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Robust multiview spectral clustering via cooperative manifold and low rank representation induced

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Abstract

This paper proposes a novel multiview low-rank clustering method to learn robust multiview clustering from two different data structures, unlike existing methods’ one data structure learning technique. Specifically, by inducing the multiview data’s manifold through dual data structures to obtain each view’s low-rank representation and a similarity matrix, respectively, the proposed method can avoid the uncertainty of one-way manifold learning and obtain optimal clustering performance. To facilitate our approach, each view’s low-rank representation is constrained to be a linear mixture of consensus and view-specific parts. In this way, the consensus part and the similarity matrix are then allowed to guide each other to find the more optimal solution adaptively. Besides, we avoid the extra computational time involved in a similarity matrix’s spectral post-processing such that our clustering structure is revealed directly through the obtained similarity matrix with the help of a rank constraint. Several experiments were conducted on WebKB, ORL, UCI digits, 3sources, and F-MNIST benchmark datasets to evaluate the effectiveness of the proposed method. Experimental results obtained on all five datasets with respect to six standard evaluation metrics: accuracy, normalized mutual information, adjusted rand index, F-score, precision, and recall reveal that the proposed method has the superior advantage over compared state-of-the-art methods with more than 2% improvements in most experiments. The results also show more than 0.5% improvements over compared deep learning techniques.

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Data Availability

https://linqs.soe.ucsc.edu/data http://cam-orl.co.uk/facedatabase.html https://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+\Handwritten+Digis http://mlg.ucd.ie/datasets/3sources.html 1708.07747

Code Availability

Custom code implemented using MATLAB 2016b installed on Windows 10 CORE i5 computer system

Notes

  1. https://linqs.soe.ucsc.edu/data

  2. http://cam-orl.co.uk/facedatabase.html

  3. https://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digis

  4. http://mlg.ucd.ie/datasets/3sources.html

  5. 1708.07747

References

  1. Abhadiomhen SE, Wang Z, Shen X (2021) Coupled low rank representation and subspace clustering. Appl Intell, pp 1–17

  2. Abhadiomhen SE, Wang Zy, Shen Xj, Fan J (2021 in press) Multiview common subspace clustering via coupled low rank representation. ACM Trans Intell Syst, pp 1–25

  3. Achanta SDM, Karthikeyan T, Kanna RV (2021) Wearable sensor based acoustic gait analysis using phase transition-based optimization algorithm on iot. International Journal of Speech Technology, pp 1–11

  4. Brbić M, Kopriva I (2018) Multi-view low-rank sparse subspace clustering. Pattern Recogn 73:247–258

    Article  Google Scholar 

  5. Cai JF, Candès EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM Journal on optimization 20(4):1956–1982

    Article  MathSciNet  MATH  Google Scholar 

  6. Cai X, Nie F, Huang H (2013) Multi-view k-means clustering on big data. In: Twenty-Third International Joint conference on artificial intelligence. Citeseer

  7. Chaudhuri K, Kakade SM, Livescu K, Sridharan K (2009) Multi-view clustering via canonical correlation analysis. In: Proceedings of the 26th annual international conference on machine learning, pp 129–136

  8. Chen J, Mao H, Wang Z, Zhang X (2021) Low-rank representation with adaptive dictionary learning for subspace clustering. Knowledge-Based Systems pp 107053

  9. Deng T, Ye D, Ma R, Fujita H, Xiong L (2020) Low-rank local tangent space embedding for subspace clustering. Inf Sci 508:1–21

    Article  MathSciNet  MATH  Google Scholar 

  10. 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 

  11. Fan K (1950) On a theorem of weyl concerning eigenvalues of linear transformations: Ii. Proc Natl Acad Sci USA 36(1):31

    Article  MathSciNet  Google Scholar 

  12. Gao W, Dai S, Abhadiomhen SE, He W, Yin X (2021) Low rank correlation representation and clustering. Sci Program, pp 1–12

  13. Guo J, Sun Y, Gao J, Hu Y, Yin B (2021) Rank consistency induced multiview subspace clustering via low-rank matrix factorization. IEEE Transactions on Neural Networks and Learning Systems

  14. Hu Y, Zhang D, Ye J, Li X, He X (2012) Fast and accurate matrix completion via truncated nuclear norm regularization. IEEE Trans Pattern Anal Mach Intell 35(9):2117–2130

    Article  Google Scholar 

  15. Jing XY, Zhang X, Zhu X, Wu F, You X, Gao Y, Shan S, Yang JY (2021) Multiset feature learning for highly imbalanced data classification. IEEE Trans Pattern Anal Mach Intell 43(1):139–156

    Article  Google Scholar 

  16. Kumar A, Daumé H (2011) A co-training approach for multi-view spectral clustering. In: Proceedings of the 28th international conference on machine learning (ICML-11), pp 393–400

  17. Kumar A, Rai P, Daume H (2011) Co-regularized multi-view spectral clustering. Advances in neural information processing systems 24:1413–1421

    Google Scholar 

  18. Li R, Zhang C, Hu Q, Zhu P, Wang Z (2019) Flexible multi-view representation learning for subspace clustering. In: IJCAI, pp 2916–2922

  19. Li Z, Hu Z, Nie F, Wang R, Li X (2020) Multi-view clustering based on generalized low rank approximation. Neurocomputing

  20. Liang Y, Huang D, Wang CD (2019) Consistency meets inconsistency: a unified graph learning framework for multi-view clustering. In: 2019 IEEE international conference on data mining (ICDM). IEEE, pp 1204–1209

  21. Liang Y, Pan Y, Lai H, Yin J (2020) Robust multi-view clustering via inter-and-intra-view low rank fusion. Neurocomputing 385:220–230

    Article  Google Scholar 

  22. Lin Z, Chen M, Ma Y (2010) The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. arXiv:10095055

  23. 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 

  24. Liu J, Liu X, Yang Y, Guo X, Kloft M, He L (2021) Multiview subspace clustering via co-training robust data representation. IEEE Transactions on Neural Networks and Learning Systems

  25. Lu C, Feng J, Lin Z, Yan S (2013) Correlation adaptive subspace segmentation by trace lasso. In: Proceedings of the IEEE international conference on computer vision, pp 1345–1352

  26. Lu C, Feng J, Lin Z, Mei T, Yan S (2018) Subspace clustering by block diagonal representation. IEEE Trans Pattern Anal Mach Intell 41 (2):487–501

    Article  Google Scholar 

  27. Lucińska M, Wierzchoń ST (2012) Spectral clustering based on k-nearest neighbor graph. In: IFIP international conference on computer information systems and industrial management. Springer, pp 254–265

  28. Murthy ASD, Karthikeyan T, Jagan BOL, Kumari CU (2020) Novel deep neural network for individual re recognizing physically disabled individuals. Materials Today: Proceedings 33:4323–4328

    Google Scholar 

  29. Ng A, Jordan M, Weiss Y (2001) On spectral clustering: Analysis and an algorithm. Adv Neural Inf Process Syst 14:849–856

    Google Scholar 

  30. Sampath Dakshina Murthy A, Karthikeyan T, Vinoth Kanna R (2021) Gait-based person fall prediction using deep learning approach. Soft Comput, pp 1–9

  31. Sun YS, Ou-Yang L, Dai DQ (2021) Wmlrr: a weighted multi-view low rank representation to identify cancer subtypes from multiple types of omics data. IEEE/ACM Transactions on Computational Biology and Bioinformatics

  32. Vidal R, Favaro P (2014) Low rank subspace clustering (lrsc). Pattern Recogn Lett 43:47–61

    Article  Google Scholar 

  33. Wang H, Yang Y, Liu B (2019) Gmc: graph-based multi-view clustering. IEEE Trans Knowl Data Eng 32(6):1116–1129

    Article  Google Scholar 

  34. Wang Q, Cheng J, Gao Q, Zhao G, Jiao L (2020) Deep multi-view subspace clustering with unified and discriminative learning. IEEE Trans Multimedia 23:3483–3493

    Article  Google Scholar 

  35. Wang S, Chen Y, Jin Y, Cen Y, Li Y, Zhang L (2021a) Error-robust low-rank tensor approximation for multi-view clustering. Knowl-Based Syst 215:106745

  36. Wang Y, Wu L, Lin X, Gao J (2018) Multiview spectral clustering via structured low-rank matrix factorization. IEEE Transactions on Neural Networks and Learning Systems 29(10):4833–4843

    Article  Google Scholar 

  37. Wang Zy, Abhadiomhen SE, Liu Zf, Shen Xj, Gao Wy, Li Sy (2021b) Multi-view intrinsic low-rank representation for robust face recognition and clustering. IET Image Processing pp 1–12

  38. Wu F, Jing XY, You X, Yue D, Hu R, Yang JY (2016) Multi-view low-rank dictionary learning for image classification. Pattern Recogn 50:143–154

    Article  MATH  Google Scholar 

  39. Wu F, Jing XY, Feng Y, Ji Ym, Wang R (2021) Spectrum-aware discriminative deep feature learning for multi-spectral face recognition. Pattern Recogn 111:107632

    Article  Google Scholar 

  40. Xia R, Pan Y, Du L, Yin J (2014) Robust multi-view spectral clustering via low-rank and sparse decomposition. In: Proceedings of the AAAI conference on artificial intelligence, vol 28

  41. Xu J, Xu K, Chen K, Ruan J (2015) Reweighted sparse subspace clustering. Comput Vis Image Underst 138:25–37

    Article  Google Scholar 

  42. Xu J, Zhang L, Zhang D, Feng X (2017) Multi-channel weighted nuclear norm minimization for real color image denoising. In: Proceedings of the IEEE international conference on computer vision, pp 1096–1104

  43. Xu J, An W, Zhang L, Zhang D (2019a) Sparse, collaborative, or nonnegative representation: which helps pattern classification? Pattern Recogn 88:679–688

  44. Xu J, Yu M, Shao L, Zuo W, Meng D, Zhang L, Zhang D (2019b) Scaled simplex representation for subspace clustering. IEEE Transactions on Cybernetics 51(3):1493–1505

  45. Xue X, Zhang X, Feng X, Sun H, Chen W, Liu Z (2020) Robust subspace clustering based on non-convex low-rank approximation and adaptive kernel. Inf Sci 513:190–205

    Article  MathSciNet  MATH  Google Scholar 

  46. Yang X, Deng C, Dang z, Tao D (2021) Deep multiview collaborative clustering. IEEE Transactions on Neural Networks and Learning Systems

  47. Yin M, Xie S, Wu Z, Zhang Y, Gao J (2018) Subspace clustering via learning an adaptive low-rank graph. IEEE Trans Image Process 27 (8):3716–3728

    Article  MathSciNet  MATH  Google Scholar 

  48. Zhai H, Zhang H, Zhang L, Li P (2018) Laplacian-regularized low-rank subspace clustering for hyperspectral image band selection. IEEE Trans Geosci Remote Sens 57(3):1723–1740

    Article  Google Scholar 

  49. Zhan K, Nie F, Wang J, Yang Y (2019) Multiview consensus graph clustering. IEEE Trans Image Process 28(3):1261–1270

    Article  MathSciNet  Google Scholar 

  50. Zhang C, Fu H, Liu S, Liu G, Cao X (2015) Low-rank tensor constrained multiview subspace clustering. In: Proceedings of the IEEE international conference on computer vision, pp 1582–1590

  51. Zhou T, Zhang C, Peng X, Bhaskar H, Yang J (2020) Dual shared-specific multiview subspace clustering. IEEE transactions on cybernetics 50 (8):3517–3530

    Article  Google Scholar 

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Acknowledgements

This research was funded in part by the Key Program of National Natural Science Foundations of China under Grant No. 41930110.

Funding

This work was funded in part by the National Natural Science Foundation of China (No.41930110).

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Authors and Affiliations

  1. Department of Electronic Engineering, School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China

    Zhiyong Xu & Sirui Tian

  2. School of Computer Science and Communication Engineering, JiangSu University, JiangSu, 212013, China

    Stanley Ebhohimhen Abhadiomhen & Xiang-Jun Shen

  3. Department of Computer Science, University of Nigeria, Nsukka, Nigeria

    Stanley Ebhohimhen Abhadiomhen

Authors
  1. Zhiyong Xu
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  2. Sirui Tian
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  3. Stanley Ebhohimhen Abhadiomhen
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  4. Xiang-Jun Shen
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Contributions

Zhiyong Xu: Conceptualization, Investigation, Methodology, Software, Validation, Formal analysis, Visualization, Writing - Original Draft, Writing - Review & Editing. Sirui Tian Software, Validation, Formal analysis. Stanley Ebhohimhen Abhadiomhen: Software, Validation, Writing - Review & Editing. Xiang-Jun Shen: Conceptualization, Supervision, Validation, Writing - Review & Editing.

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Correspondence to Xiang-Jun Shen.

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This work was funded in part by the National Natural Science Foundation of China (No.41930110)

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Xu, Z., Tian, S., Abhadiomhen, S.E. et al. Robust multiview spectral clustering via cooperative manifold and low rank representation induced. Multimed Tools Appl 82, 24445–24464 (2023). https://doi.org/10.1007/s11042-023-14557-0

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