Majorization-Minimization for sparse SVMs

TL;DR

This paper introduces a majorization-minimization approach for training sparse SVMs with a smooth regularized loss, enabling efficient feature selection and improved classification performance.

Contribution

It proposes a novel MM-based method for sparse SVM training that leverages Lipschitz differentiability for faster optimization and feature selection.

Findings

Effective in improving classification metrics

Reduces computational cost compared to existing methods

Successfully promotes sparsity in feature selection

Abstract

Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular approaches in the machine learning arena. In this work, we investigate the training of SVMs through a smooth sparse-promoting-regularized squared hinge loss minimization. This choice paves the way to the application of quick training methods built on majorization-minimization approaches, benefiting from the Lipschitz differentiabililty of the loss function. Moreover, the proposed approach allows us to handle sparsity-preserving regularizers promoting the selection of the most significant features, so enhancing the performance. Numerical tests and comparisons conducted on three different datasets demonstrate the good performance of the proposed methodology in terms of qualitative metrics (accuracy, precision, recall, and F 1 score) as well as computational cost.