PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Non positive SVM
Gaëlle Loosli and Stéphane Canu
(2010) Technical Report. LIMOS.

Abstract

Recent developments with indefinite SVM have effectively demonstrated SVM classification with a non-positive kernel. However the question of efficiency still applies. In this paper, an efficient direct solver for SVM with non-positive kernel is proposed. The chosen approach is related to existing work on learning with kernel in Krein space. In this framework, it is shown that solving a learning problem is actually a problem of stabilization of the cost function instead of a minimization. We propose to restate SVM with non-positive kernels as a stabilization by using a new formulation of the KKT conditions. This new formulation provides a practical active set algorithm to solve the indefinite SVM problem. We also demonstrate empirically that the proposed algorithm outperforms other existing solvers.

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EPrint Type:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:7179
Deposited By:Gaëlle Loosli
Deposited On:08 March 2011