An improved evolutionary extreme learning machine based on particle swarm optimization

Recently Extreme Learning Machine (ELM) for single-hidden-layer feedforward neural networks (SLFN) has been attracting attentions for its faster learning speed and better generalization performance than those of traditional gradient-based learning algorithms. However, ELM may need high number of hidden neurons and lead to ill-condition problem due to the random determination of the input weights and hidden biases. In this paper, a hybrid learning algorithm is proposed to overcome the drawbacks of ELM, which uses an improved particle swarm optimization (PSO) algorithm to select the input weights and hidden biases and Moore–Penrose (MP) generalized inverse to analytically determine the output weights. In order to obtain optimal SLFN, the improved PSO optimizes the input weights and hidden biases according to not only the root mean squared error (RMSE) on validation set but also the norm of the output weights. The proposed algorithm has better generalization performance than traditional ELM and other evolutionary ELMs, and the conditioning of the SLFN trained by the proposed algorithm is also improved. Experiment results have verified the efficiency and effectiveness of the proposed method.