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Local learning projections

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Published:20 June 2007Publication History

ABSTRACT

This paper presents a Local Learning Projection (LLP) approach for linear dimensionality reduction. We first point out that the well known Principal Component Analysis (PCA) essentially seeks the projection that has the minimal global estimation error. Then we propose a dimensionality reduction algorithm that leads to the projection with the minimal local estimation error, and elucidate its advantages for classification tasks. We also indicate that LLP keeps the local information in the sense that the projection value of each point can be well estimated based on its neighbors and their projection values. Experimental results are provided to validate the effectiveness of the proposed algorithm.

References

  1. Belhumeur, P. N., Hespanha, J. P., & Kriegman, D. J. (1997). Eigenfaces vs fisherfaces: Recognition using class-specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19, 711--720. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Belkin, M., & Niyogi, P. (2002). Laplacian eigenmaps and spectral techniques for embedding and clustering. In T. G. Dietterich, S. Becker and Z. Ghahramani (Eds.), Advances in neural information processing systems 14. Cambridge, MA: MIT Press.Google ScholarGoogle Scholar
  3. Bottou, L., & Vapnik, V. (1992). Local learning algorithms. Neural Computation, 4, 888--900. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Cook, R., & Weisberg, S. (1991). Discussion of "sliced inverse regression for dimension reduction". Journal of the American Statistical Association, 86, 328--332.Google ScholarGoogle Scholar
  5. Globerson, A., & Roweis, S. (2006). Metric learning by collapsing classes. In Y. Weiss, B. Schöölkopf and J. Platt (Eds.), Advances in neural information processing systems 18. Cambridge, MA: MIT Press.Google ScholarGoogle Scholar
  6. Goldberger, J., Roweis, S., Hinton, G., & Salakhutdinov, R. (2005). Neighbourhood components analysis. In L. K. Saul, Y. Weiss and L. Bottou (Eds.), Advances in neural information processing systems 17. Cambridge, MA: MIT Press.Google ScholarGoogle Scholar
  7. He, X., & Niyogi, P. (2004). Locality preserving projections. In S. Thrun, L. Saul and B. Schöölkopf (Eds.), Advances in neural information processing systems 16. Cambridge, MA: MIT Press.Google ScholarGoogle Scholar
  8. He, X., Yan, S., Hu, Y., Niyogi, P., & Zhang, H. (2005). Face recognition using laplacianfaces. IEEE Transactions on Pattern Analysis and machine Intelligence, 27, 328--340. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Li, K.-C. (1991). Sliced inverse regression for dimension reduction. Journal of the American Statistical Association, 86, 316--327.Google ScholarGoogle ScholarCross RefCross Ref
  10. Meinicke, P., & Ritter, H. (1999). Local PCA learning with resolution-dependent mixtures of gaussians. International Conference on Artifical Neural Networks. Edinburgh, UK: MIT Press.Google ScholarGoogle ScholarCross RefCross Ref
  11. Mukherjee, S., Wu, Q., & Zhou, D.-X. (2006). Learning gradients and feature selection on manifolds. submitted to Annals of Statistics.Google ScholarGoogle Scholar
  12. Nadaraya, E. A. (1989). Nonparametric estimation of probabiliry densities and regression curves. Dordrecht: Kluwer Academic.Google ScholarGoogle Scholar
  13. Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290, 2323--2326.Google ScholarGoogle ScholarCross RefCross Ref
  14. Schölkopf, B., & Smola, A. J. (2002). Learning with kernels. Cambridge, MA: The MIT Press.Google ScholarGoogle Scholar
  15. Shawe-Taylor, J., & Cristianini, N. (2004). Kernel methods for pattern analysis. Cambridge, UK: Cambridge University Press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Sugiyama, M. (2006). Local fisher discriminant analysis for supervised dimensionality reduction. In W. Cohen and A. Moore (Eds.), Proc. 23th international conference on machine learning. ACM Press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Tipping, M. E., & Bishop, C. M. (1999). Mixtures of probabilistic principle component analysers. Neural Computation, 11, 443--482. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Wu, M., & Schöölkopf, B. (2007). A local learning approach for clustering. In B. Schölkopf, J. Platt and T. Hoffman (Eds.), Advances in neural information processing systems 19. Cambridge, MA: MIT press.Google ScholarGoogle Scholar
  19. Xia, Y., Tong, H., Li, W. K., & Zhu, L.-X. (2002). An adaptive estimation of dimension reduction space. Journal of Royal Statistical Society, 64, 363--410.Google ScholarGoogle ScholarCross RefCross Ref
  1. Local learning projections

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      cover image ACM Other conferences
      ICML '07: Proceedings of the 24th international conference on Machine learning
      June 2007
      1233 pages
      ISBN:9781595937933
      DOI:10.1145/1273496

      Copyright © 2007 ACM

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      Publication History

      • Published: 20 June 2007

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