Modified Frank-Wolfe Algorithm for Enhanced Sparsity in Support Vector Machine Classifiers

TL;DR

This paper introduces a modified Frank-Wolfe algorithm for training a re-weighted L2 SVM that automatically adapts weights during training, resulting in sparser, more stable models with fewer support vectors and reduced computational cost.

Contribution

It proposes a novel weighted SVM model with adaptive binary weights and a variation of the Frank-Wolfe algorithm, improving sparsity and stability over traditional methods.

Findings

Fewer iterations needed for convergence

Produces models with sparser support vector sets

Models are more stable with respect to hyper-parameter selection

Abstract

This work proposes a new algorithm for training a re-weighted L2 Support Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Cand\`es et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In particular, the margin required for each training vector is set independently, defining a new weighted SVM model. These weights are selected to be binary, and they are automatically adapted during the training of the model, resulting in a variation of the Frank-Wolfe optimization algorithm with essentially the same computational complexity as the original algorithm. As shown experimentally, this algorithm is computationally cheaper to apply since it requires less iterations to converge, and it produces models with a sparser representation in terms of support vectors and which are more stable with respect to the selection of the regularization hyper-parameter.