EdMot: An Edge Enhancement Approach for Motif-aware Community Detection

Network community detection is a hot research topic in network analysis. Although many methods have been proposed for community detection, most of them only take into consideration the lower-order structure of the network at the level of individual nodes and edges. Thus, they fail to capture the higher-order characteristics at the level of small dense subgraph patterns, e.g., motifs. Recently, some higher-order methods have been developed but they typically focus on the motif-based hypergraph which is assumed to be a connected graph. However, such assumption cannot be ensured in some real-world networks. In particular, the hypergraph may become fragmented. That is, it may consist of a large number of connected components and isolated nodes, despite the fact that the original network is a connected graph. Therefore, the existing higher-order methods would suffer seriously from the above fragmentation issue, since in these approaches, nodes without connection in hypergraph can't be grouped together even if they belong to the same community. To address the above fragmentation issue, we propose an Edge enhancement approach for Motif-aware community detection (EdMot ). The main idea is as follows. Firstly, a motif-based hypergraph is constructed and the top K largest connected components in the hypergraph are partitioned into modules. Afterwards, the connectivity structure within each module is strengthened by constructing an edge set to derive a clique from each module. Based on the new edge set, the original connectivity structure of the input network is enhanced to generate a rewired network, whereby the motif-based higher-order structure is leveraged and the hypergraph fragmentation issue is well addressed. Finally, the rewired network is partitioned to obtain the higher-order community structure. Extensive experiments have been conducted on eight real-world datasets and the results show the effectiveness of the proposed method in improving the community detection performance of state-of-the-art methods.

[1]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[2]  Matthieu Latapy,et al.  Main-memory triangle computations for very large (sparse (power-law)) graphs , 2008, Theor. Comput. Sci..

[3]  Mark E. J. Newman,et al.  Stochastic blockmodels and community structure in networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Réka Albert,et al.  Near linear time algorithm to detect community structures in large-scale networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Chang-Dong Wang,et al.  Higher-Order Multi-Layer Community Detection , 2019, AAAI.

[6]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  A. Arenas,et al.  Motif-based communities in complex networks , 2007, 0710.0059.

[8]  Cynthia A. Phillips,et al.  Why do simple algorithms for triangle enumeration work in the real world? , 2014, Internet Math..

[9]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[10]  Chang-Dong Wang,et al.  Discriminative metric learning for multi-view graph partitioning , 2018, Pattern Recognit..

[11]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[12]  Mark Newman,et al.  Detecting community structure in networks , 2004 .

[13]  Delbert Dueck,et al.  Clustering by Passing Messages Between Data Points , 2007, Science.

[14]  Junming Shao,et al.  Community Detection based on Distance Dynamics , 2015, KDD.

[15]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Xiaojun Wu,et al.  Graph Regularized Nonnegative Matrix Factorization for Data Representation , 2017, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Chang-Dong Wang,et al.  Community Detection Using Attribute Homogenous Motif , 2018, IEEE Access.

[18]  Philip S. Yu,et al.  Joint Community and Structural Hole Spanner Detection via Harmonic Modularity , 2016, KDD.

[19]  Marcus Kaiser.  Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks , 2008, 0802.2512.

[20]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[21]  P. Holland,et al.  A Method for Detecting Structure in Sociometric Data , 1970, American Journal of Sociology.

[22]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[23]  Jiawei Han,et al.  Non-negative Matrix Factorization on Manifold , 2008, 2008 Eighth IEEE International Conference on Data Mining.

[24]  Sanjukta Bhowmick,et al.  On the permanence of vertices in network communities , 2014, KDD.

[25]  Peixiang Zhao,et al.  gSparsify: Graph Motif Based Sparsification for Graph Clustering , 2015, CIKM.

[26]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[27]  Samuel Leinhardt,et al.  A dynamic model for social networks , 1977 .

[28]  Chang-Dong Wang,et al.  A Harmonic Motif Modularity Approach for Multi-layer Network Community Detection , 2018, 2018 IEEE International Conference on Data Mining (ICDM).

[29]  Charu C. Aggarwal,et al.  Managing and Mining Graph Data , 2010, Managing and Mining Graph Data.

[30]  Tiago P. Peixoto.  Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Chang-Dong Wang,et al.  Overlapping Community Detection in Multi-view Brain Network , 2018, 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM).

[32]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[33]  Chang-Dong Wang,et al.  Higher-Order Brain Network Analysis for Auditory Disease , 2018, Neural Processing Letters.

[34]  Josep-Lluís Larriba-Pey,et al.  Put Three and Three Together , 2016, ACM Trans. Knowl. Discov. Data.

[35]  Jakub W. Pachocki,et al.  Scalable Motif-aware Graph Clustering , 2016, WWW.

[36]  Jure Leskovec,et al.  Local Higher-Order Graph Clustering , 2017, KDD.

[37]  Jure Leskovec,et al.  Higher-order organization of complex networks , 2016, Science.

[38]  Jean-Loup Guillaume,et al.  Fast unfolding of community hierarchies in large networks , 2008, ArXiv.