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Autonomous Semantic Community Detection via Adaptively Weighted Low-rank Approximation

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Published:15 November 2019Publication History
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Abstract

Identification of semantic community structures is important for understanding the interactions and sentiments of different groups of people and predicting the social emotion. A robust community detection method needs to autonomously determine the number of communities and community structure for a given network. Nonnegative matrix factorization (NMF), a component decomposition approach for latent sentiment discovery, has been extensively used for community detection. However, the existing NMF-based methods require the number of communities to be determined a priori, limiting their applicability in practice of affective computing. Here, we develop a novel NMF-based method to autonomously determine the number of semantic communities and community structure simultaneously. In our method, we use an initial number of semantic communities, larger than the actual number, in the NMF formulation, and then suppress some of the communities by introducing an adaptively weighted group-sparse low-rank regularization to derive the target number of communities and at the same time the corresponding community structure. Our method not only maintains the efficiency without increasing the complexity compared to the original NMF method but also can be straightforwardly extended to handle the non-network data. We thoroughly examine the new method, showing its superior performance over several competing methods on synthetic and large real-world social networks.

References

  1. Lada A. Adamic and Natalie Glance. 2005. The political blogosphere and the 2004 U.S. election. In Proceedings of the 3rd International Workshop on Link Discovery. ACM, 36--43.Google ScholarGoogle Scholar
  2. Y.-Y. Ahn, J. P. Bagrow, and S. Lehmann. 2010. Link communities reveal multiscale complexity in networks. Nature 466 (2010), 761--764.Google ScholarGoogle ScholarCross RefCross Ref
  3. H. Akaike. 1974. A new look at the statistical model identification. IEEE Trans. Automat. Control 19, 6 (Dec. 1974), 716--723. DOI:https://doi.org/10.1109/TAC.1974.1100705Google ScholarGoogle ScholarCross RefCross Ref
  4. David M. Blei, Perry R. Cook, and Matthew Hoffman. 2010. Bayesian nonparametric matrix factorization for recorded music. In Proceedings of the 27th International Conference on Machine Learning (ICML’10). Omnipress, 439--446. Retrieved from http://www.icml2010.org/papers/523.pdf.Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Vincent D. Blondel, Jean-Loup Guillaume, Renaud Lambiotte, and Etienne Lefebvre. 2008. Fast unfolding of communities in large networks. J. Stat. Mech.: Theory Exp. 2008, 10 (2008), P10008. http://stacks.iop.org/1742-5468/2008/i=10/a=P10008.Google ScholarGoogle ScholarCross RefCross Ref
  6. Emmanuel J. Candès, Xiaodong Li, Yi Ma, and John Wright. 2011. Robust principal component analysis?J. ACM 58, 3, Article 11 (June 2011), 37 pages. DOI:https://doi.org/10.1145/1970392.1970395Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Ali Taylan Cemgil. 2009. Bayesian inference for nonnegative matrix factorisation models. Intell. Neurosci. 2009, Article 4 (Jan. 2009), 17 pages. DOI:https://doi.org/10.1155/2009/785152Google ScholarGoogle Scholar
  8. James W. Demmel, Michael T. Heath, and Henk A. Van Der Vorst. 1993. Parallel numerical linear algebra. Acta Numerica 2 (1993), 111--197.Google ScholarGoogle ScholarCross RefCross Ref
  9. Guiguang Ding, Wenshuo Chen, Sicheng Zhao, Jungong Han, and Qiaoyan Liu. 2018. Real-time scalable visual tracking via quadrangle kernelized correlation filters. IEEE Trans. Intell. Transport. Syst. 19, 1 (2018), 140--150. DOI:https://doi.org/10.1109/TITS.2017.2774778Google ScholarGoogle ScholarCross RefCross Ref
  10. Jordi Duch and Alex Arenas. 2005. Community detection in complex networks using extremal optimization. Phys. Rev. E 72 (Aug. 2005), 027104. Issue 2. DOI:https://doi.org/10.1103/PhysRevE.72.027104Google ScholarGoogle ScholarCross RefCross Ref
  11. Santo Fortunato. 2010. Community detection in graphs. Phys. Rep. 486, 3 (2010), 75--174.Google ScholarGoogle ScholarCross RefCross Ref
  12. Santo Fortunato and Darko Hric. 2016. Community detection in networks: A user guide. Phys. Rep. 659 (2016), 1--44. DOI:https://doi.org/10.1016/j.physrep.2016.09.002 Community detection in networks: A user guide.Google ScholarGoogle ScholarCross RefCross Ref
  13. Michelle Girvan and Mark E. J. Newman. 2002. Community structure in social and biological networks. Proc. Natl. Acad. Sci. U.S.A. 99, 12 (2002), 7821--7826.Google ScholarGoogle Scholar
  14. 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 8 mining in large graphs. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’12). 1231--1239. DOI:https://doi.org/10.1145/2339530.2339723Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Brian Karrer and M. E. J. Newman. 2011. Stochastic blockmodels and community structure in networks. Phys. Rev. E 83 (Jan 2011), 016107. Issue 1. DOI:https://doi.org/10.1103/PhysRevE.83.016107Google ScholarGoogle ScholarCross RefCross Ref
  16. Andrea Lancichinetti, Santo Fortunato, and Filippo Radicchi. 2008. Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78, 4 (2008), 046110.Google ScholarGoogle ScholarCross RefCross Ref
  17. Daniel D. Lee and H. Sebastian Seung. 1999. Learning the parts of objects by non-negative matrix factorization. Nature 401, 6755 (1999), 788--791.Google ScholarGoogle Scholar
  18. Daniel D. Lee and H. Sebastian Seung. 2000. Algorithms for non-negative matrix factorization. In Proceedings of the Conference on Neural Information Processing Systems (NIPS’00). 556--562.Google ScholarGoogle Scholar
  19. Chao Liu, Hung-chih Yang, Jinliang Fan, Li-Wei He, and Yi-Min Wang. 2010. Distributed nonnegative matrix factorization for web-scale dyadic data analysis on mapreduce. In Proceedings of the 19th International Conference on World Wide Web. ACM, New York, NY, 681--690. DOI:https://doi.org/10.1145/1772690.1772760Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Renquan Lu, Wenwu Yu, Jinhu Lu, and Anke Xue. 2014. Synchronization on complex networks of networks. IEEE Trans. Neural Netw. Learn. Syst. 25, 11 (Nov. 2014), 2110--2118. DOI:https://doi.org/10.1109/TNNLS.2014.2305443Google ScholarGoogle ScholarCross RefCross Ref
  21. David Lusseau and Mark E. J. Newman. 2004. Identifying the role that animals play in their social networks. Proc. Roy. Soc. London. Series B: Biol. Sci. 271, S 6 (2004), 477--481.Google ScholarGoogle ScholarCross RefCross Ref
  22. Fragkiskos D. Malliaros and Michalis Vazirgiannis. 2013. Clustering and community detection in directed networks: A survey. Phys. Rep. 533, 4 (2013), 95--142.Google ScholarGoogle ScholarCross RefCross Ref
  23. Rahul Mazumder, Trevor Hastie, and Robert Tibshirani. 2010. Spectral regularization algorithms for learning large incomplete matrices. J. Mach. Learn. Res. 11 (Aug. 2010), 2287--2322. Retrieved from http://dl.acm.org/citation.cfm?id=1756006.1859931.Google ScholarGoogle Scholar
  24. M. Morup and L. K. Hansen. 2009. Tuning pruning in sparse non-negative matrix factorization. In Proceedings of the 17th European Signal Processing Conference. 1923--1927.Google ScholarGoogle Scholar
  25. Morten Morup and Lars Kai Hansen. 2009. Automatic relevance determination for multi-way models. J. Chemometr. 23, 7–8 (2009), 352--363. DOI:https://doi.org/10.1002/cem.1223Google ScholarGoogle ScholarCross RefCross Ref
  26. D. L. Nelson, McEvoy, C. L., and T. A. Schreiber. 1998. The University of South Florida word association, rhyme, and word fragment norms. Retrieved from http://w3.usf.edu/FreeAssociation/.Google ScholarGoogle Scholar
  27. Mark E. J. Newman. 2006. Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74, 3 (2006), 036104.Google ScholarGoogle ScholarCross RefCross Ref
  28. Mark E. J. Newman. 2006. Modularity and community structure in networks. Proc. Natl. Acad. Sci. U.S.A. 103, 23 (2006), 8577--8582.Google ScholarGoogle ScholarCross RefCross Ref
  29. M. E. J. Newman. 2013. Spectral methods for community detection and graph partitioning. Phys. Rev. E 88 (Oct 2013), 042822. Issue 4. DOI:https://doi.org/10.1103/PhysRevE.88.042822Google ScholarGoogle ScholarCross RefCross Ref
  30. Ioannis Psorakis, Stephen Roberts, Mark Ebden, and Ben Sheldon. 2011. Overlapping community detection using bayesian non-negative matrix factorization. Phys. Rev. E 83, 6 (2011), 066114.Google ScholarGoogle ScholarCross RefCross Ref
  31. Jiahu Qin, Huijun Gao, and Wei Xing Zheng. 2015. Exponential synchronization of complex networks of linear systems and nonlinear oscillators: A unified analysis. IEEE Trans. Neural Netw. Learn. Syst. 26, 3 (Mar. 2015), 510--521. DOI:https://doi.org/10.1109/TNNLS.2014.2316245Google ScholarGoogle ScholarCross RefCross Ref
  32. Nurlaila Rosli, Nordiana Rajaee, and David Bong. 2016. Non negative matrix factorization for music emotion classification. In Advances in Machine Learning and Signal Processing, Ping Jack Soh, Wai Lok Woo, Hamzah Asyrani Sulaiman, Mohd Azlishah Othman, and Mohd Shakir Saat (Eds.). Springer International Publishing, Cham, 175--185.Google ScholarGoogle Scholar
  33. Martin Rosvall and Carl T. Bergstrom. 2008. Maps of random walks on complex networks reveal community structure. Proc. Natl. Acad. Sci. U.S.A. 105, 4 (2008), 1118--1123. DOI:https://doi.org/10.1073/pnas.0706851105 arXiv: https://www.pnas.org/content/105/4/1118.full.pdf.Google ScholarGoogle ScholarCross RefCross Ref
  34. Gideon Schwarz. 1978. Estimating the dimension of a model. Ann. Stat. 6, 2 (3 1978), 461--464. DOI:https://doi.org/10.1214/aos/1176344136Google ScholarGoogle Scholar
  35. Bo Shen, Zidong Wang, Derui Ding, and Huisheng Shu. 2013. H state estimation for complex networks with uncertain inner coupling and incomplete measurements. IEEE Trans. Neural Netw. Learn. Syst. 24, 12 (Dec. 2013), 2027--2037. DOI:https://doi.org/10.1109/TNNLS.2013.2271357Google ScholarGoogle Scholar
  36. T. C. Silva and Liang Zhao. 2012. Stochastic competitive learning in complex networks. IEEE Trans. Neural Netw. Learn. Syst. 23, 3 (Mar. 2012), 385--398. DOI:https://doi.org/10.1109/TNNLS.2011.2181866Google ScholarGoogle Scholar
  37. Paris Smaragdis and Judith C Brown. 2003. Non-negative matrix factorization for polyphonic music transcription. In Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics. IEEE, 177--180.Google ScholarGoogle ScholarCross RefCross Ref
  38. P. Song, S. Ou, W. Zheng, Y. Jin, and L. Zhao. 2016. Speech emotion recognition using transfer non-negative matrix factorization. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’16). 5180--5184. DOI:https://doi.org/10.1109/ICASSP.2016.7472665Google ScholarGoogle Scholar
  39. Alexander Strehl and Joydeep Ghosh. 2003. Cluster ensembles—A knowledge reuse framework for combining multiple partitions. J. Mach. Learn. Res. 3 (2003), 583--617.Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. V. Y. F. Tan and C. Fevotte. 2013. Automatic relevance determination in nonnegative matrix factorization with the /spl beta/-Divergence. IEEE Trans. Pattern Anal. Mach. Intell. 35, 7 (2013), 1592--1605. DOI:https://doi.org/10.1109/TPAMI.2012.240Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Amanda L. Traud, Peter J. Mucha, and Mason A. Porter. 2012. Social structure of facebook networks. Phys. A: Stat. Mech.anics and its Appl. 391, 16 (2012), 4165--4180. DOI:https://doi.org/10.1016/j.physa.2011.12.021Google ScholarGoogle ScholarCross RefCross Ref
  42. Dingding Wang, Tao Li, Shenghuo Zhu, and Chris Ding. 2008. Multi-document summarization via sentence-level semantic analysis and symmetric matrix factorization. In Proceedings of the 31st Annual International ACM Special Interest Group on Information Retrieval (SIGIR’08). ACM, 307--314.Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. Fei Wang, Tao Li, Xin Wang, Shenghuo Zhu, and Chris Ding. 2011. Community discovery using nonnegative matrix factorization. Data Min. Knowl. Discov. 22, 3 (May 2011), 493--521. DOI:https://doi.org/10.1007/s10618-010-0181-yGoogle ScholarGoogle ScholarDigital LibraryDigital Library
  44. Yu-Xiong Wang and Yu-Jin Zhang. 2013. Nonnegative matrix factorization: A comprehensive review. IEEE Trans. Knowl. Data Eng. 25, 6 (June 2013), 1336--1353. DOI:https://doi.org/10.1109/TKDE.2012.51Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. Jierui Xie, Stephen Kelley, and Boleslaw K. Szymanski. 2013. Overlapping community detection in networks: The state-of-the-art and comparative study. ACM Comput. Surveys 45, 4 (2013), 43.Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. Liang Yang, Xiaochun Cao, Dongxiao He, Chuan Wang, Xiao Wang, and Weixiong Zhang. 2016. Modularity-based community detection with deep learning. In Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI’16). 2252--2258. http://www.ijcai.org/Abstract/16/321Google ScholarGoogle Scholar
  47. Liang Yang, Xiaochun Cao, Di Jin, Xiao Wang, and Dan Meng. 2015. A unified semi-supervised community detection framework using latent space graph regularization. IEEE Trans. Cybernet. 45, 11 (2015), 2585--2598. DOI:https://doi.org/10.1109/TCYB.2014.2377154Google ScholarGoogle ScholarCross RefCross Ref
  48. Liang Yang, Meng Ge, Di Jin, Dongxiao He, Huazhu Fu, Jing Wang, and Xiaochun Cao. 2017. Exploring the roles of cannot-link constraint in community detection via multi-variance mixed gaussian generative model. PloS One 12, 7 (2017), e0178029.Google ScholarGoogle ScholarCross RefCross Ref
  49. Liang Yang, Di Jin, Dongxiao He, Huazhu Fu, Xiaochun Cao, and Francoise Fogelman-Soulie. 2017. Improving the efficiency and effectiveness of community detection via prior-induced equivalent super-network. Sci. Rep. 7, 1 (2017), 634.Google ScholarGoogle Scholar
  50. Liang Yang, Di Jin, Xiao Wang, and Xiaochun Cao. 2015. Active link selection for efficient semi-supervised community detection. Sci. Rep. 5, 1 (2015), 9039.Google ScholarGoogle Scholar
  51. Tianbao Yang, Rong Jin, Yun Chi, and Shenghuo Zhu. 2009. Combining link and content for community detection: A discriminative approach. In Proceedings of the 15th ACM Special Interest Group on Knowledge Discovery and Data Mining (SIGKDD’09). 927--936. DOI:https://doi.org/10.1145/1557019.1557120Google ScholarGoogle ScholarDigital LibraryDigital Library
  52. W. Zachary. 1977. An information flow modelfor conflict and fission in small groups1. J. Anthropol. Res. 33, 4 (1977), 452--473.Google ScholarGoogle ScholarCross RefCross Ref
  53. Sicheng Zhao, Guiguang Ding, Yue Gao, and Jungong Han. 2017. Approximating discrete probability distribution of image emotions by multi-modal features fusion. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI’17). 4669--4675. DOI:https://doi.org/10.24963/ijcai.2017/651Google ScholarGoogle ScholarCross RefCross Ref
  54. Sicheng Zhao, Guiguang Ding, Yue Gao, Xin Zhao, Youbao Tang, Jungong Han, Hongxun Yao, and Qingming Huang. 2018. Discrete probability distribution prediction of image emotions with shared sparse learning. IEEE Trans. Affect. Comput. (2018), 1--1. DOI:https://doi.org/10.1109/TAFFC.2018.2818685Google ScholarGoogle Scholar
  55. Sicheng Zhao, Yue Gao, Guiguang Ding, and Tat-Seng Chua. 2018. Real-time multimedia social event detection in microblog. IEEE Trans. Cybernet. 48, 11 (2018), 3218--3231. DOI:https://doi.org/10.1109/TCYB.2017.2762344Google ScholarGoogle ScholarCross RefCross Ref
  56. Sicheng Zhao, Amir Gholaminejad, Guiguang Ding, Yue Gao, Jungong Han, and Kurt Keutzer. 2019. Personalized emotion recognition by personality-aware high-order learning of physiological signals. ACM Trans. Multimedia Comput. Commun. Appl. 15, 1s (2019), 14:1--14:18. DOI:https://doi.org/10.1145/3233184Google ScholarGoogle ScholarDigital LibraryDigital Library
  57. Sicheng Zhao, Hongxun Yao, Yue Gao, Guiguang Ding, and Tat-Seng Chua. 2018. Predicting personalized image emotion perceptions in social networks. IEEE Trans. Affect. Comput. 9, 4 (2018), 526--540. DOI:https://doi.org/10.1109/TAFFC.2016.2628787Google ScholarGoogle ScholarDigital LibraryDigital Library
  58. Sicheng Zhao, Hongxun Yao, Yue Gao, Rongrong Ji, and Guiguang Ding. 2017. Continuous probability distribution prediction of image emotions via multitask shared sparse regression. IEEE Trans. Multimedia 19, 3 (2017), 632--645. DOI:https://doi.org/10.1109/TMM.2016.2617741Google ScholarGoogle ScholarDigital LibraryDigital Library
  59. Sicheng Zhao, Xin Zhao, Guiguang Ding, and Kurt Keutzer. 2018. EmotionGAN: Unsupervised domain adaptation for learning discrete probability distributions of image emotions. In Proceedings of the ACM Multimedia Conference on Multimedia Conference (MM’18). 1319--1327. DOI:https://doi.org/10.1145/3240508.3240591Google ScholarGoogle ScholarDigital LibraryDigital Library
  60. Mingjun Zhong and Mark Girolami. 2009. Reversible jump MCMC for non-negative matrix factorization. In Proceedings of the International Conference on Artificial Intelligence and Statistics. 663--670.Google ScholarGoogle Scholar

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      cover image ACM Transactions on Multimedia Computing, Communications, and Applications
      ACM Transactions on Multimedia Computing, Communications, and Applications  Volume 15, Issue 3s
      Special Issue on Face Analysis for Applications and Special Issue on Affective Computing for Large-Scale Heterogeneous Multimedia Data
      November 2019
      304 pages
      ISSN:1551-6857
      EISSN:1551-6865
      DOI:10.1145/3368027
      Issue’s Table of Contents

      Copyright © 2019 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 15 November 2019
      • Accepted: 1 August 2019
      • Revised: 1 July 2019
      • Received: 1 January 2019
      Published in tomm Volume 15, Issue 3s

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