An improved incremental constructive single-hidden-layer feedforward networks for extreme learning machine based on particle swarm optimization

How to determine the network structure is an open problem in extreme learning machine (ELM). Error minimized extreme learning machine (EM-ELM) is a simple and efficient approach to determine the number of hidden nodes. However, similar to other constructive ELM, EM-ELM lays much emphasis on the convergence accuracy, which may obtain a single-hidden-layer feedforward neural networks (SLFN) with good convergence performance but bad condition. In this paper, an effective approach based on error minimized ELM and particle swarm optimization (PSO) is proposed to adaptively determine the structure of SLFN for regression problem. In the new method, to establish a compact and well-conditioning SLFN, the hidden node optimized by PSO is added to the SLFN one by one. Moreover, not only the regression accuracy but also the condition value of the hidden output matrix of the network is considered in the optimization process. Experiment results on various regression problems verify that the proposed algorithm achieves better generalization performance with fewer hidden nodes than other constructive ELM.