Elastic-net constrained multiple kernel learning using a majorization-minimization approach

This papers introduces an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights. While efficient algorithms exist for MKL problems with L₁- and L_p-norm (p > 1) constraints, a similar algorithm was lacking in the case of MKL under elastic-net constraints. For example, algorithms based on the cutting plane method require large and/or commercial libraries. The algorithm presented here can solve elastic-net constrained MKL problems very efficiently with simple code that does not rely on external libraries (except a conventional SVM solver). Based on majorization-minimization (MM), at each step it optimizes the kernel weights by minimizing a carefully designed surrogate function, called a majorizer, which can be solved in closed form. This improved efficiency and applicability facilitates the inclusion of elastic-net constrained MKL in existing open-source machine learning libraries.