Skip to main content
SpringerLink
Log in
SpringerLink
Log in

A Nonnegative Projection Based Algorithm for Low-Rank Nonnegative Matrix Approximation

  • Conference paper
  • First Online:
Neural Information Processing (ICONIP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10634))

Included in the following conference series:

  • 4659 Accesses

Abstract

Nonnegative matrix factorization/approximation (NMF/NMA) is a widely used method for data analysis. So far, many multiplicative update algorithms have been developed for NMF. In this paper, we propose a nonnegative projection based NMF algorithm, which is different from the conventional multiplicative update NMF algorithms and decreases the objective function by performing Procrustes rotation and nonnegative projection alternately. The experiment results demonstrate that the new algorithm converges much faster than traditional ones.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Wang, Y., Zhang, Y.: Nonnegative matrix factorization: a comprehensive review. IEEE Trans. Knowl. Data Eng. 25, 1336–1353 (2013)

    Article  Google Scholar 

  2. Zhou, G., Xie, S., Yang, Z., Yang, J., He, Z.: Minimum-volume-constrained nonnegative matrix factorization: enhanced ability of learning parts. IEEE Trans. Neural Netw. 20, 1626–1637 (2011)

    Article  Google Scholar 

  3. Hoyer, P.O.: Non-negative matrix factorization with sparseness constraints. J. Mach. Learn. Res. 5, 1457–1469 (2004)

    MATH  MathSciNet  Google Scholar 

  4. Cichocki, A., Zdunek, R.: Multilayer nonnegative matrix factorization using projected gradient approaches. Int. J. Neural Syst. 17, 431–446 (2007)

    Article  Google Scholar 

  5. Mohammadreza, B., Stefanos, T., Maryam, B., Gerhard, R., Mihai, D.: Discriminative nonnegative matrix factorization for dimensionality reduction. Neurocomputing 173, 212–223 (2016)

    Article  Google Scholar 

  6. Cichocki, A., Zdunek, R., Amari, S.I.: New algorithms for nonnegative matrix factorization in applications to blind source separation. In: 31st IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 621–624. IEEE Press, Florence (2006)

    Google Scholar 

  7. Schmidt, M.N., Mørup, M.: Nonnegative matrix factor 2-D deconvolution for blind single channel source separation. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 700–707. Springer, Heidelberg (2006). doi:10.1007/11679363_87

    Chapter  Google Scholar 

  8. Ozerov, A., Fevotte, C.: Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation. IEEE Trans. Audio Speech Lang. Process. 18, 550–563 (2010)

    Article  Google Scholar 

  9. Yang, Z., Xiang, Y., Rong, Y., Xie, S.: Projection-pursuit-based method for blind separation of nonnegative sources. IEEE Trans. Neural Netw. Learn. Syst. 24, 47–57 (2013)

    Article  Google Scholar 

  10. Zhou, G., Yang, Z., Xie, S., Yang, J.: Online blind source separation using incremental nonnegative matrix factorization with volume constraint. IEEE Trans. Neural Netw. 22, 550–560 (2011)

    Article  Google Scholar 

  11. Yang, Z., Zhou, G., Xie, S., Ding, S.: Blind spectral unmixing based on sparse nonnegative matrix factorization. IEEE Trans. Image Process. 20, 1112–1125 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Buciu, I., Pitas, I.: Application of non-negative and local non negative matrix factorization to facial expression recognition. In: 17th International Conference on Pattern Recognition, pp. 288–291. IEEE Press, Cambridge (2004)

    Google Scholar 

  13. Li, S., Hou, X., Zhang, H., Cheng, Q.: Learning spatially localized, parts-based representation. In: 14th IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 207–212. IEEE Press, Kauai (2001)

    Google Scholar 

  14. Chen, W., Zhao, Y., Pan, B., Chen, B.: Supervised kernel nonnegative matrix factorization for face recognition. Neurocomputing 205, 165–181 (2016)

    Article  Google Scholar 

  15. Liu, W., Zheng, N.: Non-negative matrix factorization based methods for object recognition. Pattern Recogn. Lett. 25, 893–897 (2004)

    Article  Google Scholar 

  16. Wild, S., Curry, J., Dougherty, A.: Improving non-negative matrix factorizations through structured initialization. Pattern Recogn. 37, 2217–2232 (2004)

    Article  Google Scholar 

  17. Xu, W., Liu, X., Gong, Y.: Document clustering based on nonnegative matrix factorization. In: 26th Annual International ACM SIGIR Conference on Research and Development in Informaion Retrieval, pp. 267–273. ACM Press, Toronto (2003)

    Google Scholar 

  18. He, Z., Xie, S., Zdunek, R., Zhou, G., Cichocki, A.: Symmetric nonnegative matrix factorization: algorithms and applications to probabilistic clustering. IEEE Trans. Neural Netw. 22, 2117–2131 (2011)

    Article  Google Scholar 

  19. Shahnaz, F., Berry, M.W., Pauca, V.P., Plemmons, R.J.: Document clustering using nonnegative matrix factorization. Inf. Process. Manage. 42, 373–386 (2006)

    Article  MATH  Google Scholar 

  20. Ding, C., Li, T., Peng, W., Park, H.: Orthogonal nonnegative matrix t-factorizations for clustering. In: 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 126–135. ACM Press, Philadelphia (2006)

    Google Scholar 

  21. Cai, Q., Xie, K., He, Z.: A multiplicative update algorithm for nonnegative convex polyhedral cone learning. In: 25th International Joint Conference on Neural Networks, pp. 1339–1343. IEEE Press, Beijing (2014)

    Google Scholar 

  22. Zhou, G., Cichocki, A., Xie, S.: Fast nonnegative matrix/tensor factorization based on low-rank approximation. IEEE Trans. Signal Process. 60, 2928–2940 (2012)

    Article  MathSciNet  Google Scholar 

  23. Lin, C.: Projected gradient methods for nonnegative matrix factorization. Neural Comput. 19, 2756–2779 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. Zdunek, R., Cichocki, A.: Fast nonnegative matrix factorization algorithms using projected gradient approaches for large-scale problems. Comput. Intell. Neurosci. 35, 36–48 (2008)

    Google Scholar 

  25. Gonzalez, E.F., Zhang, Y.: Accelerating the lee-seung algorithm for non-negative matrix factorization. Dept. Comput. and Appl. Math. 1, 1–13 (2005)

    Google Scholar 

  26. Zdunek, R., Cichocki, A.: Non-negative matrix factorization with quasi-newton optimization. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 870–879. Springer, Heidelberg (2006). doi:10.1007/11785231_91

    Chapter  Google Scholar 

  27. Zdunek, R., Cichocki, A.: Nonnegative matrix factorization with constrained second-order optimization. IEEE Trans. Signal Process. 87, 1904–1916 (2007)

    MATH  Google Scholar 

  28. Schonemann, P.H.: A generalized solution of the orthogonal procrustes problem. Psychometrika 31, 1–10 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  29. Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. Neural Inf. Process. Syst. 1, 556–562 (2001)

    Google Scholar 

Download references

Acknowledgments

The work was supported in part by Guangzhou Science and Technology Program under Grant 201508010007.

Author information

Authors and Affiliations

  1. School of Automation and Institute of Intelligent Signal Processing, Guangdong University of Technology, Guangzhou, 510006, China

    Peitao Wang, Zhaoshui He & Kan Xie

  2. Discipline of Business Analytics, The University of Sydney Business School, Camperdown, NSW, 2006, Australia

    Junbin Gao

  3. School of Computing and Mathematics, Charles Sturt University, Bathurst, NSW, 2795, Australia

    Michael Antolovich

Authors
  1. Peitao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhaoshui He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kan Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Junbin Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Michael Antolovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhaoshui He .

Editor information

Editors and Affiliations

  1. Guangdong University of Technology, Guangzhou, China

    Derong Liu

  2. Guangdong University of Technology, Guangzhou, China

    Shengli Xie

  3. South China University of Technology, Guangzhou, China

    Yuanqing Li

  4. Institute of Automation, Chinese Academy of Sciences, Beijing, China

    Dongbin Zhao

  5. King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    El-Sayed M. El-Alfy

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Wang, P., He, Z., Xie, K., Gao, J., Antolovich, M. (2017). A Nonnegative Projection Based Algorithm for Low-Rank Nonnegative Matrix Approximation. In: Liu, D., Xie, S., Li, Y., Zhao, D., El-Alfy, ES. (eds) Neural Information Processing. ICONIP 2017. Lecture Notes in Computer Science(), vol 10634. Springer, Cham. https://doi.org/10.1007/978-3-319-70087-8_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70087-8_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70086-1

  • Online ISBN: 978-3-319-70087-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation