Simple and Efficient Multiple Kernel Learning by Group Lasso 论文

摘要

We consider the problem of how to improve the efficiency of Multiple Kernel Learning (MKL). In literature, MKL is often solved by an alternating approach: (1) the minimization of the kernel weights is solved by compli-cated techniques, such as Semi-infinite Lin-ear Programming, Gradient Descent, or Level method; (2) the maximization of SVM dual variables can be solved by standard SVM solvers. However, the minimization step in these methods is usually dependent on its solving techniques or commercial softwares, which therefore limits the efficiency and ap-plicability. In this paper, we formulate a closed-form solution for optimizing the ker-nel weights based on the equivalence between group-lasso and MKL. Although this equiva-lence is not our invention, our derived variant equivalence not only leads to an efficient algo-rithm for MKL, but also generalizes to the case for Lp-MKL (p ≥ 1 and denoting the Lp-norm of kernel weights). Therefore, our proposed al-gorithm provides a unified solution for the en-tire family of Lp-MKL models. Experiments on multiple data sets show the promising per-formance of the proposed technique compared with other competitive methods. 1.