A kernel view of the dimensionality reduction of manifolds

Proceedings, Twenty-First International Conference on Machine Learning, ICML 2004

Volumn , Issue , 2004, Pages 369-376

  Ham, Jihun ^a   Lee, Daniel D ^a   Mika, Sebastian ^b   Schölkopf, Bernhard ^c  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b FRAUNHOFER FIRST   (Germany)

^c MAX PLANCK INSTITUTE FOR BIOLOGICAL CYBERNETICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DATA ACQUISITION; EIGENVALUES AND EIGENFUNCTIONS; LAPLACE TRANSFORMS; LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; PROBLEM SOLVING; SET THEORY;

GRAM MATRICES; GRAPH LAPLACIAN EIGENMAPS; ISOMAP; LOCALLY LINEAR EMBEDDING (LLE);

GRAPH THEORY;

EID: 11144299132     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (14)

1. Aldous, D., & Fill, J. (2002). Reversible Markov chains and random walks on graphs. In preparation.
2. Belkin, M., & Niyogi, P. (2003). Laplcian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15, 1373-1396.
3. Bengio, Y., Paiement, J.-F., & Vincent, P. (2004). Out-of-sample extension for lle, isomap, mds, eigenmaps, and spectral clustering. Advances in Neural Information Processing Systems 15. MIT Press.
4. Chung, F., & Yau, S. (2000). Discrete green's function. Journal of Combinatorical Theory (A), 91, 191-214.
5. Cox, T., & Cox, M. (1994). Multidimensional scaling. London: Chapman and Hall.
6. de Silva, V., & Tenenbaum, J. (2002). Global versus local methods in nonlinear dimensionality reduction. Advances in Neural Information Processing Systems, 15.
7. Grimes, C., & Donoho, D. (2002). When does isomap recover the natural parameterization of families of articulated images? (Technical Report 27). Stanford University.
8. Kondor, I., & Lafferty, J. (2002). Diffusion kernels on graphs and other discrete structures. Proceedings of ICML'2002.
9. Roweis, S., & Saul, L. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290, 2323-2326.
10. Schölkopf, B., Smola, A., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10, 1299-1319.
11. Schölkopf, B., & Smola, A. J. (2002). Learning with kernels. Cambridge, MA: MIT Press.
12. Tenenbaum, J., de Silva, V., & Langford, J. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290, 2319-2323.
13. Weiss, Y. (1999). Segmentation using eigenvectors: a unifying view. IEEE Proceedings of ICCV(pp. 975-982).
14. Williams, C. K. I. (2001). On a connection between kernel PCA and metric multidimensional scaling. Advances in Neural Information Processing Systems 13. MIT Press.