On implicit Lagrangian twin support vector regression by Newton method

Abstract

In this work, an implicit Lagrangian for the dual twin support vector regression is proposed. Our formulation leads to determining non-parallel ε –insensitive down- and up- bound functions for the unknown regressor by constructing two unconstrained quadratic programming problems of smaller size, instead of a single large one as in the standard support vector regression (SVR). The two related support vector machine type problems are solved using Newton method. Numerical experiments were performed on a number of interesting synthetic and real-world benchmark datasets and their results were compared with SVR and twin SVR. Similar or better generalization performance of the proposed method clearly illustrates its effectiveness and applicability.

Keywords:

• Implicit Lagrangian support vector machines
• Non parallel planes
• Support vector regression
• Twin support vector regression