Unified estimate of Gaussian kernel width for surrogate models

Abstract

This paper presents a novel approach for estimating the Gaussian kernel width widely employed in radial basis function (RBF) network, support vector machine (SVM), Kriging models, etc. As widely known, the Gaussian kernel width in these surrogate models is highly significant, and estimating the appropriate applicable width is usually an arduous task. Therefore, the need to develop a simple method to determine the kernel width becomes imperative. In this study, firstly, we examine the fundamental description of triple surrogate models, based on which a unified formulation to describe surrogate models is proposed. Thereafter, a novel unified estimate procedure based on local density of sampling points is developed. During this procedure, the calculations of numerous kernel widths are transformed into the calculation of a singular parameter, which is solved with the method of moment estimate. The proposed estimate is applicable to the wide range of surrogate models employing the Gaussian kernel. Validation of the novel method is carried out through examples in various domains, which showcases the efficacy of this proposed method.