Skip to main content
SpringerLink
Log in

Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion

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

Abstract

Matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rows to be updated, that is, we assume that samples are dependent on each other. We derive the updating rules for ICGNMF by considering the correlation. We also present tests on widely used image datasets, and show ICGNMF reduces the error by comparing other methods.

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

Similar content being viewed by others

Notes

  1. The FERET can be found at http://www.itl.nist.gov/iad/humanid/feret/feret-master.html.

  2. The Pets can be found at http://ftp.pets.rdg.ac.uk.

References

  1. Lee J, Kim S, Lebanon G, Singer Y, Bengio S (2016) LLORMA: local low-rank matrix approximation. J Mach Learn Res 17(15):1–24

    MathSciNet  MATH  Google Scholar 

  2. Hernando A, Bobadilla J, Ortega F (2016) A non negative matrix factorization for collaborative filtering recommender systems based on a Bayesian probabilistic model. Knowl Based Syst 97:188–202

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Paatero P, Tapper U (1994) Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5(2):111–126

    Article  Google Scholar 

  5. Guillamet D, Vitria J (2002) Non-negative matrix factorization for face recognition. In: Escrig MT, Toledo F, Golobardes E (eds) Topics in Artificial Intelligence. Lecture notes in computer science, vol 2504. Springer, Berlin, Heidelberg, pp 336–344

    Chapter  Google Scholar 

  6. Fogel P, Young S, Hawkins D, Ledirac N (2007) Inferential, robust non-negative matrix factorization analysis of microarray data. Bioinformatics 23(1):44–49

    Article  Google Scholar 

  7. Chen Y, Bhojanapalli S, Sanghavi S et al (2015) Completing any low-rank matrix, provably. J Mach Learn Res 16:2999–3034

    MathSciNet  MATH  Google Scholar 

  8. Wang R, Shan S, Chen X, Gao W (2008) Manifold–manifold distance with application to face recognition based on image set. In: IEEE conference on computer vision and pattern recognition. Anchorage, Alaska, pp 1–8

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

    Article  Google Scholar 

  10. Ding C, Li T, Jordan M (2010) Convex and semi-nonnegative matrix factorizations. IEEE Trans Pattern Anal Mach Intell 32(1):45–55

    Article  Google Scholar 

  11. Guan N, Tao D, Luo Z, Yuan B (2012) Online nonnegative matrix factorization with robust stochastic approximation. IEEE Trans Neural Netw Learn Syst 23(7):1087–1099

    Article  Google Scholar 

  12. Gopalan P, Hofman J, Blei D (2013) Scalable recommendation with Poisson factorization. arXiv:1311.1704

  13. Hastie T, Mazumder R, Lee J, Zadeh R (2015) Matrix completion and low-rank svd via fast alternating least squares. J Mach Learn Res 16(1):3367–3402

    MathSciNet  MATH  Google Scholar 

  14. Luo X, Zhou M, Xia Y, Zhu Q (2014) An efficient non-negative matrix-factorization-based approach to collaborative filtering for recommender systems. IEEE Trans Ind Inf 10(2):1273–1284

    Article  Google Scholar 

  15. Wu J, Chen L, Feng Y et al (2013) Predicting quality of service for selection by neighborhood-based collaborative filtering. IEEE Trans Syst Man Cybern Syst 43(2):428–439

    Article  Google Scholar 

  16. Li S, Hou X, Zhang H, Cheng Q (2001) Learning spatially localized, parts-based representation. IEEE Comput Soc Conf Comput Vis Pattern Recognit 1:1–6

    Google Scholar 

  17. Xu W, Liu X, Gong Y (2003) Document clustering based on non-negative matrix factorization. In: International ACM SIGIR conference on Research and development in information retrieval. Toronto, pp 267–273

  18. Bucak S, Gunsel B (2009) Incremental subspace learning via non-negative matrix factorization. Pattern Recognit 42(5):788–797

    Article  MATH  Google Scholar 

  19. Yu Z, Liu Y, Li B et al (2014) Incremental graph regulated nonnegative matrix factorization for face recognition. J Appl Math 2014(1):1–10

    Google Scholar 

  20. Wang F, Li P, Konig AC (2011) Efficient document clustering via online nonnegative matrix factorizations. In: Eleventh Siam international conference on data mining, Arizona, pp 908–919

  21. Lefèvre A, Bach F, Févotte C (2011) Online algorithms for nonnegative matrix factorization with the Itakura-Saito divergence. In Proceedings of IEEE workshop on applications of signal processing to audio and acoustics, vol 53. pp 313–316

  22. Zhou G, Yang Z, Xie S, Yang J (2011) Online blind source separation using incremental nonnegative matrix factorization with volume constraint. IEEE Trans Neural Netw 22(4):550–60

    Article  Google Scholar 

  23. Chen W, Pan B, Fang B et al (2008) Incremental nonnegative matrix factorization for face recognition. Math Prob Eng 2008:1–17

    MathSciNet  MATH  Google Scholar 

  24. Tenenbaum J, De Silva V, Langford J (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323

    Article  Google Scholar 

  25. Roweis S, Saul L (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326

    Article  Google Scholar 

  26. Mao Y, Saul L (2004) Modeling distances in large-scale networks by matrix factorization. In: Proceedings of the 4th ACM SIGCOMM conference on internet measurement. Taormina, Sicily, pp 278–287

  27. Chung F (1997) Spectral graph theory. CBMS Regional Conference Series in Mathematics, 92. American Mathematical Society, Providence, RI

  28. Cai D, He X, Hu Y et al (2007) Learning a spatially smooth subspace for face recognition. In: IEEE conference on computer vision and pattern recognition. IEEE, pp 1–7

Download references

Acknowledgements

This work is supported in part by the National Natural Science Fund of China (71471060), the Fundamental Research Funds for the Central Universities Support Program (2015xs71), the China Scholarship Council and the National Energy Research Scientific Computing Center (NERSC).

Author information

Authors and Affiliations

  1. School of Control and Computer Engineering, North China Electric Power University, Beijing, 102206, China

    Xiaoxia Zhang

  2. Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

    Degang Chen

  3. Computational Research Division, Lawrance Berkeley National Laboratory, Berkeley, CA, 94720, USA

    Xiaoxia Zhang & Kesheng Wu

Authors
  1. Xiaoxia Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Degang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kesheng Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoxia Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Chen, D. & Wu, K. Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion. Int. J. Mach. Learn. & Cyber. 10, 1259–1268 (2019). https://doi.org/10.1007/s13042-018-0808-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-018-0808-7

Keywords

Search

Navigation