Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 520635, 11 pages
http://dx.doi.org/10.1155/2013/520635
Research Article

A Faster Gradient Ascent Learning Algorithm for Nonlinear SVM

1Department of Informatics and Cybernetics, Bucharest University of Economic Studies, Dorobanţi 15-17, 010552 Bucharest, Romania
2Department of Mathematics and Informatics, University of Pitesti, Târgu din Vale No. 1, 110040 Pitesti, Romania
3Department of Informatics, Ionian University, Palaia Anaktora 49100 Corfu, Greece

Received 27 May 2013; Accepted 19 July 2013

Academic Editors: S. He and L. Wu

Copyright © 2013 Catalina-Lucia Cocianu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a refined gradient ascent method including heuristic parameters for solving the dual problem of nonlinear SVM. Aiming to get better tuning to the particular training sequence, the proposed refinement consists of the use of heuristically established weights in correcting the search direction at each step of the learning algorithm that evolves in the feature space. We propose three variants for computing the correcting weights, their effectiveness being analyzed on experimental basis in the final part of the paper. The tests pointed out good convergence properties, and moreover, the proposed modified variants proved higher convergence rates as compared to Platt’s SMO algorithm. The experimental analysis aimed to derive conclusions on the recognition rate as well as on the generalization capacities. The learning phase of the SVM involved linearly separable samples randomly generated from Gaussian repartitions and the WINE and WDBC datasets. The generalization capacities in case of artificial data were evaluated by several tests performed on new linearly/nonlinearly separable data coming from the same classes. The tests pointed out high recognition rates (about 97%) on artificial datasets and even higher recognition rates in case of the WDBC dataset.