research-article

Searching for polarization in signed graphs: a local spectral approach

Authors:

Bruno Ordozgoiti,

Aristides GionisAuthors Info & Claims

WWW '20: Proceedings of The Web Conference 2020

Pages 362 - 372

https://doi.org/10.1145/3366423.3380121

Published: 20 April 2020 Publication History

Abstract

Signed graphs have been used to model interactions in social networks, which can be either positive (friendly) or negative (antagonistic). The model has been used to study polarization and other related phenomena in social networks, which can be harmful to the process of democratic deliberation in our society. An interesting and challenging task in this application domain is to detect polarized communities in signed graphs. A number of different methods have been proposed for this task. However, existing approaches aim at finding globally optimal solutions. Instead, in this paper we are interested in finding polarized communities that are related to a small set of seed nodes provided as input. Seed nodes may consist of two sets, which constitute the two sides of a polarized structure.

In this paper we formulate the problem of finding local polarized communities in signed graphs as a locally-biased eigen-problem. By viewing the eigenvector associated with the smallest eigenvalue of the Laplacian matrix as the solution of a constrained optimization problem, we are able to incorporate the local information as an additional constraint. In addition, we show that the locally-biased vector can be used to find communities with approximation guarantee with respect to a local analogue of the Cheeger constant on signed graphs. By exploiting the sparsity in the input graph, an indicator-vector for the polarized communities can be found in time linear to the graph size.

Our experiments on real-world networks validate the proposed algorithm and demonstrate its usefulness in finding local structures in this semi-supervised manner.

References

[1]

Reid Andersen, Fan Chung, and Kevin Lang. 2006. Local graph partitioning using pagerank vectors. In 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS’06). IEEE, 475–486.

Digital Library

[2]

Fatihcan M Atay and Shiping Liu. 2020. Cheeger constants, structural balance, and spectral clustering analysis for signed graphs. Discrete Mathematics 343, 1 (2020), 111616.

[3]

Francesco Belardo. 2014. Balancedness and the least eigenvalue of Laplacian of signed graphs. Linear Algebra Appl. 446(2014), 133–147.

[4]

Yuchen Bian, Yaowei Yan, Wei Cheng, Wei Wang, Dongsheng Luo, and Xiang Zhang. 2018. On Multi-query Local Community Detection. In 2018 IEEE International Conference on Data Mining (ICDM). IEEE, 9–18.

[5]

Francesco Bonchi, Edoardo Galimberti, Aristides Gionis, Bruno Ordozgoiti, and Giancarlo Ruffo. 2019. Discovering polarized communities in signed networks. In Proceedings of the 28th ACM International Conference on Information and Knowledge Management. 961–970.

Digital Library

[6]

Stephen Boyd and Lieven Vandenberghe. 2004. Convex optimization. Cambridge university press.

Digital Library

[7]

Kai-Yang Chiang, Joyce Jiyoung Whang, and Inderjit S Dhillon. 2012. Scalable clustering of signed networks using balance normalized cut. In Proceedings of the 21st ACM international conference on Information and knowledge management. ACM, 615–624.

Digital Library

[8]

Lingyang Chu, Zhefeng Wang, Jian Pei, Jiannan Wang, Zijin Zhao, and Enhong Chen. 2016. Finding gangs in war from signed networks. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 1505–1514.

Digital Library

[9]

Fan Chung. [n.d.]. Four proofs for the Cheeger inequality and graph partition algorithms. ([n. d.]).

[10]

Wanyun Cui, Yanghua Xiao, Haixun Wang, and Wei Wang. 2014. Local search of communities in large graphs. In Proceedings of the 2014 ACM SIGMOD international conference on Management of data. ACM, 991–1002.

Digital Library

[11]

Santo Fortunato. 2010. Community detection in graphs. Physics reports 486, 3-5 (2010), 75–174.

[12]

Ming Gao, Ee-Peng Lim, David Lo, and Philips Kokoh Prasetyo. 2016. On detecting maximal quasi antagonistic communities in signed graphs. Data mining and knowledge discovery 30, 1 (2016), 99–146.

[13]

Kiran Garimella, Gianmarco De Francisci Morales, Aristides Gionis, and Michael Mathioudakis. 2018. Quantifying controversy on social media. ACM Transactions on Social Computing 1, 1 (2018), 3.

Digital Library

[14]

David F Gleich and C Seshadhri. 2012. Vertex neighborhoods, low conductance cuts, and good seeds for local community methods. In Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 597–605.

Digital Library

[15]

Gene H Golub and Charles F Van Loan. 2012. Matrix computations. Vol. 3. JHU press.

[16]

Xin Huang, Hong Cheng, Lu Qin, Wentao Tian, and Jeffrey Xu Yu. 2014. Querying k-truss community in large and dynamic graphs. In Proceedings of the 2014 ACM SIGMOD international conference on Management of data. ACM, 1311–1322.

Digital Library

[17]

Kyle Kloster and David F Gleich. 2014. Heat kernel based community detection. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 1386–1395.

Digital Library

[18]

Isabel M Kloumann and Jon M Kleinberg. 2014. Community membership identification from small seed sets. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 1366–1375.

Digital Library

[19]

Jérôme Kunegis, Stephan Schmidt, Andreas Lommatzsch, Jürgen Lerner, Ernesto W De Luca, and Sahin Albayrak. 2010. Spectral analysis of signed graphs for clustering, prediction and visualization. In Proceedings of the 2010 SIAM International Conference on Data Mining, Vol. 49. ACM, 559–570.

[20]

Mirko Lai, Viviana Patti, Giancarlo Ruffo, and Paolo Rosso. 2018. Stance Evolution and Twitter Interactions in an Italian Political Debate. In International Conference on Applications of Natural Language to Information Systems. Springer, 15–27.

Digital Library

[21]

Jure Leskovec, Daniel Huttenlocher, and Jon Kleinberg. 2010. Signed networks in social media. In Proceedings of the SIGCHI conference on human factors in computing systems. ACM, 1361–1370.

Digital Library

[22]

Hong-hai Li and Jiong-sheng Li. 2009. Note on the normalized Laplacian eigenvalues of signed graphs.Australasian J. Combinatorics 44 (2009), 153–162.

[23]

David Lo, Didi Surian, Philips Kokoh Prasetyo, Kuan Zhang, and Ee-Peng Lim. 2013. Mining direct antagonistic communities in signed social networks. Information Processing & Management 49, 4 (2013), 773–791.

Digital Library

[24]

Michael W Mahoney, Lorenzo Orecchia, and Nisheeth K Vishnoi. 2012. A local spectral method for graphs: With applications to improving graph partitions and exploring data graphs locally. Journal of Machine Learning Research 13, Aug (2012), 2339–2365.

[25]

Pedro Mercado, Francesco Tudisco, and Matthias Hein. 2016. Clustering signed networks with the geometric mean of Laplacians. In Advances in Neural Information Processing Systems. 4421–4429.

[26]

Kenneth E Read. 1954. Cultures of the central highlands, New Guinea. Southwestern Journal of Anthropology 10, 1 (1954), 1–43.

[27]

Satu Elisa Schaeffer. 2007. Graph clustering. Computer science review 1, 1 (2007), 27–64.

[28]

Joao Sedoc, Jean Gallier, Dean Foster, and Lyle Ungar. 2018. Semantic word clusters using signed spectral clustering. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). Springer, 939–949.

[29]

Mauro Sozio and Aristides Gionis. 2010. The community-search problem and how to plan a successful cocktail party. In Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 939–948.

Digital Library

[30]

Jiliang Tang, Yi Chang, Charu Aggarwal, and Huan Liu. 2016. A survey of signed network mining in social media. ACM Computing Surveys (CSUR) 49, 3 (2016), 42.

Digital Library

[31]

Federico Vegetti. 2019. The Political Nature of Ideological Polarization: The Case of Hungary. The ANNALS of the American Academy of Political and Social Science 681, 1(2019), 78–96.

Cited By

Yao KChang LQin L(2024)Identifying Large Structural Balanced Cliques in Signed GraphsIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.329580336:3(1145-1160)Online publication date: Mar-2024
https://doi.org/10.1109/TKDE.2023.3295803
Gullo FMandaglio DTagarelli A(2024)Neural discovery of balance-aware polarized communitiesMachine Learning10.1007/s10994-024-06581-4Online publication date: 9-Jul-2024
https://doi.org/10.1007/s10994-024-06581-4
Li QMa HLi ZChang L(2023)Multiresolution Local Spectral Attributed Community SearchACM Transactions on the Web10.1145/362458018:1(1-28)Online publication date: 3-Nov-2023
https://dl.acm.org/doi/10.1145/3624580
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Searching for polarization in signed graphs: a local spectral approach

Index terms have been assigned to the content through auto-classification.

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cover image ACM Conferences

WWW '20: Proceedings of The Web Conference 2020

April 2020

3143 pages

ISBN:9781450370233

DOI:10.1145/3366423

Editors:
Yennun Huang
Acadmica sinica, Taiwan
,
Irwin King
The Chinese University of Hong Kong, Hong Kong
,
Tie-Yan Liu
Microsoft Research Asia, China
,
Maarten van Steen
University of Twente, Netherlands

Copyright © 2020 ACM.

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Published: 20 April 2020

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Cited By

Yao KChang LQin L(2024)Identifying Large Structural Balanced Cliques in Signed GraphsIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.329580336:3(1145-1160)Online publication date: Mar-2024
https://doi.org/10.1109/TKDE.2023.3295803
Gullo FMandaglio DTagarelli A(2024)Neural discovery of balance-aware polarized communitiesMachine Learning10.1007/s10994-024-06581-4Online publication date: 9-Jul-2024
https://doi.org/10.1007/s10994-024-06581-4
Li QMa HLi ZChang L(2023)Multiresolution Local Spectral Attributed Community SearchACM Transactions on the Web10.1145/362458018:1(1-28)Online publication date: 3-Nov-2023
https://dl.acm.org/doi/10.1145/3624580
Yang FMa HYan CLi ZChang L(2023)Polarized Communities Search via Co-guided Random Walk in Attributed Signed NetworksACM Transactions on Internet Technology10.1145/361344923:4(1-22)Online publication date: 17-Nov-2023
https://dl.acm.org/doi/10.1145/3613449
Yang FMa HYan CLi ZChang LFrommholz IHopfgartner FLee MOakes MLalmas MZhang MSantos R(2023)Co-guided Random Walk for Polarized Communities SearchProceedings of the 32nd ACM International Conference on Information and Knowledge Management10.1145/3583780.3614814(2949-2958)Online publication date: 21-Oct-2023
https://dl.acm.org/doi/10.1145/3583780.3614814
Niu JSarıyüce A(2023)On Cohesively Polarized Communities in Signed NetworksCompanion Proceedings of the ACM Web Conference 202310.1145/3543873.3587698(1339-1347)Online publication date: 30-Apr-2023
https://dl.acm.org/doi/10.1145/3543873.3587698
Yang FMa HWang WLi ZChang L(2023)Adaptive fusion of structure and attribute guided polarized communities searchFrontiers of Computer Science10.1007/s11704-023-2776-718:1Online publication date: 2-Dec-2023
https://doi.org/10.1007/s11704-023-2776-7
Yang FMa HWang WLi ZChang L(2023)Local Spectral for Polarized Communities Search in Attributed Signed NetworkDatabase Systems for Advanced Applications10.1007/978-3-031-30675-4_5(58-74)Online publication date: 15-Apr-2023
https://doi.org/10.1007/978-3-031-30675-4_5
Sun RChen CWang XZhang YWang X(2022)Stable Community Detection in Signed Social NetworksIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2020.304722434:10(5051-5055)Online publication date: 1-Oct-2022
https://doi.org/10.1109/TKDE.2020.3047224
Bakhtar SHarutyunyan H(2022)A Fast Local Community Detection Algorithm in Signed Social Networks2022 Ninth International Conference on Social Networks Analysis, Management and Security (SNAMS)10.1109/SNAMS58071.2022.10062846(1-8)Online publication date: 29-Nov-2022
https://doi.org/10.1109/SNAMS58071.2022.10062846
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