Linear programming minimum sphere set covering for extreme learning machines

Authors:
Xun-Kai Wei;Ying-Hong Li
Affiliations:
School of Engineering, Air Force Engineering University, Shaanxi Province, Xian 710038, China and Beijing Aeronautical Technology Research Center, Beijing 100076, China;School of Engineering, Air Force Engineering University, Shaanxi Province, Xian 710038, China
Venue:
Neurocomputing
Year:
2008

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Abstract

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.