Linear programming minimum sphere set covering for extreme learning machines

A novel optimum extreme learning machines (ELM) construction method was proposed. We define an extended covering matrix with smooth function, relax the objective and constraints to formulate a more general linear programming method for the minimum sphere set covering problem. We call this method linear programming minimum sphere set covering (LPMSSC). We also present a corresponding kernelized LPMSSC and extended LPMSSC with non-Euclidean L1 and L-infinity metric. We then propose to apply the LPMSSC method to ELM and propose a data dependent ELM (DDELM) algorithm. We can obtain compact ELM for pattern classification via LPMSSC. We investigate the performances of the proposed method through UCI benchmark data sets.