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.
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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).
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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
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