Skip to main content
SpringerLink
Log in

Correntropy-based dual graph regularized nonnegative matrix factorization with Lp smoothness for data representation

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Nonnegative matrix factorization methods have been widely used in many applications in recent years. However, the clustering performances of such methods may deteriorate dramatically in the presence of non-Gaussian noise or outliers. To overcome this problem, in this paper, we propose correntropy-based dual graph regularized NMF with LP smoothness (CDNMFS) for data representation. Specifically, we employ correntropy instead of the Euclidean norm to measure the incurred reconstruction error. Furthermore, we explore the geometric structures of both the input data and the feature space and impose an Lp norm constraint to obtain an accurate solution. In addition, we introduce an efficient optimization scheme for the proposed model and present its convergence analysis. Experimental results on several image datasets demonstrate the superiority of the proposed CDNMFS method.

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

Access this article

Log in via an institution

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
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Lei X, Tie J, Fujita H (2020) Relational completion based non-negative matrix factorization for predicting metabolite-disease associations. Knowledge-Based Syst 204:106238.

  2. Li H, Zhang SJ, Liu G (2017) Graph-based discriminative nonnegative matrix factorization with label information. Neurocomputing 266:91–100

    Article  Google Scholar 

  3. Jiang B, Ding C, Luo B (2018) Robust data representation using locally linear embedding guided PCA. Neurocomputing 275:523–532

    Article  Google Scholar 

  4. Deng T, Ye D, Ma R et al (2020) Low-rank local tangent space embedding for subspace clustering. Inf Sci 508:1–21

    Article  MathSciNet  Google Scholar 

  5. Xue Y, Tang Y, Xu X et al (2021) Multi-objective feature selection with missing data in classification. IEEE Trans Emerg Topic Comput Intell 10:1–10

    Google Scholar 

  6. Li X, Cui G, Dong Y (2017) Graph regularized non-negative low-rank matrix factorization for image clustering. IEEE Trans Cybernetics 47(11):3840–3853

    Article  MathSciNet  Google Scholar 

  7. Yang X, Jiang X, Tian C, et al (2020) Inverse projection group sparse representation for tumor classification: a low rank variation dictionary approach. Knowl Based Syst 196:105768.

  8. Cai D, He X, Han J, Huang TS (2011) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell 33(8):1548–1560

    Article  Google Scholar 

  9. Zhang Z, Zhang Y, Liu G et al (2019) Joint label prediction based semi-supervised adaptive concept factorization for robust data representation. IEEE Trans Knowl Data Eng 32(5):952–970

    Article  Google Scholar 

  10. Zhang Z, Zhang Y, Li S et al (2021) Flexible Auto-weighted Local-coordinate concept factorization: a robust framework for unsupervised clustering. IEEE Trans Knowl Data Eng 33(4):1523–1539

    Article  Google Scholar 

  11. Lee DD, Seung HS (1999) Learning the parts of objects by nonnegative matrix factorization. Nature 401:788–791

    Article  Google Scholar 

  12. Palmer SE (1977) Hierarchical structure in perceptual representation. Cogn Psychol 6:441–474

    Article  Google Scholar 

  13. Wachsmuth E, Oram M W, Perrett DI (1994) Recognition of objects and their component parts: responses of single units in the temporal cortex of the macaque 4:509–522

  14. Logothetis N, Sheinberg D (1996) Visual object recognition. Annu Rev Neurosci 19:577–621

    Article  Google Scholar 

  15. Leng C, Zhang H, Cai G (2018) A novel data clustering method based on smooth non-negative matrix factorization, in ICSM, pp 24–26.

  16. Chen P, He Y, Lu H, et al (2015) Constrained non-negative matrix factorization with graph Laplacian, International Conference on Neural Information Processing.

  17. Guan N, Tao D, Luo Z, Yuan B (2011) Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent. IEEE Trans Image Process 20:2030–2048

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  19. He R, Zheng W, Hu B (2011) Maximum correntropy criterion for robust face recognition. IEEE Trans Pattern Anal Mach Intell 33(8):1561–1576

    Article  Google Scholar 

  20. Zhou N, Dong B, et al (2019) Maximum correntropy criterion-based robust semi-supervised concept factorization for image representation. IEEE Trans Neural Networks Learn Syst.

  21. Wang Y, Wu S, Mao B et al (2014) Correntropy induced metric based graph regularized non-negative matrix factorization. Neurocomputing 204(5):172–182

    Google Scholar 

  22. Lee DD, Seung H (2011) Algorithms for non-negative matrix factorization. Adv Neural Inform Process Syst 13.

  23. Shu Z, Fan H et al (2017) Multiple Laplacian graph regularized low-rank representation with application to image representation. IET Image Proc 6:370–378

    Article  Google Scholar 

  24. Chen B, Wang X, Li Y et al (2019) Maximum correntropy criterion with variable center. IEEE Signal Process Lett 99:1–1

    Google Scholar 

  25. Shu Z, Wu X, You C et al (2020) Rank-constrained nonnegative matrix factorization algorithm for data representation. Inf Sci 528:133–146

    Article  Google Scholar 

  26. He Y, Fei W, Li Y et al (2019) Robust matrix completion via maximum correntropy criterion and Half Quadratic optimization. IEEE Trans Signal Process 68:181–195

    Article  MathSciNet  Google Scholar 

  27. Shu Z, Wu X et al (2019) The optimal graph regularized sparse coding with application to image representation. PRCV 2:91–101

    Google Scholar 

  28. Yang J, Cao J, Xue A (2020) Robust Maximum mixture correntropy criterion-based semi-supervised ELM with variable center. IEEE Trans Circuit Syst 99:3572–3576

    Article  Google Scholar 

  29. He R, Zhen W, Hu B (2011) Maximum correntropy criterion for robust face recognition. IEEE Trans Pattern Anal Mach Intell 33(8):1561–1576

    Article  Google Scholar 

  30. Trigeorgis G, Bousmalis K, Zafeiriou S et al (2017) A deep matrix factorization method for learning attribute representations[J]. IEEE Trans Pattern Anal Mach Intell 39(3):417–429

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant No. 61603159, 62006097, 62162033], Natural Science Foundation of Jiangsu Province [Grant No. BK20160293, BK20200593], Excellent Key Teachers of QingLan Project in Jiangsu Province.

Author information

Authors and Affiliations

  1. Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, 650500, China

    Zhenqiu Shu & Zhengtao Yu

  2. School of Computer Engineering, Jiangsu University of Technology, Changzhou, 231001, China

    Zonghui Weng & Congzhe You

  3. Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Jiangnan University, Wuxi, 231001, China

    Zhen Liu & Xiaojun Wu

  4. Department of Criminal Science and Technology, Nanjing Forest Police College, Nanjing, 210023, China

    Songze Tang

Authors
  1. Zhenqiu Shu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zonghui Weng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhengtao Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Congzhe You
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Songze Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Xiaojun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenqiu Shu.

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

Shu, Z., Weng, Z., Yu, Z. et al. Correntropy-based dual graph regularized nonnegative matrix factorization with Lp smoothness for data representation. Appl Intell 52, 7653–7669 (2022). https://doi.org/10.1007/s10489-021-02826-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-02826-0

Keywords

Search

Navigation