Opening the kernel of kernel partial least squares and support vector machines

Kernel partial least squares (KPLS) and support vector regression (SVR) have become popular techniques for regression of complex non-linear data sets. The modeling is performed by mapping the data in a higher dimensional feature space through the kernel transformation. The disadvantage of such a transformation is, however, that information about the contribution of the original variables in the regression is lost. In this paper we introduce a method which can retrieve and visualize the contribution of the variables to the regression model and the way the variables contribute to the regression of complex data sets. The method is based on the visualization of trajectories using so-called pseudo samples representing the original variables in the data. We test and illustrate the proposed method to several synthetic and real benchmark data sets. The results show that for linear and non-linear regression models the important variables were identified with corresponding linear or non-linear trajectories. The results were verified by comparing with ordinary PLS regression and by selecting those variables which were indicated as important and rebuilding a model with only those variables.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► We provide a solution to visualize the contribution of variables to kernel based regression methods. ► This variable information is lost in methods like KPLS and support vector regression due to the kernel. ► The influence and non-linearity of the variables are visualized using so-called pseudo sample trajectories. ► We have tested the method on several artificial and real linear and non-linear data sets. ► Our method clearly indicates the important variables.