Stochastic approximation algorithms for support vector machines semi-supervised binary classification

Abstract

In this paper,we consider the problem of semi-supervisedbinary classificationby Support Vector Machines (SVM). This problem is explored as an unconstrained and non-smooth optimization task when part of the available data is unlabelled. We apply non-smooth optimization techniques to classification problems where the objective function considered is non-convex and non-differentiable and so difficult to minimize. We explore and compare the properties of Stochastic Approximation algorithms (Simultaneous Perturbation Stochastic Approximation (SPSA) with the Lipschitz Perturbation Operator, SPSA with the Uniform Perturbation Operator, and Standard Finite Difference Approximation) for semi-supervised SVM classification. We present some numerical results obtained by running the proposed methods on several standard test problems drawn from the binary classification literature.

Keywords

• support vector machine
• semi-supervised classification
• stochastic approximation