Research articles

Approximation of kernel matrices by circulant matrices and its application in kernel selection methods

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  • 1.Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA; 2.Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA;School of Mathematics and Computational Sciences, Sun Yat-sen University, Guangzhou 510275, China; 3.2010-03-15 9:33:37;

Published date: 05 Mar 2010

Abstract

This paper focuses on developing fast numerical algorithms for selection of a kernel optimal for a given training data set. The optimal kernel is obtained by minimizing a cost functional over a prescribed set of kernels. The cost functional is defined in terms of a positive semi-definite matrix determined completely by a given kernel and the given sampled input data. Fast computational algorithms are developed by approximating the positive semi-definite matrix by a related circulant matrix so that the fast Fourier transform can apply to achieve a linear or quasi-linear computational complexity for finding the optimal kernel. We establish convergence of the approximation method. Numerical examples are presented to demonstrate the approximation accuracy and computational efficiency of the proposed methods.

Cite this article

Guohui SONG, Yuesheng XU . Approximation of kernel matrices by circulant matrices and its application in kernel selection methods[J]. Frontiers of Mathematics in China, 2010 , 5(1) : 123 -160 . DOI: 10.1007/s11464-009-0054-0

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