Support Vector Regression Using Mahalanobis Kernels

This paper determines the covariance matrix for the Mahalanobis kernel using all the training data and estimation performance is comparable to or better than that of an RBF kernel optimized by grid search.

Abstract

In our previous work we have shown that Mahalanobis kernels are useful for support vector classifiers both from generalization ability and model selection speed. In this paper we propose using Mahalanobis kernels for function approximation. We determine the covariance matrix for the Mahalanobis kernel using all the training data. Model selection is done by line search. Namely, first the margin parameter and the error threshold are optimized and then the kernel parameter is optimized. According to the computer experiments for four benchmark problems, estimation performance of a Mahalanobis kernel with a diagonal covariance matrix optimized by line search is comparable to or better than that of an RBF kernel optimized by grid search.