Alternating Direction Method of Multipliers for L 1 - and L 2 -norm Best Fitting Hyperplane Classifier

Recently, two-sided best fitting hyperplane classifier (2S-BFHC) is proposed, which has several significant advantages over previous proximal hyperplane classifiers. Moreover, Concave-Convex Procedure (CCCP) has already been provided to solve the dual problem of 2S-BFHC. In this paper, we solve the primal problem of 2S-BFHC by the alternating direction method of multipliers (ADMM) which is well suited to solve the distributed optimization problem, and we also propose a robust L 1 -norm two-sided best fitting hyperplane classifier ( L 1 -2S-BFHC) with ADMM, which aims at giving a robust performance for the problem with outliers. Priliminary numerical results demonstrate the effectiveness of proposed methods.