Simple estimate of the width in Gaussian kernel with adaptive scaling technique

This paper presents a simple estimate to determine the width of Gaussian kernel with the adaptive scaling technique. The Gaussian kernel is widely employed in Radial Basis Function (RBF) network, Support Vector Machine (SVM), Least Squares Support Vector Machine (LS-SVM), Kriging, and so on. It is widely known that the width of the Gaussian kernel in these machine learning techniques plays an important role. Determination of the optimal width in the Gaussian kernel is the time-consuming task. Therefore, it is preferable to determine the width in Gaussian kernel with a simple manner. In this paper, we first examine a simple estimate of the width in the Gaussian kernel proposed by Nakayama et al.. Through the examination, four sufficient conditions for the simple estimate of the width are described. Then, a new simple estimate for the width in the Gaussian kernel is proposed. In order to obtain the proposed estimate of the width, all decision variables are scaled equally. A simple technique called the adaptive scaling technique is also developed. It is expected that the proposed simple estimate of the width is applicable to wide range of machine learning techniques employing the Gaussian kernel. Through examples, the validity of the proposed simple estimate of the width is examined.