research-article

Split Multiplicative Multi-View Subspace Clustering

Authors:

Qingming HuangAuthors Info & Claims

IEEE Transactions on Image Processing, Volume 28, Issue 10

Pages 5147 - 5160

https://doi.org/10.1109/TIP.2019.2913096

Published: 01 October 2019 Publication History

Abstract

Various subspace clustering methods have been successively developed to process multi-view datasets. Most of the existing methods try to obtain a consensus structure coefficient matrix based on view-specific subspace recoveries. However, since view-specific structures contain individualized components that are intrinsically different from the consensus structure, directly adopting view-specific subspace structures might not be a reasonable choice. In this paper, with this concern in mind, our goal is to seek novel strategies to extract valuable components from view-specific structures that are consistent with the consensus subspace structure. To this end, we propose a novel multi-view subspace clustering method named split multiplicative multi-view subspace clustering (SM<sup>2</sup>SC) with the joint strength of a multiplicative decomposition scheme and a variable splitting scheme. Specifically, the multiplicative decomposition scheme effectively guarantees the structural consistency of the extracted components. Then, the variable splitting scheme takes a step further via extracting the structural consistent components from view-specific structures. Furthermore, an alternating optimization algorithm is proposed to optimize the resulting optimization problem, which is non-convex and constrained. We prove that this algorithm could converge to a critical point. Finally, we provide empirical studies on real-world datasets that speak to the practical efficacy of our proposed method. The source code is released on GitHub <uri>https://github.com/joshuaas/SM2SC</uri>.

References

[1]

R. Vidal, R. Tron, and R. Hartley, “Multiframe motion segmentation with missing data using powerfactorization and GPCA,” Int. J. Comput. Vis., vol. 79, no. 1, pp. 85–105, 2008.

Digital Library

[2]

T. Zhang, A. Szlam, Y. Wang, and G. Lerman, “Hybrid linear modeling via local best-fit flats,” Int. J. Comput. Vis., vol. 100, no. 3, pp. 217–240, 2012.

Digital Library

[3]

K.-C. Lee, J. Ho, and D. Kriegman, “Acquiring linear subspaces for face recognition under variable lighting,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 5, pp. 684–698, May 2005.

Digital Library

[4]

C. Lu, J. Feng, Z. Lin, T. Mei, and S. Yan, “Subspace clustering by block diagonal representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 41, no. 2, pp. 487–501, Feb. 2019.

Digital Library

[5]

E. Elhamifar and R. Vidal, “Sparse subspace clustering,” in Proc. CVPR, Jun. 2009, pp. 2790–2797.

[6]

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust recovery of subspace structures by low-rank representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 35, no. 1, pp. 171–184, Jan. 2013.

Digital Library

[7]

Y.-X. Wang, H. Xu, and C. Leng, “Provable subspace clustering: When LRR meets SSC,” in Proc. NIPS, 2013, pp. 64–72.

[8]

S. Wang, X. Yuan, T. Yao, S. Yan, and J. Shen, “Efficient subspace segmentation via quadratic programming,” in Proc. AAAI, vol. 1, 2011, pp. 519–524.

[9]

C. Lu, J. Feng, Z. Lin, and S. Yan, “Correlation adaptive subspace segmentation by trace lasso,” in Proc. ICCV, Dec. 2013, pp. 1345–1352.

[10]

P. Ji, M. Salzmann, and H. Li, “Efficient dense subspace clustering,” in Proc. IEEE Winter Conf. Appl. Comput. Vis., Mar. 2014, pp. 461–468.

[11]

C.-Y. Lu, H. Min, Z.-Q. Zhao, L. Zhu, D.-S. Huang, and S. Yan, “Robust and efficient subspace segmentation via least squares regression,” in Proc. ECCV. Florence, Italy: Springer, 2012, pp. 347–360.

[12]

X. Peng, C. Lu, Z. Yi, and H. Tang, “Connections between nuclear-norm and Frobenius-norm-based representations,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 1, pp. 218–224, Jan. 2018.

[13]

X. Xie, X. Guo, G. Liu, and J. Wang, “Implicit block diagonal low-rank representation,” IEEE Trans. Image Process., vol. 27, no. 1, pp. 477–489, Jan. 2018.

[14]

C. G. Li and R. Vidal, “Structured sparse subspace clustering: A unified optimization framework,” in Proc. CVPR, Jun. 2015, pp. 277–286.

[15]

D. P. Wipf, Y. Dong, and B. Xin, “Subspace clustering with a twist,” in Proc. UAI, 2016, pp. 1–10.

[16]

B. Xin, Y. Wang, W. Gao, and D. P. Wipf, “Data-dependent sparsity for subspace clustering,” in Proc. UAI, 2017, pp. 1–10.

[17]

J. Shen, P. Li, and H. Xu, “Online low-rank subspace clustering by basis dictionary pursuit,” in Proc. ICML, 2016, pp. 622–631.

[18]

C. You, D. Robinson, and R. Vidal, “Scalable sparse subspace clustering by orthogonal matching pursuit,” in Proc. CVPR, Jun. 2016, pp. 3918–3927.

[19]

V. R. De Sa, “Spectral clustering with two views,” in Proc. 22nd ICML, Bonn, Germany, 2005.

[20]

D. Zhou and C. J. C. Burges, “Spectral clustering and transductive learning with multiple views,” in Proc. ICML, 2007, pp. 1159–1166.

[21]

A. Kumar and H. Daumé, III., “A co-training approach for multi-view spectral clustering,” in Proc. ICML, 2011, pp. 393–400.

[22]

A. Kumar, P. Rai, and H. Daumé, III, “Co-regularized multi-view spectral clustering,” in Proc. NIPS, 2011, pp. 1413–1421.

[23]

R. Xia, Y. Pan, L. Du, and J. Yin, “Robust multi-view spectral clustering via low-rank and sparse decomposition,” in Proc. AAAI, 2014, pp. 2149–2155.

[24]

C. Lu, S. Yan, and Z. Lin, “Convex sparse spectral clustering: Single-view to multi-view,” IEEE Trans. Image Process., vol. 25, no. 6, pp. 2833–2843, Jun. 2016. 10.1109/TIP.2016.2553459.

Digital Library

[25]

Y. Li, F. Nie, H. Huang, and J. Huang, “Large-scale multi-view spectral clustering via bipartite graph,” in Proc. AAAI, 2015, pp. 2750–2756.

[26]

F. Nie, J. Li, and X. Li, “Parameter-free auto-weighted multiple graph learning: A framework for multiview clustering and semi-supervised classification,” in Proc. IJCAI, 2016, pp. 1881–1887.

[27]

F. Nie, J. Li, and X. Li, “Self-weighted multiview clustering with multiple graphs,” in Proc. IJCAI, 2017, pp. 2564–2570.

[28]

C. Zhang, H. Fu, S. Liu, G. Liu, and X. Cao, “Low-rank tensor constrained multiview subspace clustering,” in Proc. CVPR, Dec. 2015, pp. 1582–1590.

[29]

H. Gao, F. Nie, X. Li, and H. Huang, “Multi-view subspace clustering,” in Proc. ICCV, Dec. 2015, pp. 4238–4246.

[30]

X. Cao, C. Zhang, H. Fu, S. Liu, and H. Zhang, “Diversity-induced multi-view subspace clustering,” in Proc. CVPR, Jun. 2015, pp. 586–594.

[31]

K. Fukumizu, A. Gretton, X. Sun, and B. Schölkopf, “Kernel measures of conditional dependence,” in Proc. NIPS, 2008, pp. 489–496.

[32]

Y. Wang, X. Lin, L. Wu, W. Zhang, Q. Zhang, and X. Huang, “Robust subspace clustering for multi-view data by exploiting correlation consensus,” IEEE Trans. Image Process., vol. 24, no. 11, pp. 3939–3949, Nov. 2015.

Digital Library

[33]

L. Wang, D. Li, T. He, and Z. Xue, “Manifold regularized multi-view subspace clustering for image representation,” in Proc. ICPR, Dec. 2016, pp. 283–288.

[34]

X. Wang, X. Guo, Z. Lei, C. Zhang, and S. Z. Li, “Exclusivity-consistency regularized multi-view subspace clustering,” in Proc. CVPR, Jul. 2017, pp. 923–931.

[35]

C. Zhang, Q. Hu, H. Fu, P. Zhu, and X. Cao, “Latent multi-view subspace clustering,” in Proc. CVPR, Jul. 2017, pp. 4279–4287.

[36]

C. Zhanget al., “Generalized latent multi-view subspace clustering,” IEEE Trans. Pattern Anal. Mach. Intell., to be published.

Digital Library

[37]

F. R. Chung and F. C. Graham, Spectral Graph Theory, no. 92. Providence, RI, USA: AMS, 1997.

[38]

U. von Luxburg. (2007). “A tutorial on spectral clustering.” [Online]. Available: https://arxiv.org/abs/0711.0189

Digital Library

[39]

C. Xu, D. Tao, and C. Xu. (2013). “A survey on multi-view learning.” [Online]. Available: https://arxiv.org/abs/1304.5634

[40]

J. Dattorro, Convex Optimization & Euclidean Distance Geometry. Morrisville, NC, USA: Lulu Press, 2010.

[41]

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1–122, Jan. 2011.

Digital Library

[42]

Y. Wang, W. Yin, and J. Zeng, “Global convergence of ADMM in nonconvex nonsmooth optimization,” J. Sci. Comput., vol. 78, no. 1, pp. 29–63, Jan. 2019.

Digital Library

[43]

G.-J. Peng, “Adaptive ADMM for dictionary learning in convolutional sparse representation,” IEEE Trans. Image Process., to be published.

[44]

J. Xu, J. Han, and F. Nie, “Discriminatively embedded k-means for multi-view clustering,” in Proc. CVPR, Jun. 2016, pp. 5356–5364.

[45]

N. Ikizler, R. G. Cinbis, S. Pehlivan, and P. Duygulu, “Recognizing actions from still images,” in Proc. ICPR, Dec. 2008, pp. 1–4.

[46]

R. Xia, Y. Pan, L. Du, and J. Yin, “Robust multi-view spectral clustering via low-rank and sparse decomposition,” in Proc. AAAI, 2014, pp. 2149–2155.

[47]

A. Y. Ng, M. I. Jordan, and Y. Weiss, “On spectral clustering: Analysis and an algorithm,” in Proc. NIPS, 2001, pp. 849–856.

[48]

E. Achtert, S. Goldhofer, H.-P. Kriegel, E. Schubert, and A. Zimek, “Evaluation of clusterings–metrics and visual support,” in Proc. ICDE, 2012, pp. 1285–1288.

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cover image IEEE Transactions on Image Processing

IEEE Transactions on Image Processing Volume 28, Issue 10

Oct. 2019

241 pages

ISSN:1057-7149

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1057-7149 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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Published: 01 October 2019

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Cited By

Fu LHuang SZhang LYang JZheng ZZhang CChen C(2024)Subspace-Contrastive Multi-View ClusteringACM Transactions on Knowledge Discovery from Data10.1145/367483918:9(1-35)Online publication date: 28-Jun-2024
https://dl.acm.org/doi/10.1145/3674839
Wang YXu QJiang YDai SHuang QCai JKankanhalli MPrabhakaran BBoll SSubramanian RZheng LSingh VCesar PXie LXu D(2024)Regularized Contrastive Partial Multi-view Outlier DetectionProceedings of the 32nd ACM International Conference on Multimedia10.1145/3664647.3681125(8711-8720)Online publication date: 28-Oct-2024
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https://dl.acm.org/doi/10.1145/3645108
Gu ZLi ZFeng SBaeza-Yates RBonchi F(2024)Topology-Driven Multi-View Clustering via Tensorial Refined Sigmoid Rank MinimizationProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3672070(920-931)Online publication date: 25-Aug-2024
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Luo QYang MLi WXiao M(2023)Hyper-Laplacian Regularized Multi-View Clustering with Exclusive L21 Regularization and Tensor Log-Determinant Minimization ApproachACM Transactions on Intelligent Systems and Technology10.1145/358703414:3(1-29)Online publication date: 16-Mar-2023
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Huang SLiu YTsang IXu ZLv J(2023)Multi-View Subspace Clustering by Joint Measuring of Consistency and DiversityIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2022.319958735:8(8270-8281)Online publication date: 1-Aug-2023
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Li JQiang WZheng CSu BRazzak FWen JXiong H(2023)Modeling Multiple Views via Implicitly Preserving Global Consistency and Local ComplementarityIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2022.319874635:7(7220-7238)Online publication date: 1-Jul-2023
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