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Multi-view clustering indicator learning with scaled similarity

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Abstract

The similarity of data plays an important role in clustering task, and good clustering performance often requires a reliable similarity matrix. A variety of metrics are used to define a similarity matrix in the past, and great achievements are obtained. However, due to the noise and outliers of data in the real world, the quality of the similarity matrix is often poor. Besides, the similarity matrix is often inflexible, which will degrade the clustering performance. To solve this problem, in this paper, we proposed a novel Multi-view Clustering Indicator Learning with Scaled Similarity (MCILSS). Our model uses the self-representation method to reconstruct the data matrix, and then obtain the similarity matrix by minimizing the reconstruction error. More importantly, in our model, we can adjust s \(\left( {0 < s \le 1} \right)\) to constrain the similarity matrix to gain the best clustering indicator matrix. In addition, the rank constraint is further used to improve the clustering performance. Finally, the indicator matrix is applied to obtain clustering results by k-means. Considering the nonlinear relationship in the data, we also proposed the kernel MCILSS which maps the original data to the kernel space. To solve the proposed models, two efficient optimization algorithms based on Augmented Lagrange Method (ALM) are also designed. The experimental results on some data sets show that our algorithm has better clustering performance than some representative algorithms.

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Data availability

The used datasets that support the findings of this study are openly available: Coil20: http://www1.cs.columbia.edu/CAVE/software/softlib/coil-100.php, ORL: https://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html, BBCsport: http://mlg.ucd.ie/datasets/bbc.html, EyaleB: https://computervisiononline.com/dataset/1105138686, 3Sources: http://mlg.ucd.ie/datasets/3sources.html, MSRCV1: https://mldta.com/dataset/msrc-v1/, The datasets and the codes of our methods can also be obtained from the corresponding author.

References

  1. Elhamifar E and Vidal R (2009) Sparse subspace clustering. In: IEEE Conference on computer vision and pattern recognition, pp 2790–2797

  2. Liu G et al. (2012) Robust and efficient subspace segmentation via least squares regression. In: Springer-Verlag, pp 347–360

  3. Elhamifar E, Vidal R (2012) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35:2765–2781

    Article  Google Scholar 

  4. Kang Z et al (2020) Robust graph learning from noisy data. IEEE Int Conf Acoustics, Speech Signal Process 50:1833–1843

    Google Scholar 

  5. Cai D et al. (2011) Graph regularized nonnegative matrix factorization for data representation. In: IEEE Transactions on pattern analysis and machine intelligence, pp 1548–1560

  6. Zhou P, et al. (2015) Recovery of corrupted multiple kernels for clustering. In: Proceedings of the twenty-fourth international joint conference on artificial intelligence, pp 4105–4111

  7. Ren Z and Sun Q (2021) Simultaneous global and local graph structure preserving for multiple kernel clustering. In: IEEE international conference on acoustics, speech and signal processing, pp 4057–4064

  8. Huang J et al. (2013) Spectral rotation versus K-means in spectral clustering. In: Proceedings of the Twenty-Seventh AAAI conference on artificial intelligence, pp 431–437

  9. Wilkin GA and Huang X (2007) K-means clustering algorithms: implementation and comparison. In: Second international multi-symposiums on computer and computational sciences, pp 133–136

  10. Austin A et al. (2009) Robust subspace segmentation by low rank representation. In: Proceedings of the 27th international conference on international conference on machine learning, pp 663–670

  11. Kang Z et al (2020) Structure learning with similarity preserving. Neural Netw 129:138–148

    Article  Google Scholar 

  12. Gao H et al. (2015) "Multi-view Subspace Clustering. In: 2015 IEEE international conference on computer vision, Santiago, Chile, pp 4238–4246

  13. Lele Fu et al (2020) An overview of recent multi-view clustering. Neurocomputing 402:148–161

    Article  Google Scholar 

  14. Zheng Q et al (2020) Feature concatenation multi-view subspace clustering. Neurocomputing 379:89–102

    Article  Google Scholar 

  15. Zhang C et al. (2017) Latent multi-view subspace clustering. In: 2017 IEEE conference on computer vision and pattern recognition, pp 4333–4341

  16. Xie D et al (2020) Adaptive latent similarity learning for multi-view clustering. Neural Netw 121:409–418

    Article  Google Scholar 

  17. Zhan K et al (2018) Adaptive structure concept factorization for multiview clustering. Neural Comput 30:1080–1103

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang P et al. (2020) Consensus one-step multi-view subspace clustering. In: IEEE transactions on knowledge and data engineering, pp 1–1

  19. Lin Z et al. (2011) Linearized alternating direction method with adaptive penalty for low-rank representation. In: Advances in neural information processing systems, pp 612–620

  20. Yin M et al (2015) Dual graph regularized latent low-rank representation for subspace clustering. IEEE Trans Image Process 24:4918–4933

    Article  MathSciNet  MATH  Google Scholar 

  21. Chao G et al (2021) A survey on multiview clustering. IEEE Trans Artif Intell 2:146–168

    Article  Google Scholar 

  22. Chen M-S et al (2022) Representation learning in multi-view clustering: a literature review. Data Sci Eng 7:225–241

    Article  Google Scholar 

  23. Li Y et al (2019) A survey of multi-view representation learning. IEEE Trans Knowl Data Eng 31:1863–1883

    Article  Google Scholar 

  24. Xu J et al (2021) Scaled simplex representation for subspace clustering. IEEE Trans Cybern 51:1493–1505

    Article  Google Scholar 

  25. Das KCh (2004) The Laplacian spectrum of a graph. Comput Math Appl 48:715–724

    Article  MathSciNet  MATH  Google Scholar 

  26. Fan K (1950) On a theorem of weyl concerning eigenvalues of linear transformations: II. In: Proceedings of the national academy of sciences of the United States of America, pp 31–35

  27. He B, Yang H (1998) Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities. Op Res Lett 23:151–161

    Article  MathSciNet  MATH  Google Scholar 

  28. Hestenes MR (1969) Multiplier and gradient methods. J Optim Theory Appl 4(5):303–320

    Article  MathSciNet  MATH  Google Scholar 

  29. Powell MJD (1978) Algorithms for nonlinear constraints that use Lagrangian functions. Math Progr 14:224–248

    Article  MathSciNet  MATH  Google Scholar 

  30. He S et al (2012) A nonlinear Lagrangian for constrained optimization problems. J Appl Math Comput 38:669–685

    Article  MathSciNet  MATH  Google Scholar 

  31. Wen J et al (2018) Low-rank representation with adaptive graph regularization. Neural Netw 108:83–96

    Article  MATH  Google Scholar 

  32. Iliadis M, et al. (2017) Robust and low-rank representation for fast face identification with occlusions. In: IEEE international conference on acoustics, speech and signal processing, pp 2203–2218

  33. Elhamifar E et al. (2016) Dissimilarity-based sparse subset selection. In: IEEE Transactions on pattern analysis and machine intelligence, pp 2182–2197

  34. Michelot C (1986) A finite algorithm for finding the projection of a point onto the canonical simplex of RN. J Optim Theory Appl 50:195–200

    Article  MathSciNet  MATH  Google Scholar 

  35. Duchi J et al. (2008) Efficient projections onto the L1-Ball for learning in high dimensions. In: Proceedings of the 25th international conference on machine learning, pp. 272–279

  36. Kuybeda O et al (2013) A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography. J Struct Biol 181:116–127

    Article  Google Scholar 

  37. Wang Q et al. (2019) Spectral embedded adaptive neighbors clustering. In: IEEE transactions on neural networks and learning systems, pp 1265–1271

  38. Chen M et al. (2020) Multi-view clustering in latent embedding space. In: AAAI

  39. Wang Y et al. (2015) Consistent multiple graph embedding for multi-view clustering. In: IEEE transactions on multimedia

  40. Guowang Du et al (2021) Deep multiple auto-encoder-based multi-view clustering. Data Sci Eng 6:323–338

    Article  Google Scholar 

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Acknowledgements

This research is supported by NSFC of China (No. 61976005) and the Natural Science Research Project of Anhui Province University (No. 2022AH050970).

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Authors and Affiliations

  1. School of Electrical Engineering, AnHui Polytechnic University, WuHu, 241000, AnHui, China

    Liang Yao

  2. School of Computer Science and Information, AnHui Polytechnic University, WuHu, 241000, AnHui, China

    Gui-Fu Lu

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  1. Liang Yao
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Correspondence to Gui-Fu Lu.

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Yao, L., Lu, GF. Multi-view clustering indicator learning with scaled similarity. Pattern Anal Applic 26, 1395–1406 (2023). https://doi.org/10.1007/s10044-023-01167-7

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  • DOI: https://doi.org/10.1007/s10044-023-01167-7

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