Abstract
Graph Convolutional Networks (GCNs) have been proven to be effective in various graph-related tasks, such as community detection. Essentially graph convolution is simply a special form of Laplacian smoothing, acting as a low-pass filter that makes the features of nodes linked to each other similarly. For community detection, however, the similarity of intra-community nodes and the difference of inter-community nodes are equally vital. To bridge the gap between GCNs and community detection, we develop a novel Community-Centric Dual Filter (CCDF) framework for community detection. The central idea is that, besides of low-pass filter in GCN, we define network modularity enhanced high-pass filter to separate the discriminative signals from the raw features. In addition, we design a scheme to jointly optimize low-frequency and high-frequency information extraction on statistical modeling of Markov Random Fields. Extensive experiments demonstrate that the proposed CCDF model can consistently outperform or match state-of-the-art baselines in terms of semi-supervised community detection.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
References
Nowozin, S., Lampert, C.H.: Structured Learning and Prediction in Computer Vision. Now publishers Inc. (2011)
Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016)
Nt, H., Maehara, T.: Revisiting graph neural networks: all we have is low-pass filters. arXiv preprint arXiv:1905.09550 (2019)
Li, Q., Wu, X.M., Liu, H., et al.: Label efficient semi-supervised learning via graph filtering. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9582–9591 (2019)
Jin, D., Liu, Z., Li, W., et al.: Graph convolutional networks meet Markov random fields: semi-supervised community detection in attribute networks. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, no. 01, pp. 152–159 (2019)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Jin, W., Derr, T., Wang, Y., et al.: Node similarity preserving graph convolutional networks. Proceedings of the 14th ACM International Conference on Web Search and Data Mining, pp. 148–156 (2021)
Bo, D., Wang, X., Shi, C., Shen, H.: Beyond low-frequency information in graph convolutional networks. arXiv preprint arXiv:2101.00797 (2021)
Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. arXiv preprint arXiv:1606.09375 (2016)
Xu, K., Li, C., Tian, Y., et al.: Representation learning on graphs with jumping knowledge networks. In: International Conference on Machine Learning, pp. 5453–5462. PMLR (2018)
Wu, F., Souza, A., Zhang, T., et al.: Simplifying graph convolutional networks. International International Conference on Machine Learning, pp. 6861–6871. PMLR (2019)
Veličković, P., Cucurull, G., Casanova, A., et al.: Graph attention networks. arXiv preprint arXiv:1710.10903 (2017)
Rong, Y., Huang, W., Xu, T., et al.: DropEdge: towards deep graph convolutional networks on node classification. arXiv preprint arXiv:1907.10903 (2019)
Xie, Y., Li, S., Yang, C., et al.: When Do GNNs work: understanding and improving neighborhood aggregation. In: Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI (2020)
Xu, B., Shen, H., Cao, Q., et al.: Graph convolutional networks using heat kernel for semi-supervised learning. arXiv preprint arXiv:2007.16002 (2020)
Yin, H., Hu, Z., Zhou, X., et al.: Discovering interpretable geosocial communities for user behavior prediction. In: IEEE 32nd International Conference on Data Engineering (ICDE), pp. 942–953 (2016)
Bernardes, D., Diaby, M., Fournier, R., et al.: A social formalism and survey for recommender systems. ACM SIGKDD Explor. Newsl. 16(2), 20–37 (2015)
Blondel, V.D., Guillaume, J.L., Lambiotte, R., et al.: Fast unfolding of communities in large networks. J. Stat. Mech.: Theory Exp. P10008 (2008)
Jin, D., Yang, B., Baquero, C., et al.: A Markov random walk under constraint for discovering overlapping communities in complex networks. J. Stat. Mech.: Theory Exp. P05031 (2011)
Qu, M., Bengio, Y., Tang, J.: GMNN: Graph Markov neural networks. In: International Conference on Machine Learning. pp. 5241–5250. PMLR (2019)
Abu-El-Haija, S., Perozzi, B., Kapoor, A., et al.: MixHop: higher-order graph convolutional architectures via sparsified neighborhood mixing. In: International Conference on Machine Learning, pp. 21–29. PMLR (2019)
Li, Y., Sha, C., Huang, X., et al.: Community detection in attributed graphs: an embedding approach. In: Proceedings of the AAAI Conference on Artificial Intelligence (2018)
Newman, M.E., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)
Zhu, J., Yan, Y., Zhao, L., et al.: Generalizing graph neural networks beyond homophily. arXiv preprint arXiv:2006.11468 (2020)
Chien, E., Peng, J., Li, P., et al.: Adaptive universal generalized PageRank graph neural network. arXiv preprint arXiv:2006.07988 (2020)
Cui, G., Zhou, J., Yang, C., et al.: Adaptive graph encoder for attributed graph embedding. In: Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2020)
Newman, M.E.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. U.S.A. 103(23), 8577–8582 (2006)
Oono, K., Suzuki, T.: Graph neural networks exponentially lose expressive power for node classification. arXiv preprint arXiv:1905.10947 (2019)
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 61773215, 61802206).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Ai, G., Yan, H., Yang, J., Li, X. (2021). Beyond Laplacian Smoothing for Semi-supervised Community Detection. In: Qiu, H., Zhang, C., Fei, Z., Qiu, M., Kung, SY. (eds) Knowledge Science, Engineering and Management. KSEM 2021. Lecture Notes in Computer Science(), vol 12817. Springer, Cham. https://doi.org/10.1007/978-3-030-82153-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-82153-1_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-82152-4
Online ISBN: 978-3-030-82153-1
eBook Packages: Computer ScienceComputer Science (R0)