Newton's method for nonparallel plane proximal classifier with unity norm hyperplanes

In our previous research we observed that the nonparallel plane proximal classifier (NPPC) obtained by minimizing two related regularized quadratic optimization problems performs equally with that of other support vector machine classifiers but with a very lower computational cost. NPPC classifies binary patterns by the proximity of it to one of the two nonparallel hyperplanes. Thus to calculate the distance of a pattern from any hyperplane we need the Euclidean norm of the normal vector of the hyperplane. Alternatively, this should be equal to unity. But in the formulation of NPPC these equality constraints were not considered. Without these constraints the solutions of the objective functions do not guarantee to satisfy the constraints. In this work we have reformulated NPPC by considering those equality constraints and solved it by Newton's method and the solution is updated by solving a system of linear equations by conjugate gradient method. The performance of the reformulated NPPC is verified experimentally on several bench mark and synthetic data sets for both linear and nonlinear classifiers. Apart from the technical improvement of adding those constraints in the NPPC formulation, the results indicate enhanced computational efficiency of nonlinear NPPC on large data sets with the proposed, NPPC framework. (C) 2009 Elsevier B.V. All rights reserved.