Skip to main content
Log in

Multi-view data clustering via non-negative matrix factorization with manifold regularization

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Nowadays, non-negative matrix factorization (NMF) based cluster analysis for multi-view data shows impressive behavior in machine learning. Usually, multi-view data have complementary information from various views. The main concern behind the NMF is how to factorize the data to achieve a significant clustering solution from these complementary views. However, NMF does not focus to conserve the geometrical structures of the data space. In this article, we intensify on the above issue and evolve a new NMF clustering method with manifold regularization for multi-view data. The manifold regularization factor is exploited to retain the locally geometrical structure of the data space and gives extensively common clustering solution from multiple views. The weight control term is adopted to handle the distribution of each view weight. An iterative optimization strategy depended on multiplicative update rule is applied on the objective function to achieve optimization. Experimental analysis on the real-world datasets are exhibited that the proposed approach achieves better clustering performance than some state-of-the-art algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. http://mlg.ucd.ie/datasets/segment.html.

  2. http://mlg.ucd.ie/datasets/bbc.html.

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

  4. http://lig-membres.imag.fr/grimal/data.html.

  5. http://www.svcl.ucsd.edu/projects/crossmodal/.

  6. http://lig-membres.imag.fr/grimal/data.html.

  7. http://lig-membres.imag.fr/grimal/data.html.

References

  1. Yang Y, Wang H (2018) Multi-view clustering: a survey. Big Data Min Anal 1(2):83–107

    Article  Google Scholar 

  2. Li J, Zhou G, Qiu Y, Wang Y, Xie S (2020) Deep graph regularized non-negative matrix factorization for multi-view clustering. Neurocomputing 390:108–116

    Article  Google Scholar 

  3. Akrami A, Habib R, Khosravi MR (2020) Design of a reservoir for cloud-enabled echo state network with high clustering coefficient. EURASIP J Wirel Commun Netw 2020(1):1–14

    Article  Google Scholar 

  4. Zhao J, Xie X, Xu X, Sun S (2017) Multi-view learning overview: recent progress and new challenges. Inf Fusion 38:43–54

    Article  Google Scholar 

  5. Bickel S, Scheffer T (2004) Multi-view clustering. In: Proc. of the 4th international conference on data mining, ICDM, vol 4, pp 19–26

  6. Tavallali P, Tavallali P, Khosarvi MR, Mukesh S ( 2020) Interpretable synthetic reduced nearest neighbor: an expectation maximization approach. In: Proc.of the 27th IEEE international conference on image processing, ICIP, pp 1921–1925

  7. Abbasi M, Shokrollahi A, Khosaravi MR, Menon VG (2020) High-performance flow classification using hybrid clusters in software defined mobile edge computing. Comput Commun 160:643–660

    Article  Google Scholar 

  8. Yang S, Hou C, Zhang C, Wu Y, Weng S (2013) Robust non-negative matrix factorization via joint sparse and graph regularization. In: Proc. of international joint conference on neural networks, IJCNN, pp 1–5

  9. Sun F, Xu M, Hu X, Jiang X (2016) Graph regularized and sparse nonnegative matrix factorization with hard constraints for data representation. Neurocomputing 173:233–244

    Article  Google Scholar 

  10. Gao S, Yu Z, Jin T, Yin M (2019) Multi-view low-rank matrix factorization using multiple manifold regularization. Neurocomputing 335:143–152

    Article  Google Scholar 

  11. Ren P, Xiao Y, Xu P, Guo J, Chen X, Wang X, Fang D (2019) Robust auto-weighted multi-view clustering. In: Proc. of 27th international joint conference on artificial intelligence, IJCAI, pp 2644–2650

  12. Khan GA, Hu J, Li T, Diallo B, Huang Q (2019) Weighted multi-view data clustering via joint non-negative matrix factorization. In: Proc. of 14th international conference on intelligent systems and knowledge engineering, ISKE, pp 1159–1165

  13. Liu J, Wang C, Gao J, Han J (2013) Multi-view clustering via joint nonnegative matrix factorization. In: Proc. of SIAM international conference on data mining, pp 252–260

  14. Wang J, Wang X, Tian F, Liu CH, Yu H, Liu Y (2016) Adaptive multi-view semi-supervised nonnegative matrix factorization. In: Proc. of 23th international conference on neural information processing, ICONIP, pp 435–444

  15. Cai X, Nie F, Huang H (2013) Multi-view \(k\)-means clustering on big data. In: Proc. of 23rd international joint conference on artificial intelligence, IJCAI, pp 2598C–2604

  16. Zong L, Zhang X, Zhao L, Yu H, Zhao Q (2017) Multi-view clustering via multi-manifold regularized non-negative matrix factorization. Neural Netw 88:74–89

    Article  MATH  Google Scholar 

  17. Wang Y-X, Zhang Y-J (2012) Nonnegative matrix factorization: a comprehensive review. IEEE Trans Knowl Data Eng 25(6):1336–1353

    Article  MathSciNet  Google Scholar 

  18. Cai D, He X, Han J, Huang TS (2010) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell 33(8):1548–1560

    Google Scholar 

  19. Cai D, He X, Wu X, Han J (2008) Non-negative matrix factorization on manifold. In: Proc. of 8th international conference on data mining, ICDM, pp 63–72

  20. Zhang X, Zhao L, Zong L, Liu X, Yu H (2014) Multi-view clustering via multi-manifold regularized nonnegative matrix factorization. In: Proc. of 14th international conference on data mining, ICDM, pp 1103–1108

  21. Wang H, Yang Y, Li T (2016) Multi-view clustering via concept factorization with local manifold regularization. In: Proc. of 16th international conference on data mining, ICDM, pp 1245–1250

  22. Wu B, Wang E, Zhu Z, Chen W, Xiao P (2018) Manifold NMF with \(L_{21}\) norm for clustering. Neurocomputing 273:78–88

    Google Scholar 

  23. Pu J, Zhang Q, Zhang L, Du B, You J (2016) Multi-view clustering based on robust and regularized matrix approximation. In: Proc. of 23rd international conference on pattern recognition, ICPR, pp 2550–2555

  24. Jia Y, Liu H, Hou J, Kwong S (2020) Semisupervised adaptive symmetric non-negative matrix factorization. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.2969684

  25. Zhao Q, Zong L, Zhang X-C, Liu X, Yu H (2020) Multi-view clustering via clusterwise weights learning. Knowl Based Syst 193:105459

    Article  Google Scholar 

  26. Huang S, Xu Z, Kang Z, Ren Y (2020) Regularized nonnegative matrix factorization with adaptive local structure learning. Neurocomputing 382:196–209

    Article  Google Scholar 

  27. Liang N, Yang Z, Li Z, Su CY (2020) Semi-supervised multi-view clustering with graph-regularized partially shared non-negative matrix factorization. Knowl Based Syst 190:105185

    Article  Google Scholar 

  28. Liang N, Yang Z, Li Z, Sun W, Xie S (2020) Multi-view clustering by non-negative matrix factorization with co-orthogonal constraints. Knowl Based Syst 194:105582

    Article  Google Scholar 

  29. Tao SJ, Yu ZQ (2020) Completion of multiview missing data based on multi-manifold regularised non-negative matrix factorisation. Artif Intell Rev 53:5411–5428. https://doi.org/10.1007/s10462-020-09824-7

  30. Chen F, Li G, Li Z, Wang S, Pan Z (2019) Multiview clustering via robust neighboring constraint non-negative matrix factorization. Math Probl Eng 2019:1–10

    MATH  Google Scholar 

  31. Yang Z, Liang N, Yan W, Li Z, Xie S (2020) Uniform distribution non-negative matrix factorization for multi-view clustering. IEEE Tran Syst Man Cybern 1–14 PMID: 32386175. https://doi.org/10.1109/TCYB.2020.2984552

  32. Yang Z, Liang N, Yan W, Li Z, Xie S (2020) Multi-view non-negative matrix factorization discriminant learning via cross entropy loss. In: Proc. of the 32nd Chinese control and decision conference, CCDC, pp 3964–3971

  33. Zhu X, Guo J, Nejdl W, Liao X, Dietze S (2020) Multi-view image clustering based on sparse coding and manifold consensus. Neurocomputing 403:53–62

    Article  Google Scholar 

  34. Rai N, Negi S, Chaudhury S, Deshmukh O (2016) Partial multi-view clustering using graph regularized NMF. In: Proc. of 23rd international conference on pattern recognition, ICPR, pp 2192–2197

  35. Shen B, Si L (2010) Non-negative matrix factorization clustering on multiple manifolds. In: Proc. of 24th AAAI conference on artificial intelligence, AAAI, pp 575–580

  36. Qian B, Shen X, Gu Y, Tang Z, Ding Y (2016) Double constrained NMF for partial multi-view clustering. In: Proc. of international conference on digital image computing: techniques and applications, DICTA, pp 1–7

  37. Luo P, Peng J, Guan Z, Fan J (2018) Dual regularized multi-view non-negative matrix factorization for clustering. Neurocomputing 294:1–11

    Article  Google Scholar 

  38. Wang Z, Kong X, Fu H, Li M, Zhang Y (2015) Feature extraction via multi-view non-negative matrix factorization with local graph regularization. In: Proc. of international conference on image processing, ICIP, pp 3500–3504

  39. Wang X, Zhang T, Gao X (2018) Multiview clustering based on non-negative matrix factorization and pairwise measurements. IEEE Trans Cybern 49(9):3333–3346

    Article  Google Scholar 

  40. Ou W, Long F, Tan Y, Yu S, Wang P (2018) Co-regularized multi-view nonnegative matrix factorization with correlation constraint for representation learning. Multimed Tools Appl 77(10):12955–12978

    Article  Google Scholar 

  41. Wang J, Tian F, Yu H, Liu CH, Zhan K, Wang X (2017) Diverse non-negative matrix factorization for multi-view data representation. IEEE Trans Cybern 48(9):2620–2632

    Article  Google Scholar 

  42. Babaee M, Tsoukalas S, Babaee M, Rigoll G, Datcu M (2016) Discriminative nonnegative matrix factorization for dimensionality reduction. Neurocomputing 173:212–223

    Article  Google Scholar 

  43. Yang S, Zhang L (2017) Non-redundant multiple clustering by nonnegative matrix factorization. Mach Learn 106(5):695–712

    Article  MathSciNet  MATH  Google Scholar 

  44. Lee DD, Seung HS (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401(6755):788–791

    Article  MATH  Google Scholar 

  45. Cai D, He X, Wang X, Bao H, Han J (2009) Locality preserving nonnegative matrix factorization. In: Proc. of 21st international joint conference on artificial intelligence, IJCAI, pp 1010–1015

  46. Zhang Z, Zhao K (2012) Low-rank matrix approximation with manifold regularization. IEEE Trans Pattern Anal Mach Intell 35(7):1717–1729

    Article  MathSciNet  Google Scholar 

  47. Tzortzis G, Likas A (2012) Kernel-based weighted multi-view clustering. In: Proc. of 12th international conference on data mining, ICDM, pp 675–C684

  48. Shang F, Jiao LC, Wang F (2012) Graph dual regularization non-negative matrix factorization for co-clustering. Pattern Recognit 45(6):2237–2250

    Article  MATH  Google Scholar 

  49. Nie F, Li J, Li X (2016) Parameter-free auto-weighted multiple graph learning: A framework for multiview clustering and semi-supervised classification. In: Proc. of 25th international joint conference on artificial intelligence, IJCAI, pp 1881–C1887

  50. Shao W, He L, Yu Philip S (2015) Multiple incomplete views clustering via weighted nonnegative matrix factorization with \(l_{2,1}\) regularization. In: Joint European conference on machine learning and knowledge discovery in databases, pp 318–334

  51. Zhao H, Ding Z, Fu Y (2017) Multi-view clustering via deep matrix factorization. In: Proc. of 31st AAAI conference on artificial intelligence, AAAI, pp 2921C–2927

Download references

Acknowledgements

This work is supported by the National Key R&D Program of China (No. 2020AAA0105101) and the National Science Foundation of China (Nos. 61772435, 61976182, 61876157).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jie Hu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, G.A., Hu, J., Li, T. et al. Multi-view data clustering via non-negative matrix factorization with manifold regularization. Int. J. Mach. Learn. & Cyber. 13, 677–689 (2022). https://doi.org/10.1007/s13042-021-01307-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-021-01307-7

Keywords

Navigation