Discovering Communities and Anomalies in Attributed Graphs: Interactive Visual Exploration and Summarization

Abstract

Given a network with node attributes, how can we identify communities and spot anomalies? How can we characterize, describe, or summarize the network in a succinct way? Community extraction requires a measure of quality for connected subgraphs (e.g., social circles). Existing subgraph measures, however, either consider only the connectedness of nodes inside the community and ignore the cross-edges at the boundary (e.g., density) or only quantify the structure of the community and ignore the node attributes (e.g., conductance). In this work, we focus on node-attributed networks and introduce: (1) a new measure of subgraph quality for attributed communities called normality, (2) a community extraction algorithm that uses normality to extract communities and a few characterizing attributes per community, and (3) a summarization and interactive visualization approach for attributed graph exploration. More specifically, (1) we first introduce a new measure to quantify the normality of an attributed subgraph. Our normality measure carefully utilizes structure and attributes together to quantify both the internal consistency and external separability. We then formulate an objective function to automatically infer a few attributes (called the “focus”) and respective attribute weights, so as to maximize the normality  score of a given subgraph. Most notably, unlike many other approaches, our measure allows for many cross-edges as long as they can be “exonerated;” i.e., either (i) are expected under a null graph model, and/or (ii) their boundary nodes do not exhibit the focus attributes. Next, (2) we propose AMEN (for Attributed Mining of Entity Networks), an algorithm that simultaneously discovers the communities and their respective focus in a given graph, with a goal to maximize the total normality. Communities for which a focus that yields high normality  cannot be found are considered low quality or anomalous. Last, (3) we formulate a summarization task with a multi-criteria objective, which selects a subset of the communities that (i) cover the entire graph well, are (ii) high quality and (iii) diverse in their focus attributes. We further design an interactive visualization interface that presents the communities to a user in an interpretable, user-friendly fashion. The user can explore all the communities, analyze various algorithm-generated summaries, as well as devise their own summaries interactively to characterize the network in a succinct way. As the experiments on real-world attributed graphs show, our proposed approaches effectively find anomalous communities and outperform several existing measures and methods, such as conductance, density, OddBall, and SODA. We also conduct extensive user studies to measure the capability and efficiency that our approach provides to the users toward network summarization, exploration, and sensemaking.

References

1. Leman Akoglu, Duen Horng Chau, U. Kang, Danai Koutra, and Christos Faloutsos. 2012. OPAvion: Mining and visualization in large graphs. In SIGMOD Conference. 717--720.
2. Leman Akoglu, Mary McGlohon, and Christos Faloutsos. 2010. Oddball: Spotting anomalies in weighted graphs. In PAKDD. 410--421.
3. Leman Akoglu, Hanghang Tong, and Danai Koutra. 2014. Graph-based anomaly detection and description: A survey. DAMI 28, 4 (2014).
4. Leman Akoglu, Hanghang Tong, Brendan Meeder, and Christos Faloutsos. 2012. PICS: Parameter-free identification of cohesive subgroups in large attributed graphs. In SDM. 439--450.
5. R. Andersen, F. Chung, and K. Lang. 2006. Local graph partitioning using pagerank vectors. In FOCS.
6. Reid Andersen and Kevin J. Lang. 2006. Communities from seed sets. In WWW. 223--232.
7. Valerio Arnaboldi, Marco Conti, Andrea Passarella, and Fabio Pezzoni. 2012. Analysis of ego network structure in online social networks.. In SocialCom/PASSAT. IEEE, 31--40.
8. James Bailey. 2013. Alternative clustering analysis: A review. In Data Clustering: Algorithms and Applications. CRC Press, 535--550.
9. Mikhail Belkin and Partha Niyogi. 2003. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15, 6 (2003), 1373--1396.
10. V. D. Blondel, J. L. Guillaume, R. Lambiotte, and E. L. J. S. Mech. 2008. Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment 10 (2008), 10008.
11. Shiyu Chang, Wei Han, Jiliang Tang, Guo-Jun Qi, Charu C. Aggarwal, and Thomas S. Huang. 2015. Heterogeneous network embedding via deep architectures. In KDD. 119--128.
12. Moses Charikar. 2000. Greedy approximation algorithms for finding dense components in a graph. In APPROX.
13. Duen Horng Chau, Christos Faloutsos, Hanghang Tong, Jason I. Hong, Brian Gallagher, and Tina Eliassi-Rad. 2008. GRAPHITE: A visual query system for large graphs. In ICDM Workshops. 963--966.
14. Duen Horng Chau, Aniket Kittur, Jason I. Hong, and Christos Faloutsos. 2011. Apolo: Interactive large graph sensemaking by combining machine learning and visualization. In KDD. 739--742.
15. Aaron Clauset. 2005. Finding local community structure in networks. Physical Review E 72 (2005), 6.
16. A. Clauset, M. E. J. Newman, and C. Moore. 2004. Finding community structure in very large networks. Physical Review E 70, 6 (2004), 066111.
17. Diane J. Cook and Lawrence B. Holder. 1994. Substructure discovery using minimum description length and background knowledge. Journal of Artificial Intelligence Research 1 (1994), 231--255.
18. Michele Coscia, Giulio Rossetti, Fosca Giannotti, and Dino Pedreschi. 2012. DEMON: A local-first discovery method for overlapping communities. In KDD. 615--623.
19. Cody Dunne and Ben Shneiderman. 2013. Motif simplification: Improving network visualization readability with fan, connector, and clique glyphs. In CHI. 3247--3256.
20. M. Faloutsos, P. Faloutsos, and C. Faloutsos. 1999. On power-law relationships of the internet topology. In ACM SIGCOMM. 251--262.
21. Gary William Flake, Steve Lawrence, and C. Lee Giles. 2000. Efficient identification of web communities. In KDD.
22. Esther Galbrun, Aristides Gionis, and Nikolaj Tatti. 2014. Overlapping community detection in labeled graphs. Data Mining and Knowledge Discovery 28, 5--6 (2014), 1586--1610.
23. Jing Gao, Feng Liang, Wei Fan, Chi Wang, Yizhou Sun, and Jiawei Han. 2010. On community outliers and their efficient detection in information networks. In KDD. 813--822.
24. David F. Gleich and C. Seshadhri. 2012. Vertex neighborhoods, low conductance cuts, and good seeds for local community methods. In KDD. 597--605.
25. A. V. Goldberg. 1984. Finding a Maximum Density Subgraph. Technical Report CSD-84-171. UC Berkeley.
26. Aditya Grover and Jure Leskovec. 2016. node2vec: Scalable feature learning for networks. In KDD. 855--864.
27. Stephan Günnemann, Ines Färber, Brigitte Boden, and Thomas Seidl. 2010. Subspace clustering meets dense subgraph mining: A synthesis of two paradigms. In ICDM. 845--850.
28. Stephan Günnemann, Ines Farber, Sebastian Raubach, and Thomas Seidl. 2013. Spectral subspace clustering for graphs with feature vectors. In ICDM. IEEE, 231--240.
29. Manish Gupta, Arun Mallya, Subhro Roy, Jason H. D. Cho, and Jiawei Han. 2014. Local learning for mining outlier subgraphs from network datasets. In SIAM SDM. 73--81.
30. Keith Henderson, Brian Gallagher, Tina Eliassi-Rad, Hanghang Tong, Sugato Basu, Leman Akoglu, Danai Koutra, Christos Faloutsos, and Lei Li. 2012. RolX: Structural role extraction and mining in large graphs. In KDD. ACM, 1231--1239.
31. Xiao Huang, Jundong Li, and Xia Hu. 2017. Accelerated attributed network embedding. In SDM. 633--641.
32. G. Karpis and V. Kumar. 1998. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing 20, 1 (1998), 359--392.
33. George Karypis and Vipin Kumar. 1998. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing 20 (1998), 359--392.
34. Danai Koutra, Di Jin, Yuanshi Ning, and Christos Faloutsos. 2015. Perseus: An interactive large-scale graph mining and visualization tool. PVLDB 8, 12 (2015), 1924--1927.
35. Danai Koutra, U. Kang, Jilles Vreeken, and Christos Faloutsos. 2014. VOG: Summarizing and understanding large graphs. In SDM. 91--99.
36. Darong Lai, Xiangjun Wu, Hongtao Lu, and Christine Nardini. 2011. Learning overlapping communities in complex networks via non-negative matrix factorization. International Journal of Modern Physics C 22, 10 (2011), 1173--1190.
37. Jure Leskovec, Jon Kleinberg, and Christos Faloutsos. 2005. Graphs over time: Densification laws, shrinking diameters and possible explanations. In KDD. ACM, 177--187.
38. Jure Leskovec, Jon M. Kleinberg, and Christos Faloutsos. 2005. Graphs over time: Densification laws, shrinking diameters and possible explanations. In KDD. 177--187.
39. Jure Leskovec, Kevin J. Lang, Anirban Dasgupta, and Michael W. Mahoney. 2008. Statistical properties of community structure in large social and information networks. In WWW. 695--704.
40. Nan Li, Ziyu Guan, Lijie Ren, Jian Wu, Jiawei Han, and Xifeng Yan. 2013. gIceberg: Towards iceberg analysis in large graphs. In ICDE. 1021--1032.
41. Nan Li, Huan Sun, Kyle Chipman, Jemin George, and Xifeng Yan. 2014. A probabilistic approach to uncovering attributed graph anomalies. In SIAM SDM. 82--90.
42. Rui Li, Chi Wang, and Kevin Chen-Chuan Chang. 2014. User profiling in an ego network: Co-profiling attributes and relationships. In WWW. 819--830.
43. Yike Liu, Abhilash Dighe, Tara Safavi, and Danai Koutra. 2016. A graph summarization: A survey. CoRR abs/1612.04883 (2016).
44. Bo Long, Zhongfei (Mark) Zhang, Xiaoyun Wu, and Philip S. Yu. 2006. Spectral clustering for multi-type relational data. In ICML, vol. 148. 585--592.
45. Douglas S. Massey and Nancy A. Denton. 1988. The dimensions of residential segregation. Social Forces 67, 2 (1988), 218--315.
46. Julian J. McAuley and Jure Leskovec. 2014. Discovering social circles in ego networks. ACM Transactions on Knowledge Discovery from Data 8, 1 (2014), 4:1--4:28.
47. Mary McGlohon, Leman Akoglu, and Christos Faloutsos. 2008. Weighted graphs and disconnected components: patterns and a generator. In KDD. 524--532.
48. Miller McPherson, Lynn Smith-Lovin, and James M. Cook. 2001. Birds of a feather: Homophily in social networks. Annual Review of Sociology 27, 1 (2001), 415--444.
49. J. Moody. 2001. Race, school integration, and friendship segregation in America. American Journal of Sociology 107, 3 (2001), 679--716.
50. George L. Nemhauser and Laurence A. Wolsey. 1978. Best algorithms for approximating the maximum of a submodular set function. Mathematics of Operations Research 3, 3 (1978), 177--188.
51. M. E. J. Newman and M. Girvan. 2003. Mixing patterns and community structure in networks. In Statistical Mechanics of Complex Networks, Vol. 625. 66--87.
52. M. E. J. Newman. 2002. Assortative mixing in networks. Physical Review Letters 89, 20 (2002).
53. M. E. J. Newman. 2003. Mixing patterns in networks. Physical Review E 67 (2003).
54. M. E. J. Newman. 2006. Modularity and community structure in networks. Proceedings of the National Academy of Sciences of the United States of America 103, 23 (2006), 8577--8582.
55. M. E. J. Newman. 2010. Networks: An Introduction. Oxford University Press, Oxford; New York.
56. Andrew Y. Ng, Michael I. Jordan, and Yair Weiss. 2001. On spectral clustering: Analysis and an algorithm. In NIPS.
57. Donglin Niu, Jennifer G. Dy, and Michael I. Jordan. 2014. Iterative discovery of multiple alternative clustering views. IEEE Transactions on Pattern Analysis and Machine Intelligence 36, 7 (2014), 1340--1353.
58. Caleb C. Noble and Diane J. Cook. 2003. Graph-based anomaly detection. In KDD. ACM, 631--636.
59. Jeffrey Pattillo, Alexander Veremyev, Sergiy Butenko, and Vladimir Boginski. 2013. On the maximum quasi-clique problem. Discrete Applied Mathematics 161, 1--2 (2013), 244--257.
60. Bryan Perozzi and Leman Akoglu. 2016. Scalable anomaly ranking of attributed neighborhoods. In SIAM SDM.
61. Bryan Perozzi, Leman Akoglu, Patricia Iglesias Sánchez, and Emmanuel Müller. 2014. Focused clustering and outlier detection in large attributed graphs. In KDD. 1346--1355.
62. Bryan Perozzi, Rami Al-Rfou’, and Steven Skiena. 2014. DeepWalk: Online learning of social representations. In KDD. 701--710.
63. Robert Pienta, James Abello, Minsuk Kahng, and Duen Horng Chau. 2015. Scalable graph exploration and visualization: Sensemaking challenges and opportunities. In BigComp. IEEE Computer Society, 271--278.
64. Robert Pienta, Minsuk Kahng, Zhiyuan Lin, Jilles Vreeken, Partha Talukdar, James Abello, Ganesh Parameswaran, and Duen Horng Chau. 2017. FACETS: Adaptive local exploration of large graphs. In SDM.
65. Zijie Qi and Ian Davidson. 2009. A principled and flexible framework for finding alternative clusterings. In KDD. 717--726.
66. Eunsu Ryu, Yao Rong, Jie Li, and Ashwin Machanavajjhala. 2013. Curso: Protect yourself from curse of attribute inference: A social network privacy-analyzer. In DBSocial. 13--18.
67. Hiroaki Shiokawa, Yasuhiro Fujiwara, and Makoto Onizuka. 2013. Fast algorithm for modularity-based graph clustering. In AAAI.
68. Arlei Silva, Wagner Meira Jr., and Mohammed J. Zaki. 2012. Mining attribute-structure correlated patterns in large attributed graphs. PVLDB 5, 5 (2012), 466--477.
69. Daniel A. Spielman and Shang-Hua Teng. 2004. Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In STOC. 81--90.
70. Jian Tang, Meng Qu, Mingzhe Wang, Ming Zhang, Jun Yan, and Qiaozhu Mei. 2015. LINE: Large-scale information network embedding. In WWW. 1067--1077.
71. Yuanyuan Tian, Richard A. Hankins, and Jignesh M. Patel. 2008. Efficient aggregation for graph summarization. In SIGMOD. 567--580.
72. Amanda L. Traud, Peter J. Mucha, and Mason A. Porter. 2012. Social structure of Facebook networks. Physica A: Statistical Mechanics and its Applications 391, 16 (2012), 4165--4180.
73. Charalampos E. Tsourakakis, Francesco Bonchi, Aristides Gionis, Francesco Gullo, and Maria A. Tsiarli. 2013. Denser than the densest subgraph: Extracting optimal quasi-cliques with quality guarantees. In KDD.
74. Charalampos E. Tsourakakis, U. Kang, Gary L. Miller, and Christos Faloutsos. 2009. DOULION: Counting triangles in massive graphs with a coin. In KDD. 837--846.
75. Tatiana von Landesberger, Arjan Kuijper, Tobias Schreck, Jrn Kohlhammer, Jarke J. van Wijk, Jean-Daniel Fekete, and Dieter W. Fellner. 2011. Visual analysis of large graphs: State-of-the-art and future research challenges. Computer Graphics Forum 30, 6 (2011), 1719--1749.
76. Joyce Jiyoung Whang, David F. Gleich, and Inderjit S. Dhillon. 2013. Overlapping community detection using seed set expansion. In CIKM. 2099--2108.
77. Jierui Xie, Stephen Kelley, and Boleslaw K. Szymanski. 2013. Overlapping community detection in networks: The state-of-the-art and comparative study. ACM Computing Surveys 45, 4 (2013), 43.
78. Jaewon Yang and Jure Leskovec. 2012. Community-affiliation graph model for overlapping network community detection. In ICDM. 1170--1175.
79. Jaewon Yang and Jure Leskovec. 2012. Defining and evaluating network communities based on ground-truth. In ICDM. 745--754.
80. Jaewon Yang and Jure Leskovec. 2013. Overlapping community detection at scale: A nonnegative matrix factorization approach. In WSDM. 587--596.
81. Jaewon Yang, Julian J. McAuley, and Jure Leskovec. 2013. Community detection in networks with node attributes. In ICDM. 1151--1156.
82. Shengqi Yang, Yanan Xie, Yinghui Wu, Tianyi Wu, Huan Sun, Jian Wu, and Xifeng Yan. 2014. SLQ: A user-friendly graph querying system. In SIGMOD. 893--896.
83. Ning Zhang, Yuanyuan Tian, and Jignesh M. Patel. 2010. Discovery-driven graph summarization. In ICDE. 880--891.
84. Yang Zhang and Srinivasan Parthasarathy. 2012. Extracting, analyzing and visualizing triangle k-core motifs within networks. In ICDE. 1049--1060.
85. Elena Zheleva and Lise Getoor. 2009. To join or not to join: The illusion of privacy in social networks with mixed public and private user profiles. In WWW. 531--540.
86. Yang Zhou, Hong Cheng, and Jeffrey Xu Yu. 2009. Graph clustering based on structural/attribute similarities. Proceedings of the VLDB Endowment 2, 1 (2009), 718--729.

Index Terms

• Computing methodologies

  • Machine learning

    • Learning paradigms

      • Unsupervised learning

        • Anomaly detection

        • Cluster analysis

• Human-centered computing

  • Human computer interaction (HCI)

    • Interactive systems and tools

• Information systems

  • Information systems applications

    • Data mining