Sigma Tuning of Gaussian Kernels Detection of Ischemia from Magnetocardiograms

Abstract

This chapter introduces a novel Levenberg-Marquardt like second-order algorithm for tuning the Parzen window s in a Radial Basis Function (Gaussian) kernel. In this case, each attribute has its own sigma parameter associated with it. The values of the optimized s are then used as a gauge for variable selection. In this study, the Kernel Partial Least Squares (K-PLS) model is applied to several benchmark data sets in order to estimate the effectiveness of the second-order sigma tuning procedure for an RBF kernel. The variable subset selection method based on these sigma values is then compared with different feature selection procedures such as random forests and sensitivity analysis. The sigma-tuned RBF kernel model outperforms K-PLS and SVM models with a single sigma value. K-PLS models also compare favorably with Least Squares Support Vector Machines (LS-SVM), epsilon-insensitive Support Vector Regression and traditional PLS. The sigma tuning and variable selection procedure introduced in this chapter is applied to industrial magnetocardiogram data for the detection of ischemic heart disease from measurement of the magnetic field around the heart.