Skip to main content
SpringerLink
Log in

A Local Method for Canonical Correlation Analysis

  • Conference paper
  • First Online:
Natural Language Processing and Chinese Computing (NLPCC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9362))

  • 2325 Accesses

Absract

Canonical Correlation Analysis (CCA) is a standard statistical technique for finding linear projections of two arbitrary vectors that are maximally correlated. In complex situations, the linearity of CCA is not applicable. In this paper, we propose a novel local method for CCA to handle the non-linear situations.We aim to find a series of local linear projections instead of a single globe one. We evaluate the performance of our method and CCA on two real-world datasets. Our experiments show that local method outperforms original CCA in several realistic cross-modal multimedia retrieval tasks.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaho, S.: A kernel method for canonical correlation analysis (2006). arXiv preprint cs/0609071

    Google Scholar 

  2. Andrew, G., Arora, R., Bilmes, J., Livescu, K.: Deep canonical correlation analysis. In: Proceedings of the 30th International Conference on Machine Learning, pp. 1247–1255 (2013)

    Google Scholar 

  3. Asoh, H., Takechi, O.: An approximation of nonlinear canonical correlation analysis by multilayer perceptrons. In: ICANN 1994, pp. 713–716. Springer (1994)

    Google Scholar 

  4. Bach, F.R., Jordan, M.I.: Kernel independent component analysis. The Journal of Machine Learning Research 3, 1–48 (2003)

    MathSciNet  MATH  Google Scholar 

  5. Barnard, K., Duygulu, P., Forsyth, D., De Freitas, N., Blei, D.M., Jordan, M.I.: Matching words and pictures. The Journal of Machine Learning Research 3, 1107–1135 (2003)

    MATH  Google Scholar 

  6. Bießmann, F., Meinecke, F.C., Gretton, A., Rauch, A., Rainer, G., Logothetis, N.K., Müller, K.R.: Temporal kernel CCA and its application in multimodal neuronal data analysis. Machine Learning 79(1–2), 5–27 (2010)

    Article  MathSciNet  Google Scholar 

  7. Bishop, C.M.: Pattern recognition and machine learning. Springer (2006)

    Google Scholar 

  8. Costa Pereira, J., Coviello, E., Doyle, G., Rasiwasia, N., Lanckriet, G.R., Levy, R., Vasconcelos, N.: On the role of correlation and abstraction in cross-modal multimedia retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence 36(3), 521–535 (2014)

    Article  Google Scholar 

  9. Dhillon, P., Foster, D.P., Ungar, L.H.: Multi-view learning of word embeddings via CCA. In: Advances in Neural Information Processing Systems, pp. 199–207 (2011)

    Google Scholar 

  10. Friedman, J., Hastie, T., Tibshirani, R.: The elements of statistical learning. Springer series in statistics, vol. 1. Springer, Berlin (2001)

    Google Scholar 

  11. Hardoon, D.R., Szedmak, S., Shawe-Taylor, J.: Canonical correlation analysis: An overview with application to learning methods. Neural Computation 16(12), 2639–2664 (2004)

    Article  MATH  Google Scholar 

  12. Hsieh, W.W.: Nonlinear canonical correlation analysis by neural networks. Neural Networks 13(10), 1095–1105 (2000)

    Article  Google Scholar 

  13. Kambhatla, N., Leen, T.K.: Dimension reduction by local principal component analysis. Neural Computation 9(7), 1493–1516 (1997)

    Article  Google Scholar 

  14. Lee, J., Kim, S., Lebanon, G., Singer, Y.: Local low-rank matrix approximation. In: Proceedings of the 30th International Conference on Machine Learning, pp. 82–90 (2013)

    Google Scholar 

  15. Rasiwasia, N., Costa Pereira, J., Coviello, E., Doyle, G., Lanckriet, G.R., Levy, R., Vasconcelos, N.: A new approach to cross-modal multimedia retrieval. In: Proceedings of the International Conference on Multimedia, pp. 251–260. ACM (2010)

    Google Scholar 

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

    Article  Google Scholar 

  17. Thompson, B.: Canonical correlation analysis. Encyclopedia of Statistics in Behavioral Science (2005)

    Google Scholar 

  18. Vinokourov, A., Cristianini, N., Shawe-Taylor, J.S.: Inferring a semantic representation of text via cross-language correlation analysis. In: Advances in Neural Information Processing Systems, pp. 1473–1480 (2002)

    Google Scholar 

  19. Wand, M.P., Jones, M.C.: Kernel smoothing. CRC Press (1994)

    Google Scholar 

  20. Zheng, N., Loizou, G., Jiang, X., Lan, X., Li, X.: Computer vision and pattern recognition (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, Fudan University, Shanghai, China

    Tengju Ye, Zhipeng Xie & Ang Li

Authors
  1. Tengju Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhipeng Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tengju Ye .

Editor information

Editors and Affiliations

  1. Tsinghua University, Beijing, China

    Juanzi Li

  2. Rensselaer Polytechnic Institute, Troy, NY, USA

    Heng Ji

  3. Peking University, Beijing, China

    Dongyan Zhao

  4. Peking University, Beijing, China

    Yansong Feng

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Ye, T., Xie, Z., Li, A. (2015). A Local Method for Canonical Correlation Analysis. In: Li, J., Ji, H., Zhao, D., Feng, Y. (eds) Natural Language Processing and Chinese Computing. NLPCC 2015. Lecture Notes in Computer Science(), vol 9362. Springer, Cham. https://doi.org/10.1007/978-3-319-25207-0_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25207-0_39

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25206-3

  • Online ISBN: 978-3-319-25207-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation