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Mixed structure low-rank representation for multi-view subspace clustering

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Abstract

Multi-view clustering method utilizes the diversity of multi-view information to access better clustering results than a single view. Most existing multi-view clustering methods do not take full advantage of the diversity of information views, which makes the affinity matrix insufficiently clear and accurate to precisely describe the potential structure of multi-view data, resulting in poor clustering results. To solve the above problems, mixed structure low-rank representation (MSLRR) for multi-view subspace clustering and its kernel version (ker-MSLRR) are proposed in this paper. The mixed low-rank structure algorithm takes the multi-view data after the feature concatenation as input and then uses the nested mixed structure of least squares regression (LSR) and low-rank representation (LRR) as the unified model to effectively reduce the noise of the affinity matrix. In addition, to effectively deal with nonlinear data, the kernel method ker-MSLRR based on MSLRR is proposed, which improves the processing ability of processing nonlinear data. The experimental results of five real datasets demonstrate that the proposed methods have better clustering performance than other existing methods.

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References

  1. MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Le Cam LM, Neyman J (eds) Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability - Vol. 1. University of California Press, Berkeley, CA, USA, pp 281–297

    Google Scholar 

  2. Liu L, Huang W, Chen D-R (2014) Exact minimum rank approximation via schatten-norm minimization. J Comput Appl Math 267:218–227

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang X, Chen B, Sun H, Liu Z, Ren Z, Li Y (2020) Robust low-rank kernel subspace clustering based on the schatten p-norm and correntropy. IEEE Trans Knowl Data Eng 32(12):2426–2437

    Article  Google Scholar 

  4. You C, Robinson DP, Vidal R (2016) Scalable sparse subspace clustering by orthogonal matching pursuit. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3918–3927

  5. Baek S, Yoon G, Song J, Yoon S (2021) Deep self-representative subspace clustering network. Pattern Recogn 118:108041

    Article  Google Scholar 

  6. Si X, Yin Q, Zhao X, Yao L (2021) Consistent and diverse multi-view subspace clustering with structure constraint. Pattern Recogn 121:108196

    Article  Google Scholar 

  7. Zhang X, Zhenwen R, Sun H, Bai K, Feng X, Liu Z (2020) Multiple kernel low-rank representation-based robust multi-view subspace clustering. Inf Sci 551:12

    MathSciNet  MATH  Google Scholar 

  8. Han M, Zhang H (2022) Multiple kernel learningfor label relation and class imbalance in multi- label learning. Inf Sci 613:09

    Article  Google Scholar 

  9. Wei S, Wang J, Yu G-X, Domeniconi C, Zhang X (2020) Multi-view multiple clusterings using deep matrix factorization. Proc AAAI Conf Artif Intell 34:6348–6355

    Google Scholar 

  10. Guérin J, Stéphane T, Nyiri E, Gibaru O, Boots B (2021) Combining pretrained cnn feature extractors to enhance clustering of complex natural images. Neurocomputing 423:551–571

    Article  Google Scholar 

  11. Wang Y-X, Xu H, Leng C (2013) Provable subspace clustering: When lrr meets ssc. Advances in Neural Information Processing Systems, vol. PP

  12. Zhenwen R, Haoran L, Yang C, Sun Q (2019) Multiple kernel subspace clustering with local structural graph and low-rank consensus kernel learning. Knowl-Based Syst 188:105040

    Google Scholar 

  13. Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell 35(1):171–184

    Article  Google Scholar 

  14. Elhamifar E, Vidal R (2013) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781

    Article  Google Scholar 

  15. Ojala T, Pietikainen M, Maenpaa T (2002) Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE Trans Pattern Anal Mach Intell 24(7):971–987

    Article  MATH  Google Scholar 

  16. Gao H, Nie F, Li X, Huang H (2015) Multi-view subspace clustering. In: 2015 IEEE International Conference on Computer Vision (ICCV), pp. 4238–4246

  17. Brbić M, Kopriva I (2017) Multi-view low-rank sparse subspace clustering. Pattern Recogn 73:08–258

    Google Scholar 

  18. Lin S-X, Zhong G, Shu T (2020) Simultaneously learning feature-wise weights and local structures for multi-view subspace clustering. Knowl-Based Syst 205:106280

    Article  Google Scholar 

  19. Zheng Q, Zhu J, Li Z, Pang S, Wang J, Li Y (2019) Feature concatenation multi-view subspace clustering. Neurocomputing 379:10

    Google Scholar 

  20. Yao L, Lu G-F (2022) Double structure scaled simplex representation for multi-view subspace clustering. Neural Netw 151:04

    Article  Google Scholar 

  21. Tang C, Zhu X, Liu X, Li M, Wang P, Zhang C, Wang L (2019) Learning a joint affinity graph for multiview subspace clustering. IEEE Trans Multimed 21(7):1724–1736

    Article  Google Scholar 

  22. Zhong G, Shu T, Huang G, Yan X (2021) Multi-view spectral clustering by simultaneous consensus graph learning and discretization. Knowl-Based Syst 235:107632

    Article  Google Scholar 

  23. Zeng Z, Xiao S, Jia K, Chan T-H, Gao S, Xu D, Ma Y (2013) Learning by associating ambiguously labeled images. In: IEEE Conference on Computer Vision and Pattern Recognition, pp 708–715

  24. Xu X, Tsang IW, Xu D (2013) Soft margin multiple kernel learning. IEEE Trans Neural Netw Learn Syst 24(5):749–761

    Article  Google Scholar 

  25. Chao G, Sun S, Bi J (2021) A survey on multiview clustering. IEEE Trans Artif Intell 2(2):146–168

    Article  Google Scholar 

  26. Xiao S, Tan M, Xu D, Dong ZY (2016) Robust kernel low-rank representation. IEEE Trans Neural Netw Learn Syst 27(11):2268–2281

    Article  MathSciNet  Google Scholar 

  27. Bartels RH, Stewart GW (1972) Solution of the matrix equation ax + xb =c [f4]. Commun ACM 15(9):820–826

    Article  MATH  Google Scholar 

  28. Condat L (2016) Fast projection onto the simplex and the l1 ball. Math Program 158:575–585

  29. Lin Z, Liu R, Su Z (2011) Linearized alternating direction method with adaptive penalty for low-rank representation. NIPS 2:article 6

    Google Scholar 

  30. Luxburg U, Belkin M, Bousquet O (2008) Consistency of spectral clustering. Ann Stat 36:05

    MathSciNet  MATH  Google Scholar 

  31. Canyi L, Hai M, Zhao Z-Q, Zhu L, Huang D-S, Yan S (2012) Robust and efficient subspace segmentation via least squares regression. In: Proceedings of the 12th European conference on Computer Vision, vol. 7578, pp 347–360

  32. Xu J, Yu M, Shao L, Zuo W, Meng D, Zhang L, Zhang D (2021) Scaled simplex representation for subspace clustering. IEEE Trans Cybern 51(3):1493–1505

    Article  Google Scholar 

  33. Chen M-S, Huang L, Wang C-D, Huang D, Lai J-H (2021) Relaxed multi-view clustering in latent embedding space. Inf Fusion 68:8–21

    Article  Google Scholar 

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Acknowledgements

.This work was supported by the Key Project of Anhui University Natural Science Foundation (Grant No. YJS20210453, KJ2020A0361, KJ2021A1028), Anhui Province scientific research planning project(Grant No. 2022AH050953), National Natural Science Foundation of China under project (Grant No. 62002084, 61976005), the University Synergy Innovation Program of Anhui Province (Grant No. GXXT-2022-047 ), the Key Project of Natural Science Research of Higher Education Institution of Anhui Province of China (Grant No. KJ2020A0363, KJ2021A1028).

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  1. School of Computer and Information, Anhui Polytechnic University, Wuhu, Anhui, 241000, China

    Shouhang Wang, Yong Wang, Guifu Lu & Wenge Le

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  1. Shouhang Wang
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  2. Yong Wang
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  3. Guifu Lu
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  4. Wenge Le
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Correspondence to Yong Wang.

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Wang, S., Wang, Y., Lu, G. et al. Mixed structure low-rank representation for multi-view subspace clustering. Appl Intell 53, 18470–18487 (2023). https://doi.org/10.1007/s10489-023-04474-y

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