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Dual local learning regularized NMF with sparse and orthogonal constraints

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Abstract

Non-negative matrix factorization (NMF) has shown remarkable competitiveness in the past few years. To fully exploit various known prior knowledge hidden in data, this paper proposes a dual local learning regularized NMF with sparse and orthogonal constraints (DLLNMF-SO) algorithm. DLLNMF-SO constructs two local learning regularizers to consider the geometric structure and discriminative information embedded in data and feature space, respectively. Besides, it makes full use of sparse self-representation information by adding the l2,1-norm constraint. Meanwhile, the orthogonal constraint is imposed on the basis vectors to preserve the correspondence between samples and basic vectors. We give an efficient iterative updating scheme for the optimization problem of DLLNMF-SO and provides its convergence guarantee. We demonstrate that our proposed approach outperforms other competitors by conducting serval experiments on three benchmark datasets.

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References

  1. Shu Z, Weng Z, Yu Z et al (2022) Correntropy-based dual graph regularized nonnegative matrix factorization with Lp smoothness for data representation. Appl Intell 52(7):7653–7669

  2. Zhang Z, Zhang Y, Liu G et al (2020) 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 

  3. Shu Z, Wu X, Fan H et al (2017) Parameter-less auto-weighted multiple graph regularized nonnegative matrix factorization for data representation. Knowl-Based Syst 131:105–112

    Article  Google Scholar 

  4. Jolliffe I (1989) Principal component analysis. Springer-Verlag, New York, NY, USA, pp 41–64

    Google Scholar 

  5. Belhumeur P, Hespanha J, Kriegman D (1997) Eigenfaces vs fisherfaces: recognition using class specific linear projection. IEEE Trans Patt Anal Mach Intell 19(7):711–720

    Article  Google Scholar 

  6. Lee DD, Seung HS (2000) Learning the parts of objects by non-negative matrix factorization. Nature 401(6755):788–791

    Article  MATH  Google Scholar 

  7. Yan S, Xu D, Zhang B (2007) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1):40–51

    Article  Google Scholar 

  8. Cai H, Liu B, Xiao Y (2020) Semi-supervised multi-view clustering based on orthonormality-constrained nonnegative matrix factorization. Inf Sci 536(10):171–184

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang D, Wu X-J (2020) Scalable discrete matrix factorization and semantic autoencoder for cross-media retrieval. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.3032017

  10. Jiao C, Gao Y, Yu N et al (2020) Hyper-graph regularized constrained NMF for selecting differentially expressed genes and tumor classification. IEEE J Biomed Health Inform 99:3002–3011

    Article  Google Scholar 

  11. Lu X, Dong L, Yuan Y (2020) Subspace clustering constrained sparse NMF for hyperspectral unmixing. IEEE Trans Geosci Remote Sens 58(5):3007–3019. https://doi.org/10.1109/TGRS.2019.2946751

    Article  Google Scholar 

  12. Xiu X, Fan J, Yang Y et al (2021) Fault detection using structured joint sparse nonnegative matrix factorization. IEEE Trans Instrum Meas 70:1–11

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Gu Q, Zhou J (2009) Local learning regularized nonnegative matrix factorization. Twenty-first Int Joint Conf Artif Intell:1044–1051

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

    Article  MATH  Google Scholar 

  16. Wang C, Yu N, Wu M et al (2019) Dual hyper-graph regularized supervised NMF for selecting differentially expressed genes and tumor classification. IEEE Trans Comput Biol Bioinform 24(10):3002–3011

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Shu Z, Zhou J, Huang P et al (2016) Local and global regularized sparse coding for data representation. Neurocomputing 198(29):188–197

    Article  Google Scholar 

  19. Shu Z, Sun Y, Tang J et al (2022) Adaptive graph regularized deep semi-nonnegative matrix factorization for data representation. Neural Process Lett. https://doi.org/10.1007/s11063-022-10882-x

  20. Liu H, Wu Z, Cai D, Huang TS (2012) Constrained nonnegative matrix factorization for image representation. IEEE Trans Pattern Anal Mach Intell 34(7):1299–1311

    Article  Google Scholar 

  21. Li Z, Tang J (2018) Robust structured nonnegative matrix factorization for image representation. IEEE Trans Neural Networks Learn Syst 29(5):1947–1960

    Article  MathSciNet  Google Scholar 

  22. Trigeorgis G, Bousmalis K et al (2017) A deep matrix factorization method for learning attribute representations. IEEE Trans Pattern Anal Mach Intell 39(3):1692–1700

    Article  Google Scholar 

  23. Lu Y, Lai Z, Xu Y, Li X et al (2017) Nonnegative discriminant matrix factorization. IEEE Trans Circ Syst Video Technol 27(7):1392–1405

    Article  Google Scholar 

  24. Ma J, Zhang Y, Zhang L (2021) Discriminative subspace matrix factorization for multi-view data clustering. Patt Recogn. https://doi.org/10.1016/j.patcog.2020.107676

  25. Li X, Zhang Y, Ge Z et al (2021) Adaptive nonnegative sparse representation for hyperspectral image super-resolution. IEEE J Selected Topics Appl Earth Observ Remote Sensing 14:4267–4283

    Article  Google Scholar 

  26. Chen J, Yang S, Wang Z et al (2021) Efficient sparse representation for learning with high-dimensional data. IEEE Trans Neural Networks Learn Syst. https://doi.org/10.1109/TNNLS.2021.3119278

  27. Ding C, Li T, Pen W et al (2006) Orthogonal nonnegative matrix tri-factorizations for clustering. ACM SIGKDD Int Conf Knowledge Discovery Data Mining:126–135

  28. Shang R, Zhang Z, Jiao L et al (2016) Self-representation based dual-graph regularized feature selection clustering. Neurocomputing 171:1242–1253

    Article  Google Scholar 

  29. Meng Y, Shang R, Jiao L, et al. Dual-graph regularized non-negative matrix factorization with sparse and orthogonal constraints Eng Appl Artif Intell, 2018, 69: 24–35

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Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant No. 61603159, 61902160, U21B2027, 62162033], Yunnan Fundamental Research Projects [Grant No. 202101BE070001–056, 202101AT070438], Yunnan Provincial Major Science and Technology Special Plan Projects [Grant No. 202002AD080001, 202103AA080015].

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Authors and Affiliations

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

    Zhenqiu Shu

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

    Furong Zuo, Wenli Wu & Congzhe You

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  1. Zhenqiu Shu
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  2. Furong Zuo
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  3. Wenli Wu
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  4. Congzhe You
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Correspondence to Zhenqiu Shu.

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Shu, Z., Zuo, F., Wu, W. et al. Dual local learning regularized NMF with sparse and orthogonal constraints. Appl Intell 53, 7713–7727 (2023). https://doi.org/10.1007/s10489-022-03881-x

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