Facilitating the application of Support Vector Regression by using a universal Pearson VII function based kernel

In the last few years, application of Support Vector Machines (SVMs) for solving classification and regression problems has increased, in particular, due to its high generalization performance and its ability to model non-linear relationships. The latter can only be realised if a suitable kernel function is applied. This kernel function transforms the non-linear input space into a high dimensional feature space in which the solution of the problem can be represented as being a straight linear classification or regression problem. However, there are a lot of possible kernel functions that can be used to create such high dimensional feature space. The most commonly used kernel functions are the linear and polynomial inner-product functions and the Radial Basis Function (RBF). Since the nature of the data is usually unknown, it is very difficult to make, on beforehand, a proper choice out of the mentioned kernels. 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 universal kernel function based on the Pearson VII function (PUK) is introduced in this paper. This function is well-known in the field of spectroscopy. The applicability, suitability, performance and robustness of this alternative kernel in comparison to the commonly applied kernels is investigated by applying this to simulated as well as real-world data sets. From the outcome of these examinations, it was concluded that the PUK kernel is robust and has an equal or even stronger mapping power as compared to the standard kernel functions leading to an equal or better generalization performance of SVMs. In general, PUK can be used as a universal kernel that is capable to serve as a generic alternative to the common linear, polynomial and RBF kernel functions. (c) 2005 Elsevier B.V. All rights reserved.