  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.
