We propose a preliminary investigation on the benefits and limitations of classifiers based on sparse representations. We specifically focus on the union of subspaces data model and examine binary classifiers built on a sparse non linear mapping (in a redundant dictionary) followed by a linear classifier. We study two common sparse non linear mappings (namely \ell_0 and \ell_1) and show that, in both cases, there exists a finite dictionary such that the classifier discriminates the two classes correctly. This result paves the way towards a better understanding of the increasingly popular classifiers based on sparse representation
David Atienza Alonso, Adriana Arza Valdes, Fabio Isidoro Tiberio Dell'Agnola, Niloofar Momeni
Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Anna You-Lai Song