The Doubly Regularized SVM (DrSVM) is an extension of SVM using a mixture of L_2 and L_1 norm penalties. This kind of penalty, sometimes referred as the elastic net, allows to perform variable selection while taking into account correlations between variables. Introduced by Wang, an efficient algorithm to compute the whole DrSVM solution path has been proposed. Unfortunately, in some cases, this path is discontinuous, and thus not piecewise linear. To solve this problem, we propose here a new sub gradient formulation of the DrSVM problem. This led us to propose an alternative L_1 regularization path algorithm. This reformulation efficiently addresses the aforementioned problem and makes the initialization step more generic. The results show the validity of our sub-gradient formulation and the efficiency compared to the initial formulation.
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