Support Vector Method for Function Approximation, Regression Estimation and Signal Processing

Abstract

The Support Vector (SV) method was recently proposed for estimating regressions, constructing multidimensional splines, and solving linear operator equations [Vapnik, 1995]. In this presentation we report results of applying the SV method to these problems. 1 Introduction The Support Vector method is a universal tool for solving multidimensional function estimation problems. Initially it was designed to solve pattern recognition problems, where in order to find a decision rule with good generalization ability one selects some (small) subset of the training data, called the Support Vectors (SVs). Optimal separation of the SVs is equivalent to optimal separation the entire data. This led to a new method of representing decision functions where the decision functions are a linear expansion on a basis whose elements are nonlinear functions parameterized by the SVs (we need one SV for each element of the basis). This type of function representation is especially useful for high dimensional...