A majorization-minimization approach to Lq norm multiple kernel learning

Multiple kernel learning (MKL) usually searches for linear (nonlinear) combinations of predefined kernels by optimizing some performance measures. However, previous MKL algorithms cannot deal with Lq norm MKL if q<1 due to the non-convexity of Lq (q<1) norm. In order to address this problem, we apply a majorization-minimization approach to solve Lq norm MKL in this paper. It is noted that the proposed method only involves solving a series of support vector machine problems, which makes the proposed method simple and effective. We also theoretically demonstrate that the limit points of the sequence generated from our iterative scheme are stationary points of the optimization problem under proper conditions. Experiments on synthetic data and some benchmark data sets, and gene data sets are carried out to show the effectiveness of the proposed method.