Kernel dimensionality reduction for supervised learning

Advances in Neural Information Processing Systems

Volumn , Issue , 2004, Pages

  Fukumizu, Kenji ^a   Bach, Francis R ^b   Jordan, Michael I ^b  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SUPERVISED LEARNING;

CONDITIONAL DISTRIBUTION; CONDITIONAL INDEPENDENCES; COVARIANCE OPERATORS; DIMENSIONALITY REDUCTION; MARGINAL DISTRIBUTION; OPTIMIZATION PROBLEMS; REPRODUCING KERNEL HILBERT SPACES; STATISTICAL RELATIONSHIP;

VECTORS;

EID: 78650280736     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (12)

1. Friedman, J.H. and Stuetzle, W. Projection pursuit regression. J. Amer. Stat. Assoc., 76:817- 823, 1981.
2. Breiman, L. and Friedman, J.H. Estimating optimal transformations for multiple regression and correlation. J. Amer. Stat. Assoc., 80:580-598, 1985.
3. Wold, H. Partial least squares. in S. Kotz and N.L. Johnson (Eds.), Encyclopedia of Statistical Sciences, Vol. 6, Wiley, New York. pp.581-591. 1985.
4. Li, K.-C. Sliced inverse regression for dimension reduction (with discussion). J. Amer. Stat. Assoc., 86:316-342, 1991.
5. Li, K.-C. On principal Hessian directions for data visualization and dimension reduction: Another application of Stein's lemma. J. Amer. Stat. Assoc., 87:1025-1039, 1992.
6. Aronszajn, N. Theory of reproducing kernels. Trans. Amer. Math. Soc., 69(3):337-404, 1950.
7. Scḧolkopf, B., Burges, C.J.C., and Smola, A. (eds.) Advances in Kernel Methods: Support Vector Learning. MIT Press. 1999.
8. Scḧolkopf, B., Smola, A and M̈uller, K.-R. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10:1299-1319, 1998.
9. Bach, F.R. and Jordan, M.I. Kernel independent component analysis. JMLR, 3:1-48, 2002.
10. Baker, C.R. Joint measures and cross-covariance operators. Trans. Amer. Math. Soc., 186:273- 289, 1973.
11. Fukumizu, K., Bach, F.R. and Jordan, M.I. Dimensionality reduction for supervised learning with reproducing kernel Hilbert spaces. JMLR, 5:73-99, 2004.
12. Golub T.R. et al. Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring. Science, 286:531-537, 1999.