A simple yet efficient algorithm for multiple kernel learning under elastic-net constraints

This report presents an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights. Please see Sun et al. (2013) and Yang et al. (2011) for a review on multiple kernel learning and its extensions. In particular Yang et al. (2011) introduced the generalized multiple kernel learning (GMKL) model where the kernel weights are subject to elastic-net constraints. While Xu et al. (2010) presents an elegant algorithm to solve MKL problems with L1norm and Lp-norm (p ≥ 1) constraints, a similar algorithm is lacking in the case of MKL under elastic-net constraints. In fact, the algorithm that Yang et al. (2011) propose for the solution of their GMKL model is implemented as an extensive piece of code that depends on large and possibly commercial libraries (e.g. MOSEK). The algorithm presented in this report provides an extremely simple and efficient solution to the elastic-net constrained MKL (GMKL) problem. Because it can be implemented in few lines of code and does not depend on external libraries (except a conventional L2norm SVM solver), it has a wider applicability and can be readily included in existing open-source machine learning libraries.