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Published in: Cognitive Computation 6/2020

06-11-2020

Graph Convolutional Network Based on Manifold Similarity Learning

Authors: Si-Bao Chen, Xiu-Zhi Tian, Chris H. Q. Ding, Bin Luo, Yi Liu, Hao Huang, Qiang Li

Published in: Cognitive Computation | Issue 6/2020

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Abstract

In the area of large-scale graph data representation and semi-supervised learning, deep graph-based convolutional neural networks have been widely applied. However, typical graph convolutional network (GCN) aggregates information of neighbor nodes based on binary neighborhood similarity (adjacency matrix). It treats all neighbor nodes of one node equally, which does not suppress the influence of dissimilar neighbor nodes. In this paper, we investigate GCN based on similarity matrix instead of adjacency matrix of graph nodes. Gaussian heat kernel similarity in Euclidean space is first adopted, which is named EGCN. Then biologically inspired manifold similarity is trained in reproducing kernel Hilbert space (RKHS), based on which a manifold GCN (named MGCN) is proposed for graph data representation and semi-supervised learning with four different kernel types. The proposed method is evaluated with extensive experiments on four benchmark document citation network datasets. The objective function of manifold similarity learning converges very quickly on different datasets using various kernel functions. Compared with state-of-the-art methods, our method is very competitive in terms of graph node recognition accuracy. In particular, the recognition rates of MGCN (Gaussian kernel) and MGCN (Polynomial Kernel) outperform that of typical GCN about 3.8% on Cora dataset, 3.5% on Citeseer dataset, 1.3% on Pubmed dataset and 4% on Cora_ML dataset, respectively. Although the proposed MGCN is relatively simple and easy to implement, it can discover local manifold structure by manifold similarity learning and suppress the influence of dissimilar neighbor nodes, which shows the effectiveness of the proposed MGCN.

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Literature
1.
go back to reference Bruna J, Zaremba W, Szlam A, LeCun Y. Spectral networks and locally connected networks on graphs. 2013. arXiv preprint arXiv:13126203 Bruna J, Zaremba W, Szlam A, LeCun Y. Spectral networks and locally connected networks on graphs. 2013. arXiv preprint arXiv:​13126203
2.
go back to reference Scarselli F, Gori M, Tsoi AC, Hagenbuchner M, Monfardini G. The graph neural network model. IEEE Transactions on Neural Networks. 2008;20(1):61–80.CrossRef Scarselli F, Gori M, Tsoi AC, Hagenbuchner M, Monfardini G. The graph neural network model. IEEE Transactions on Neural Networks. 2008;20(1):61–80.CrossRef
3.
go back to reference Defferrard M, Bresson X, Vandergheynst P. Convolutional neural networks on graphs with fast localized spectral filtering. In: Advances in neural information processing systems. 2016;3844-3852. Defferrard M, Bresson X, Vandergheynst P. Convolutional neural networks on graphs with fast localized spectral filtering. In: Advances in neural information processing systems. 2016;3844-3852.
4.
5.
go back to reference Al-Saffar AAM, Tao H, Talab MA. Review of deep convolution neural network in image classification. In: International Conference on Radar, Antenna, Microwave, Electronics, and Telecommunications. 2017;26-31. Al-Saffar AAM, Tao H, Talab MA. Review of deep convolution neural network in image classification. In: International Conference on Radar, Antenna, Microwave, Electronics, and Telecommunications. 2017;26-31.
6.
go back to reference Velickovic P, Cucurull G, Casanova A, Romero A, Lio P, Bengio Y. Graph attention networks. 2017. arXiv preprint arXiv:171010903 Velickovic P, Cucurull G, Casanova A, Romero A, Lio P, Bengio Y. Graph attention networks. 2017. arXiv preprint arXiv:​171010903
7.
go back to reference Thekumparampil KK, Wang C, Oh S, Li LJ. Attention-based graph neural network for semi-supervised learning. 2018. arXiv preprint arXiv:180303735 Thekumparampil KK, Wang C, Oh S, Li LJ. Attention-based graph neural network for semi-supervised learning. 2018. arXiv preprint arXiv:​180303735
8.
go back to reference Wu F, Zhang T, Souza Jr AHd, Fifty C, Yu T, Weinberger KQ. Simplifying graph convolutional networks. In: International conference on machine learning. 2019;6861-6871. Wu F, Zhang T, Souza Jr AHd, Fifty C, Yu T, Weinberger KQ. Simplifying graph convolutional networks. In: International conference on machine learning. 2019;6861-6871.
9.
go back to reference Vashishth S, Yadav P, Bhandari M, Talukdar P. Confidence-based graph convolutional networks for semi-supervised learning. 2019. arXiv preprint arXiv:190108255 Vashishth S, Yadav P, Bhandari M, Talukdar P. Confidence-based graph convolutional networks for semi-supervised learning. 2019. arXiv preprint arXiv:​190108255
10.
go back to reference Yang Y, Hu Y, Wu F. Sparse and low-rank subspace data clustering with manifold regulariza- tion learned by local linear embedding. Applied Sciences. 2018;8(11):2175.CrossRef Yang Y, Hu Y, Wu F. Sparse and low-rank subspace data clustering with manifold regulariza- tion learned by local linear embedding. Applied Sciences. 2018;8(11):2175.CrossRef
11.
go back to reference Gretton A. Introduction to RKHS, and some simple kernel algorithms. Adv Top Mach Learn Lecture Conducted from University College London 16. 2013. Gretton A. Introduction to RKHS, and some simple kernel algorithms. Adv Top Mach Learn Lecture Conducted from University College London 16. 2013.
12.
go back to reference Chen SB, Ding CH, Luo B. Similarity learning of manifold data. IEEE Transactions on Cybernetics. 2015;45(9):1744–56.CrossRef Chen SB, Ding CH, Luo B. Similarity learning of manifold data. IEEE Transactions on Cybernetics. 2015;45(9):1744–56.CrossRef
13.
go back to reference Fangyuan L, Kewen X, Wenjia N. Improved reconstruction weight-based locally linear embedding algorithm. Journal of Image and Graphics. 2018;01. Fangyuan L, Kewen X, Wenjia N. Improved reconstruction weight-based locally linear embedding algorithm. Journal of Image and Graphics. 2018;01.
14.
go back to reference Roweis ST, Saul LK. Nonlinear dimensionality reduction by locally linear embedding. science. 2000;290(5500):2323-2326. Roweis ST, Saul LK. Nonlinear dimensionality reduction by locally linear embedding. science. 2000;290(5500):2323-2326.
15.
16.
go back to reference Sen P, Namata G, Bilgic M, Getoor L, Galligher B, Eliassi-Rad T. Collective classification in network data. AI magazine. 2008;29(3):93–106.CrossRef Sen P, Namata G, Bilgic M, Getoor L, Galligher B, Eliassi-Rad T. Collective classification in network data. AI magazine. 2008;29(3):93–106.CrossRef
17.
go back to reference Bojchevski A, Gunnemann S. Deep gaussian embedding of graphs: Unsupervised inductive learning via ranking. 2017. arXiv preprint arXiv:170703815 Bojchevski A, Gunnemann S. Deep gaussian embedding of graphs: Unsupervised inductive learning via ranking. 2017. arXiv preprint arXiv:​170703815
18.
go back to reference Yang Z, Cohen WW, Salakhutdinov R. Revisiting semi-supervised learning with graph embeddings. In: International conference on machine learning. 2016;40-48. Yang Z, Cohen WW, Salakhutdinov R. Revisiting semi-supervised learning with graph embeddings. In: International conference on machine learning. 2016;40-48.
20.
go back to reference Zhu X, Ghahramani Z, Lafferty JD. Semisupervised learning using gaussian fields and harmonic functions. In: International conference on machine learning. 2003;912-919. Zhu X, Ghahramani Z, Lafferty JD. Semisupervised learning using gaussian fields and harmonic functions. In: International conference on machine learning. 2003;912-919.
21.
go back to reference Belkin M, Niyogi P, Sindhwani V. Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. Journal of machine learning research. 2006;2399-2434. Belkin M, Niyogi P, Sindhwani V. Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. Journal of machine learning research. 2006;2399-2434.
22.
go back to reference Weston J, Ratle F, Mobahi H, Collobert R. Deep learning via semi-supervised embedding. In: Neural Networks: Tricks of the Trade, Springer. 2012;639-655. Weston J, Ratle F, Mobahi H, Collobert R. Deep learning via semi-supervised embedding. In: Neural Networks: Tricks of the Trade, Springer. 2012;639-655.
23.
go back to reference Perozzi B, Al-Rfou R, Skiena S. Deepwalk: Online learning of social representations. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. 2014. 701-710. Perozzi B, Al-Rfou R, Skiena S. Deepwalk: Online learning of social representations. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. 2014. 701-710.
24.
go back to reference Arora S, Hu W, Kothari PK. An analysis of the t-SNE algorithm for data visualization. Conference On Learning Theory. 2018;75:1455–62. Arora S, Hu W, Kothari PK. An analysis of the t-SNE algorithm for data visualization. Conference On Learning Theory. 2018;75:1455–62.
Metadata
Title
Graph Convolutional Network Based on Manifold Similarity Learning
Authors
Si-Bao Chen
Xiu-Zhi Tian
Chris H. Q. Ding
Bin Luo
Yi Liu
Hao Huang
Qiang Li
Publication date
06-11-2020
Publisher
Springer US
Published in
Cognitive Computation / Issue 6/2020
Print ISSN: 1866-9956
Electronic ISSN: 1866-9964
DOI
https://doi.org/10.1007/s12559-020-09788-4

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