Skip to main content
SpringerLink
Log in

Constrained Non-negative Matrix Factorization with Graph Laplacian

  • Conference paper
  • First Online:
Neural Information Processing (ICONIP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9491))

Included in the following conference series:

Abstract

Non-negative Matrix Factorization (NMF) is proven to be a very effective decomposition method for dimensionality reduction in data analysis, and has been widely applied in computer vision, pattern recognition and information retrieval. However, NMF is virtually an unsupervised method since it is unable to utilize prior knowledge about data. In this paper, we present Constrained Non-negative Matrix Factorization with Graph Laplacian (CNMF-GL), which not only employs the geometrical information, but also properly uses the label information to enhance NMF. Specifically, we expect that a graph regularized term could preserve the local structure of original data, meanwhile data points both having the same label and possessing different labels will have corresponding constraint conditions. As a result, the learned representations will have more discriminating power. The experimental results on image clustering manifest the effectiveness of our algorithm.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Notes

  1. 1.

    http://www.cad.zju.edu.cn/home/dengcai/Data/FaceData.html.

  2. 2.

    http://www.cad.zju.edu.cn/home/dengcai/Data/FaceData.html.

  3. 3.

    http://www-prima.inrialpes.fr/FGnet/data/05-ARFace/tarfd_markup.html.

  4. 4.

    http://en.wikipedia.org/wiki/Caltech_101.

  5. 5.

    http://vision.stanford.edu/lijiali/event_dataset/.

References

  1. Gersho, A., Gray, R.M.: Vector Quantization and Signal Compression. Kluwer Academic Press, Boston (1992)

    Book  MATH  Google Scholar 

  2. Belkin, M., Niyogi, P., Sinndhwani, V.: Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J. Mach. Learn. Res. 7(11), 2399–2434 (2006)

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  4. Chapelle, O., Scholkopf, B., Zien, A., et al.: Semi-supervised Learning, vol. 2. MIT Press, Cambridge (2006)

    Book  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. Jolliffe, I.: Principal Component Analysis. Springer, New York (1986)

    Book  MATH  Google Scholar 

  8. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. WileyInterscience, New York (2000)

    MATH  Google Scholar 

  9. Gao, S., Chen, Z., Zhang, D.: Learning mid-perpendicular hyperplane similarity from cannot-link constraints. Neurocomputing 113(3), 195–203 (2013)

    Article  Google Scholar 

  10. Li, S., Hou, X., Zhang, H., Cheng, Q.: Learning spatially localized, parts-based representation. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, pp. 207–212 (2001)

    Google Scholar 

  11. Xu, W., Liu, X., Gong, Y.: Document clustering based on non-negative matrix factorization. In: Proceedings of the Annual ACM SIGIR Conference on Research and Development in Information Retrieval (2003)

    Google Scholar 

  12. Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised learning using gaussian fields and harmonic functions. In: Proceedings of the 20th International Conference on Machine Learning (2003)

    Google Scholar 

  13. Yang, Y., Hu, B.: Pairwise constraints-guided non-negative matrix factorization for document clustering. In: IEEE/WIC/ACM International Conference on Web Intelligence, pp. 250–256. IEEE (2007)

    Google Scholar 

Download references

Acknowledgments

This work is supported by NSFC (No. 61272247,61472075, 61533012), the Science and Technology Commission of Shanghai Municipality (No. 13511500200, 15JC1400103), 863 (No. SS2015AA020501, No. 2008AA02Z310) in China and Arts and Science Cross Special Fund of SJTU under Grant 13JCY14.

Author information

Authors and Affiliations

  1. Key Laboratory of Shanghai Education Commission for Intelligent Interaction and Cognitive Engineering, Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Pan Chen, Yangcheng He, Hongtao Lu & Li Wu

Authors
  1. Pan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yangcheng He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongtao Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Li Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongtao Lu .

Editor information

Editors and Affiliations

  1. University of Istanbul, Istanbul, Turkey

    Sabri Arik

  2. University at Qatar, Doha, Qatar

    Tingwen Huang

  3. Tunku Abdul Rahman University College, Kuala Lumpur, Malaysia

    Weng Kin Lai

  4. University of Science Technology, Wuhan, China

    Qingshan Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Chen, P., He, Y., Lu, H., Wu, L. (2015). Constrained Non-negative Matrix Factorization with Graph Laplacian. In: Arik, S., Huang, T., Lai, W., Liu, Q. (eds) Neural Information Processing. ICONIP 2015. Lecture Notes in Computer Science(), vol 9491. Springer, Cham. https://doi.org/10.1007/978-3-319-26555-1_72

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26555-1_72

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26554-4

  • Online ISBN: 978-3-319-26555-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation