGCN(MN)	$0 . 849 \pm 0 . 005$	$0 . 883 \pm 0 . 005$	$0 . 747 \pm 0 . 009$	$0 . 791 \pm 0 . 004$

表4

表5

分子数据集下各神经网络的结果"

模型	Tox21（AUC-ROC）		Lipo（RMSE）		Freesolv（RMSE）		eSOL（RMSE）
模型	val	test	val	test	val	test	val	test
RF	0.78±0.01	0.75±0.02	0.87±0.02	0.86±0.03	1.98±0.82	1.62±0.14	1.27±0.07	1.18±0.11
Weave	0.79±0.02	0.80±0.01	0.88±0.11	0.89±0.09	1.35±0.25	1.37±0.19	0.90±0.08	0.85±0.03
GCN	0.82±0.01	0.83±0.02	0.70±0.03	0.68±0.03	1.24±0.26	1.14±0.10	0.76±0.08	0.80±0.17
GAT	0.83±0.02	0.83±0.01	0.85±0.02	0.84±0.01	1.73±0.25	1.45±0.25	0.86±0.02	1.01±0.03
MPNN	—	—	0.70±0.04	0.68±0.04	1.38±0.42	1.40±0.08	0.78±0.07	0.80±0.06
EIGNN	—	—	$0 . 63 \pm 0 . 02$	$0 . 65 \pm 0 . 02$	1.24±0.13	1.27±0.14	0.75±0.08	0.77±0.07
EGNN	0.82±0.01	0.82±0.01	0.79±0.02	0.75±0.01	1.09±0.08	1.01±0.12	0.70±0.03	0.72±0.02
EGCN	$0 . 85 \pm 0 . 01$	$0 . 86 \pm 0 . 01$	0.66±0.08	0.65±0.04	$0 . 99 \pm 0 . 12$	$0 . 97 \pm 0 . 13$	$0 . 63 \pm 0 . 06$	$0 . 69 \pm 0 . 10$

表5

表6

EGCN在Freesolv与eSOL分子数据集上的消融实验结果"

模型	Freesolv		eSOL
模型	val	test	val	test
EGCN₅	$0 . 99 \pm 0 . 13$	$0 . 97 \pm 0 . 12$	$0 . 65 \pm 0 . 06$	$0 . 68 \pm 0 . 07$
EGCN₄	1.08±0.16	1.04±0.14	0.65±0.06	0.69±0.08
EGCN₃	1.11±0.08	1.10±0.13	0.67±0.07	0.71±0.04
EGCN₂	1.16±0.18	1.22±0.09	0.68±0.08	0.73±0.07
GCN	1.24±0.26	1.14±0.10	0.76±0.08	0.80±0.17

表6

图2

图3

参考文献 15

[1]	LECUN Y , BOTTOU L , BENGIO Y ,et al. Gradient-based learning applied to document recognition[J]. Proceedings of the IEEE, 1998,86(11): 2278-2324.
[2]	DEFFERRARD M , BRESSON X , VANDERGHEYNST P . Convolutional neural networks on graphs with fast localized spectral filtering[C]// Proceedings of 30th Conference on Neural Information Processing Systems. New York:ACM Press, 2016.
[3]	KIPF T N , WELLING M . Semi-supervised classification with graph convolutional networks[C]// Proceedings of 5th International Conference on Learning Representations(ICLR 2017).[S.l.:s.n.], 2017.
[4]	VELI?KOVI? P , CUCURULL G , CASANOVA A ,et al. Graph attention networks[C]// Proceedings of 6th International Conference on Learning Representations(ICLR 2018).[S.l.:s.n.], 2018.
[5]	BRUNA J , ZAREMBA W , SZLAM A ,et al. Spectral networks and deep locally connected networks on graphs[C]// Proceedings of 2nd International Conference on Learning Representations. Netherlands:Elsevier Press, 2014.
[6]	GONG L , CHENG Q . Exploiting edge features for graph neural networks[C]// Proceedings of 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition. Piscataway:IEEE Press, 2019.
[7]	CHEN P , LIU W , HSIEH C Y ,et al. Utilizing edge features in graph neural networks via variational information maximization[J]. arXiv preprint arXiv:1906.05488, 2019.
[8]	GILMER J , SCHOENHOLZ S S , RILEY P F ,et al. Neural message passing for quantum chemistry[C]// Proceedings of the 34th International Conference on Machine Learning. New York:ACM Press, 2017.
[9]	HAMILTON W , YING Z , LESKOVEC J . Inductive representation learning on large graphs[C]// Proceedings of 31st Conference on Neural Information Processing Systems. New York:ACM Press, 2017.
[10]	LI Q , HAN Z , WU X M . Deeper insights into graph convolutional networks for semi-supervised learning[C]// Proceedings of 32nd AAAI Onference on Artificial Intelligence. New York:ACM Press, 2018.
[11]	SUN K , LIN Z , ZHU Z . Multi-stage self-supervised learning for graph convolutional networks on graphs with few labeled nodes[C]// Proceedings of the 34th AAAI Conference on Artificial Intelligence. Palo Alto:AAAI Press, 2020: 5892-5899.
[12]	CARON M , BOJANOWSKI P , JOULIN A ,et al. Deep clustering for unsupervised learning of visual features[C]// Proceedings of the European Conference on Computer Vision. New York:Springer Press, 2018: 132-149.
[13]	YANG H , MA K , CHENG J . Rethinking graph regularization for graph neural networks[C]// Proceedings of the 35th AAAI Conference on Artificial Intelligence. Palo Alto:AAAI Press, 2021: 4573-4581.
[14]	YING Z , YOU J , MORRIS C ,et al. Hierarchical graph representation learning with differentiable pooling[C]// Proceedings of 32nd Conference on Neural Information Processing Systems. New York:ACM Press, 2018.
[15]	WU Z , RAMSUNDAR B , FEINBERG E N ,et al. MoleculeNet:a benchmark for molecular machine learning[J]. Chemical science, 2018,9(2): 513-530.

数据集	节点数（分子数）/个	边/个	标签数/个	任务类型
Cora	2 708	5 429	7	分类
CiteSeer	3 327	4 732	6	分类
Tox21	7 433	—	13	分类
Freesolv	642	—	2	回归
eSOL	1 125	—	2	回归
Lipo	4 190	—	9	回归

基于多通道的边学习图卷积网络

Multi-channel based edge-learning graph convolutional network

在线阅读

PDF下载

可视化

摘要/Abstract

引用本文

使用本文

图/表 9

参考文献 15

相关文章 2

Metrics

推荐阅读 0

[1]	陈燕雷, 孟俊仙, 刘玮, 王勋. 5G室内新型覆盖方案对比与分析[J]. 电信科学, 2021, 37(4): 151-158.
[2]	潘毅,李晖晖,曾磊,蔡伟文. 5G室内场景多通道联合收发技术性能与关键问题[J]. 电信科学, 2020, 36(7): 168-174.