Learning sparse kernel classifiers in the primal

Abstract

The increasing number of classification applications in large data sets demands that efficient classifiers be designed not only in training but also for prediction. In this paper, we address the problem of learning kernel classifiers with reduced complexity and improved efficiency for prediction in comparison to those trained by standard methods. A single optimisation problem is formulated for classifier learning which optimises both classifier weights and eXpansion Vectors (XVs) that define the classification function in a joint fashion. Unlike the existing approach of Wu et al, which performs optimisation in the dual formulation, our approach solves the primal problem directly. The primal problem is much more efficient to solve, as it can be converted to the training of a linear classifier in each iteration, which scales linearly to the size of the data set and the number of expansions. This makes our primal approach highly desirable for large-scale applications, where the dual approach is inadequate and prohibitively slow due to the solution of cubic-time kernel SVM involved in each iteration. Experimental results have demonstrated the efficiency and effectiveness of the proposed primal approach for learning sparse kernel classifiers that clearly outperform the alternatives. © 2012 Springer-Verlag Berlin Heidelberg.