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Spectral clustering based on hypergraph and self-re-presentation

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Abstract

Traditional spectral clustering methods cluster data samples with pairwise relationships usually illustrated as graphs. However, the relationships among the data in real life are much more complex than pairwise. Merely representing the complex relationships into pairwise will result in loss of information which is helpful for improving clustering results. Moreover, the data in real life are often with noise and outliers. Therefore, to solve the problems mentioned above, we introduce hypergraph to fully consider the complex relationships of the data and use the self-representation based row sparse ℓ 2,1-norm to weaken the effect of the noise. The main contribution of this work is to integrate self-representation and hypergraph together and extend graph based spectral clustering to hypergraph. After that, we propose the spectral hypergraph clustering method named Spectral Clustering based on Hypergraph and Self-representation (HGSR). Finally, we put forward an efficient optimal method to solve the proposed problem. Experiment results showed that our method prominently outperforms the graph based methods.

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References

  1. Agarwal S, Lim J, Zelnik-Manor L et al (2005) Beyond pairwise clustering [C]. In: CVPR 838–845

  2. Bulo SR, Pelillo M (2013) A game-theoretic approach to hypergraph clustering [J]. IEEE Trans Pattern Anal Mach Intell 35(6):1312–1327

    Article  Google Scholar 

  3. Elhamifar E, Vidal R (2009) Sparse subspace clustering [C]. In CVPR, pages: 2790–2797

  4. Fergus R, Feifei L, Perona P et al (2005) Learning object categories from Google’s I-mage search [J]. Proceedings 2(2):1816–1823

    Google Scholar 

  5. Fiedler M (1973) Algebraic connectivity of graphs [J]. Czechoslov Math J 23(98):298–305

    MathSciNet  MATH  Google Scholar 

  6. Franjoine MR, Gunther JS, Taylor MJ (2003) Pediatric Balance Scale: a modified version of the Berg-Balance Scale for the school age child with mild to moderate motor impairment[J]. Pediatr Phys Ther 15(2):114–128

    Article  Google Scholar 

  7. Hagen L, Kahng AB (1992) New spectral methods for ratio cut partitioning and clustering [J]. IEEE Trans Comput Aided Des Integr Circuits Syst 11(9):1074–1085

    Article  Google Scholar 

  8. Hartigan JA, Wong MA (2013) A k-means clustering algorithm [J]. Appl Stat 28(1):100–108

    Article  MATH  Google Scholar 

  9. Hu H, Lin Z, Feng J et al (2014) Smooth representation clustering [C]. In CVPR, 3834–3841

  10. Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice Hall, Englewood Cliffs, 32(32):227–229

  11. Jain A, Murty M, Flynn P (1999) Data clustering: a review [J]. ACM Comput Surv 31(3):264–323

    Article  Google Scholar 

  12. Kuhn H (1955) The Hungarian method for the assignment problem. Nav Res Logist Q 2(1–2):83–97

    Article  MathSciNet  MATH  Google Scholar 

  13. Lancaster P (1970) Explicit solutions of linear matrix equations [J]. SIAM Rev 12(4):544–566

    Article  MathSciNet  MATH  Google Scholar 

  14. Li F, Perona P (2005) A Bayesian hierarchical model for learning natural scene categories [C]. In CVPR, 2: 524–531

  15. Liu G, Lin Z, Yan S et al (2013) Robust recovery of subspace structures by low-rank representation [J]. IEEE Trans Pattern Anal Mach Intell 35(1):171–184

    Article  Google Scholar 

  16. Lu CY, Min H, Zhao ZQ et al (2012) Robust and efficient subspace segmentation via least squares regression [C]. In ECCV, pages: 347–360

  17. MacQueen JB (1967) Some methods for classification and analysis of multi variate observations [J]. Berkeley Symposium on Math, 281–297

  18. Purkait P et al (2014) Clustering with hypergraphs: the case for large hyper-edges [C]. In ECCV, 672–687

  19. Qin Y, Zhang S, Zhu X et al (2007) Semi-parametric optimization for missing data imputation. Appl Intell 27(1):79–88

    Article  MATH  Google Scholar 

  20. Russell BC, Efros AA, Sivic J et al (2006) Using multiple segmentations to discover objects and their extent in image collections [C]. In CVPR, 2: 1605–1614

  21. Shi J, Malik J (2000) Normalized cuts and image segmentation [J]. IEEE Trans Pattern Anal Mach Intell 22(8):888–905

    Article  Google Scholar 

  22. Sivic J, Russell BC, Efros AA et al (2005) Discovering objects and their location in images [C]. In ICCV, 1: 370–377

  23. Sivic J, Russell BC, Zisserman A et al (2008) Unsupervised discovery of visual obj-ect class hierarchies [C]. In CVPR, 1–8

  24. Sun L, Ji S, Ye J (2008) Hypergraph spectral learning for multi-label classification [C]. In ACM SIGKDD, 668–676

  25. Tron R, Vidal R (2007) A benchmark for the comparison of 3-d motion segmentation algorithm. In CVPR, pp. 1–8

  26. von Luxburg U (2007) A tutorial on spectral clustering [J]. Stat Comput 17(4):395–416

    Article  MathSciNet  Google Scholar 

  27. Zass R, Shashua A (2008) Probabilistic graph and hypergraph matching [C]. In CVPR, 1–8

  28. Zhang S, Li X, Zong M et al (2016) Learning k for kNN classification. ACM Trans Intell Syst Technol, (accepted)

  29. Zhang C, Qin Y, Zhu X et al (2006) Clustering-based missing value imputation for data preprocessing. In 2006 4th IEEE International Conference on Industrial Informatics, 1081–1086

  30. Zhao F, Jiao L, Liu H et al (2010) Spectral clustering with eigenvector selection based on entropy ranking. Neurocomputing 73(10–12):1704–1717

    Article  Google Scholar 

  31. Zhu Y, Cox M, Lucey S (2011) 3D motion reconstruction for real-world camera motion. In CVPR, pp. 1–8

  32. Zhu Y, Huang D, De la Torre F et al (2014) Complex non-rigid motion 3D reconstruction by union of subspaces. In CVPR, 1542–1549

  33. Zhu X, Huang Z, Shen HT et al (2012) Dimensionality reduction by Mixed Kernel Canonical Correlation Analysis[J]. Pattern Recogn 45(8):3003–3016

    Article  MATH  Google Scholar 

  34. Zhu X, Huang Z, Shen HT et al (2013) Linear cross-modal hashing for efficient multimedia search [C]. In ACM International Conference on Multimedia, pp. 143–152

  35. Zhu X, Li X, Zhang S (2016) Block-row sparse multi-view multi-label learning for image classification. IEEE Trans Cybern 46(2):450–461

    Article  Google Scholar 

  36. Zhu Y, Lucey S (2015) Convolutional sparse coding for trajectory reconstruction. IEEE Trans Pattern Anal Mach Intell 37(3):529–540

    Article  Google Scholar 

  37. Zhu X, Suk HI, Lee SW et al (2016) Subspace regularized sparse multi-task le-arning for multi-class neurodegenerative disease identification [J]. IEEE Trans Biomed Eng 63(3):607–618

    Article  Google Scholar 

  38. Zhu X, Suk HI, Shen D (2014) A novel matrix-similarity based loss function for joint regression and classification in AD diagnosis [J]. Neuroimaging 100:91–105

    Article  Google Scholar 

  39. Zhu X, Zhang S, Jin Z et al (2011) Missing value estimation for mixed-attribute data sets. IEEE Trans Knowl Data Eng 23(1):110–121

    Article  Google Scholar 

  40. Zhu X, Zhang S, Zhang J et al (2007) Cost-sensitive imputing missing values with ordering. AAAI press, 2: 1922–1923

  41. Zhu X, Zhang L, Huang Z (2014) A sparse embedding and least variance encode-ng approach to hashing [J]. IEEE Trans Image Process 23(9):3737–3750

    Article  MathSciNet  Google Scholar 

  42. Zykov AA (1974) Hypergraphs [J]. Russ Math Surv 29(6):89–154

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the China “1000-Plan” National Distinguished Professorship; the National Natural Science Foundation of China (Grant Nos: 61263035, 61573270, 61602353, and 61672177), the China 973 Program (Grant no: 2013CB329404); the China Key Research Program (Grant no: 2016YFB1000905); the Guangxi Natural Science Foundation (Grant no: 2015GXNSFCB139011); the China Postdoctoral Science Foundation (Grant No: 2015M570837); the Guangxi Higher Institutions’ Program of Introducing 100 High-Level Overseas Talents; the Guangxi Collaborative Innovation Center of Multi-Source Information Integration and Intelligent Processing; and the Guangxi “Bagui” Teams for Innovation and Research; Innovation Project of Guangxi Graduate Education under grant YCSZ2016046 and YCSZ2016045 and the project “Application and Research of Big Data Fusion in Inter-City Traffic Integration of The Xijiang River - Pearl River Economic Belt (da shu jv rong he zai xijiang zhujiang jing ji dai cheng ji jiao tong yi ti hua zhong de ying yong yu yan jiu)”.

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Authors and Affiliations

  1. Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin, Guangxi, 541004, China

    Yonggang Li, Shichao Zhang, Debo Cheng, Wei He & Guoqiu Wen

  2. Wuhan University of Technology, Wuhan, Hubei, 430070, China

    Qing Xie

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  1. Yonggang Li
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  2. Shichao Zhang
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  3. Debo Cheng
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  4. Wei He
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  5. Guoqiu Wen
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  6. Qing Xie
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Correspondence to Shichao Zhang.

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Li, Y., Zhang, S., Cheng, D. et al. Spectral clustering based on hypergraph and self-re-presentation. Multimed Tools Appl 76, 17559–17576 (2017). https://doi.org/10.1007/s11042-016-4131-6

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  • DOI: https://doi.org/10.1007/s11042-016-4131-6

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