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Coupled low rank representation and subspace clustering

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Abstract

Subspace clustering is a technique utilized to find clusters within multiple subspaces. However, most existing methods cannot obtain an accurate block diagonal clustering structure to improve clustering performance. This drawback exists because these methods learn the similarity matrix in advance by utilizing a low dimensional matrix obtained directly from the data, where two unrelated data samples can stay related easily due to the influence of noise. This paper proposes a novel method based on coupled low-rank representation to tackle the above problem. First, our method constructs a manifold recovery structure to correct inadequacy in the low-rank representation of data. Then it obtains a clustering projection matrix that obeys the k-block diagonal property to learn an ideal similarity matrix. This similarity matrix denotes our clustering structure with a rank constraint on its normalized Laplacian matrix. Therefore, we avoid k-means spectral post-processing of the low dimensional embedding matrix, unlike most existing methods. Furthermore, we couple our method to allow the clustering structure to adaptively approximate the low-rank representation so as to find more optimal solutions. Several experiments on benchmark datasets demonstrate that our method outperforms similar state-of-the-art methods in Accuracy, Normalized Mutual Information, F-score, Recall, Precision, and Adjusted Rand Index evaluation metrics.

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Code Availability

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

Notes

  1. https://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits

  2. https://www.kaggle.com/bistaumanga/usps-dataset

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

  4. http://vision.ucsd.edu/content/yale-face-database

  5. https://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php

  6. http://www.vision.caltech.edu/archive.html

References

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

    Article  Google Scholar 

  2. Brbić M, Kopriva I (2020) ℓ0 -motivated low-rank sparse subspace clustering. IEEE Trans Cybern 50(4):1711–1725. https://doi.org/10.1109/TCYB.2018.2883566

  3. Cai J F, Candès E J, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982

    Article  MathSciNet  Google Scholar 

  4. Cai X, Huang D, Wang CD, Kwoh CK (2020) Spectral clustering by subspace randomization and graph fusion for high-dimensional data. In: Pacific-Asia Conference on Knowledge Discovery and Data Mining. Springer, pp 330–342

  5. Chen J, Zhang H, Mao H, Sang Y, Yi Z (2016a) Symmetric low-rank representation for subspace clustering. Neurocomputing 173:1192–1202

  6. Chen Y, Zhang L, Yi Z (2016b) A novel low rank representation algorithm for subspace clustering. Int J Pattern Recogn Artif Intell 30(04):1650007

  7. Chung FR, Graham FC (1997) Spectral graph theory. 92, American Mathematical Society

  8. Cui G, Li X, Dong Y (2018) Subspace clustering guided convex nonnegative matrix factorization. Neurocomputing 292:38–48

    Article  Google Scholar 

  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  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 J, Tian Z, Zhao M, Chow T W (2018) Accelerated low-rank representation for subspace clustering and semi-supervised classification on large-scale data. Neural Netw 100:39–48

    Article  Google Scholar 

  12. Fan K (1950) On a theorem of weyl concerning eigenvalues of linear transformations i. Proc Natl Acad Sci U S A 35(11):652

    Article  MathSciNet  Google Scholar 

  13. Gruber A, Weiss Y (2004) Multibody factorization with uncertainty and missing data using the em algorithm. In: Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2004, vol 1. IEEE, pp I–I

  14. Hinojosa C, Bacca J, Arguello H (2018) Coded aperture design for compressive spectral subspace clustering. IEEE J Sel Top Signal Process 12(6):1589–1600

    Article  Google Scholar 

  15. Li A, Qin A, Shang Z, Tang Y Y (2019) Spectral-spatial sparse subspace clustering based on three-dimensional edge-preserving filtering for hyperspectral image. Int J Pattern Recogn Artif Intell 33(03):1955003

  16. Li C, Wang C L, Wang J (2016) Convergence analysis of the augmented lagrange multiplier algorithm for a class of matrix compressive recovery. Appl Math Lett 59:12–17

    Article  MathSciNet  Google Scholar 

  17. Li C G, You C, Vidal R (2017) Structured sparse subspace clustering: a joint affinity learning and subspace clustering framework. IEEE Trans Image Process 26(6):2988–3001

    Article  MathSciNet  Google Scholar 

  18. Liu G, Xu H, Yan S (2012) Exact subspace segmentation and outlier detection by low-rank representation. In: Artificial Intelligence and Statistics, pp 703–711

  19. 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 

  20. Liu M, Wang Y, Sun J, Ji Z (2020) Structured block diagonal representation for subspace clustering. Appl Intell:1–14

  21. Liu T, Lekamalage C K L, Huang G B, Lin Z (2018) An adaptive graph learning method based on dual data representations for clustering. Pattern Recogn 77:126–139

    Article  Google Scholar 

  22. 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

  23. Lu C, Feng J, Lin Z, Mei T, Yan S (2019) Subspace clustering by block diagonal representation. IEEE Trans Pattern Anal Mach Intell 41(2):487–501

    Article  Google Scholar 

  24. Luo S, Zhang C, Zhang W, Cao X (2018) Consistent and specific multi-view subspace clustering. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 32

  25. Muthu S, Tennakoon R, Rathnayake T, Hoseinnezhad R, Suter D, Bab-Hadiashar A (2020) Motion segmentation of rgb-d sequences: Combining semantic and motion information using statistical inference. IEEE Trans Image Process 29:5557–5570

    Article  Google Scholar 

  26. Ng AY, Jordan MI, Weiss Y (2002) On spectral clustering: Analysis and an algorithm. In: Advances in neural information processing systems, pp 849–856

  27. Nie F, Wang X, Jordan MI, Huang H (2016) The constrained laplacian rank algorithm for graph-based clustering. In: AAAI. Citeseer, pp 1969–1976

  28. Shen J, Li P (2016) Learning structured low-rank representation via matrix factorization. In: Artificial Intelligence and Statistics, pp 500–509

  29. Sun W, Ma J, Yang G, Du B, Zhang L (2017) A poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery. ISPRS J Photogramm Remote Sens 128:27–39

    Article  Google Scholar 

  30. Tipping M E, Bishop C M (1999) Mixtures of probabilistic principal component analyzers. Neural Comput 11(2):443– 482

    Article  Google Scholar 

  31. Tolić D, Antulov-Fantulin N, Kopriva I (2018) A nonlinear orthogonal non-negative matrix factorization approach to subspace clustering. Pattern Recogn 82:40–55

    Article  Google Scholar 

  32. Tsakiris MC, Vidal R (2017a) Algebraic clustering of affine subspaces. IEEE Trans Pattern Anal Mach Intell 40(2):482–489

  33. Tsakiris MC, Vidal R (2017b) Filtrated algebraic subspace clustering. SIAM J Imaging Sci 10(1):372–415

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

    Article  Google Scholar 

  35. Vidal R, Ma Y, Sastry S (2005) Generalized principal component analysis (gpca). IEEE Trans Pattern Anal Mach Intell 27(12):1945–1959

    Article  Google Scholar 

  36. Von Luxburg U (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416

    Article  MathSciNet  Google Scholar 

  37. Wang J, Shi D, Cheng D, Zhang Y, Gao J (2016) Lrsr: low-rank-sparse representation for subspace clustering. Neurocomputing 214:1026–1037

    Article  Google Scholar 

  38. Wu Z, Yin M, Zhou Y, Fang X, Xie S (2018) Robust spectral subspace clustering based on least square regression. Neural Process Lett 48(3):1359–1372

    Article  Google Scholar 

  39. Xiao Y, Wei J, Wang J, Ma Q, Zhe S, Tasdizen T (2020) Graph constraint-based robust latent space low-rank and sparse subspace clustering. Neural Comput Appl 32(12):8187–8204

    Article  Google Scholar 

  40. Xie X, Guo X, Liu G, Wang J (2018) Implicit block diagonal low-rank representation. IEEE Trans Image Process 27(1):477–489

    Article  MathSciNet  Google Scholar 

  41. Xu J, Yu M, Shao L, Zuo W, Meng D, Zhang L, Zhang D (2019) Scaled simplex representation for subspace clustering. IEEE Transactions on Cybernetics

  42. Xu X, Cheong LF, Li Z (2018) Motion segmentation by exploiting complementary geometric models. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp 2859–2867

  43. Yang J, Liang J, Wang K, Rosin PL, Yang M (2020) Subspace clustering via good neighbors. IEEE Trans Pattern Anal Mach Intell 42(6):1537–1544, https://doi.org/10.1109/TPAMI.2019.2913863

  44. Yang X, Jiang X, Tian C, Wang P, Zhou F, Fujita H (2020a) Inverse projection group sparse representation for tumor classification: A low rank variation dictionary approach. Knowl-Based Syst 196:105768

  45. Yang Z, Liang N, Yan W, Li Z, Xie S (2020b) Uniform distribution non-negative matrix factorization for multiview clustering. IEEE Transactions on Cybernetics

  46. Zhang H, Zhai H, Zhang L, Li P (2016) Spectral–spatial sparse subspace clustering for hyperspectral remote sensing images. IEEE Trans Geosci Remote Sens 54(6):3672–3684

    Article  Google Scholar 

  47. Zhang X, Yang Y, Li T, Zhang Y, Wang H, Fujita H (2021) Cmc: a consensus multi-view clustering model for predicting alzheimer’s disease progression. Comput Methods Prog Biomed 199:105895

    Article  Google Scholar 

  48. Zhang Y, Yang Y, Li T, Fujita H (2019) A multitask multiview clustering algorithm in heterogeneous situations based on lle and le. Knowl-Based Syst 163:776–786

    Article  Google Scholar 

  49. Zheng R, Li M, Liang Z, Wu F X, Pan Y, Wang J (2019) Sinnlrr: a robust subspace clustering method for cell type detection by non-negative and low-rank representation. Bioinformatics 35(19):3642–3650

    Article  Google Scholar 

  50. Zhu P, Zhu W, Hu Q, Zhang C, Zuo W (2017) Subspace clustering guided unsupervised feature selection. Pattern Recogn 66:364–374

    Article  Google Scholar 

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Funding

This work was funded in part by the National Natural Science Foundation of China (No.61572240).

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Authors and Affiliations

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

    Stanley Ebhohimhen Abhadiomhen, ZhiYang Wang & XiangJun Shen

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

    Stanley Ebhohimhen Abhadiomhen

Authors
  1. Stanley Ebhohimhen Abhadiomhen
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  2. ZhiYang Wang
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  3. XiangJun Shen
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Contributions

Stanley Ebhohimhen Abhadiomhen: Conceptualization, Data Curation, Methodology, Software, Investigation, Validation, Formal analysis, Visualization, Writing - Original Draft, Writing - Review & Editing

ZhiYang Wang: Software, Validation, Formal analysis.

XiangJun Shen: Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Validation, Review & Editing.

Corresponding author

Correspondence to XiangJun Shen.

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Conflicts of interest/Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Availability of data and material

https://www.kaggle.com/bistaumanga/usps-dataset https://www.kaggle.com/bistaumanga/usps-dataset https://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits https://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits http://cam-orl.co.uk/facedatabase.html http://vision.ucsd.edu/content/yale-face-database https://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php https://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php http://www.vision.caltech.edu/archive.html http://www.vision.caltech.edu/archive.html

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Abhadiomhen, S.E., Wang, Z. & Shen, X. Coupled low rank representation and subspace clustering. Appl Intell 52, 530–546 (2022). https://doi.org/10.1007/s10489-021-02409-z

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