Multi-dimensional Function Approximation and Regression Estimation

Fernando Pérez-Cruz, Gustavo Camps-Valls, Emilio Soria-Olivas, Juan José Pérez-Ruixo, Aníbal R. Figueiras-Vidal, Antonio Artés-Rodríguez

Abstract: In this communication, we generalize the Support Vector Machines (SVM) for regression estimation and function approximation to multi-dimensional problems. We propose a multi-dimensional Support Vector Regressor (MSVR) that uses a cost function with a hyperspherical insensitive zone, capable of obtaining better predictions than using an SVM independently for each dimension. The resolution of the MSVR is achieved by an iterative procedure over the Karush-Kuhn-Tucker conditions. The proposed algorithm is illustrated by computers experiments.