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Dealing with large Diagonals in Kernel Matrices

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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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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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Citation

Weston, J., Schölkopf, B., Eskin, E., leslie, C., & Noble, W. (2003). Dealing with large Diagonals in Kernel Matrices. Annals of the Institute of Statistical Mathematics, 55(2), 391-408. doi:10.1007/BF02530507.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-DC41-0
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, which is a common kernel approach for pattern recognition.