Support Vector Machine Based on Universal Kernel Function and Its Application in Quantitative Structure - Toxicity Relationship Model

Abstract

Comparing with traditional statistical modeling methods, support vector machine (SVM) has much advantage for solving regression and classification problems. For nonlinear regression, the kernel function of SVM transforms the nonlinear input space into a high dimensional feature space in which the solution of the problem can be represented as being a linear regression problem. Therefore, in all probability the performance of SVM models is decided by the kernel function, and choosing a proper kernel function is very important. Whereas the nature of the data is usually unknown, it is very difficult to make, on beforehand, a proper choice out of the possible kernel functions. For this reason, during the model building process, usually more than one kernel is applied to select the one which gives the best prediction performance. Unfortunately, this will lead to a very time-consuming optimization procedure. To circumvent this disadvantage, a novel universal kernel function based on the Pearson VII function (PUKF) is introduced in this paper. PUKF can replace the common kernel functions, and simplifies the training process of SVM nonlinear regression. SVM based on PUKF was applied to model the Quantitative Structure-Toxicity Relationship (QSTR) to investigate its potential in nonlinear regression. As a case, the QSTR of the toxicity of a heterogeneous set of compounds to Vibrio fischeri was researched, the results showed the excellent generalization performance and robustness of the SVM based on PUKF.