Variable Sparse Multiple Kernels Learning for Novelty Detection

Abstract

Novelty detection from multiple information sources is an important problem and selecting appropriate features is a crucial step for solving this problem. In this paper, we propose a novel data domain description algorithm which is inspired by multiple kernel learning and elastic-net-type constrain on the kernel weight. Most Multiple kernel learning algorithms employ the 1-norm constraints on the kernel combination weights, which enforce a sparsity solution but maybe lose useful information. In contrast, imposing the p-norm(p>1) constraint on the kernel weights will keep all the information in the base kernels, which lead to non-sparse solutions and brings the risk of being sensitive to noise and incorporating redundant information. To address this problem, we introduce an elastic-net-type constrain on the kernel weights. It finds the best trade-off between sparsity and accuracy. Furthermore, our algorithm facilitates the grouping effect. The proposed algorithm can be equivalently formalized as a convex-concave problem that can be effectively resolved with level method. Experimental results show that the proposed algorithm converges rapidly and demonstrate its efficiency comparing to other data description algorithms.