An integrated chaotic time series prediction model based on efficient extreme learning machine and differential evolution

In this paper, an integrated model based on efficient extreme learning machine (EELM) and differential evolution (DE) is proposed to predict chaotic time series. In the proposed model, a novel learning algorithm called EELM is presented and used to model the chaotic time series. The EELM inherits the basic idea of extreme learning machine (ELM) in training single hidden layer feedforward networks, but replaces the commonly used singular value decomposition with a reduced complete orthogonal decomposition to calculate the output weights, which can achieve a much faster learning speed than ELM. Moreover, in order to obtain a more accurate and more stable prediction performance for chaotic time series prediction, this model abandons the traditional two-stage modeling approach and adopts an integrated parameter selection strategy which employs a modified DE algorithm to optimize the phase space reconstruction parameters of chaotic time series and the model parameter of EELM simultaneously based on a hybrid validation criterion. Experimental results show that the proposed integrated prediction model can not only provide stable prediction performances with high efficiency but also achieve much more accurate prediction results than its counterparts for chaotic time series prediction.