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arXiv · 1501.03669

A Proximal Approach for Sparse Multiclass SVM

G. Chierchia·Nelly Pustelnik·Jean-Christophe Pesquet·B. Pesquet-Popescu
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Abstract

Sparsity-inducing penalties are useful tools to design multiclass support vector machines (SVMs). In this paper, we propose a convex optimization approach for efficiently and exactly solving the multiclass SVM learning problem involving a sparse regularization and the multiclass hinge loss formulated by Crammer and Singer. We provide two algorithms: the first one dealing with the hinge loss as a penalty term, and the other one addressing the case when the hinge loss is enforced through a constraint. The related convex optimization problems can be efficiently solved thanks to the flexibility offered by recent primal-dual proximal algorithms and epigraphical splitting techniques. Experiments carried out on several datasets demonstrate the interest of considering the exact expression of the hinge loss rather than a smooth approximation. The efficiency of the proposed algorithms w.r.t. several state-of-the-art methods is also assessed through comparisons of execution times.

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G. Chierchia, Nelly Pustelnik, Jean-Christophe Pesquet, B. Pesquet-Popescu. 2015-12-14. A Proximal Approach for Sparse Multiclass SVM. https://arxiv.org/abs/1501.03669

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