Linear Programming Regressive Support Vector Machine

Abstract

Based on the analysis of the general norm in structure risk to control model complexity for regressive problem, two kinds of linear programming support vector machine corresponding to l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> -norm are presented including linear and nonlinear SVMs. A numerical experiment has been done for these two kinds of linear programming support vector machines and classic support vector machine by artificial data. Simulation results show that the generalization performance of this two kind linear programming SVM is similar to classic one, l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -SVM has less number of support vectors and faster learning speed, and learning result is not sensitive to learning parameters