A kernel approach for learning from almost orthogonal patterns

Schölkopf, B; Weston, J; Eskin , E; Leslie, C; Noble, WS

doi:10.1007/3-540-36755-1_44

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A kernel approach for learning from almost orthogonal patterns

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Schölkopf, B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Weston, J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Schölkopf, B., Weston, J., Eskin, E., Leslie, C., & Noble, W. (2002). A kernel approach for learning from almost orthogonal patterns. In T. Elomaa, H. Mannila, & H. Toivonen (Eds.), Machine Learning: ECML 2002: 13th European Conference on Machine Learning Helsinki, Finland, August 19–23, 2002 (pp. 511-528). Berlin, Germany: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-E0E3-9

Abstract

In kernel methods, all the information about the training data is contained in the Gram matrix. If this matrix has large diagonal values, which arises for many types of kernels, then kernel methods do not perform well. We propose and test several methods for dealing with this problem by reducing the dynamic range of the matrix while preserving the positive definiteness of the Hessian of the quadratic programming problem that one has to solve when training a Support Vector Machine.