Alternating Direction Multiplier Method for Matrix l2,1-Norm Optimization in Multitask Feature Learning Problems

Abstract

The joint feature selection problem can be resolved by solving a matrix l2,1-norm minimization problem. For l2,1-norm regularization, one of the most fascinating features is that some similar sparsity structures can be employed by multiple predictors. However, the nonsmooth nature of the problem brings great challenges to the problem. In this paper, an alternating direction multiplier method combined with the spectral gradient method is proposed for solving the matrix l2,1-norm optimization problem involved with multitask feature learning. Numerical experiments show the effectiveness of the proposed algorithm.