Learning high-order fuzzy cognitive maps via multimodal artificial bee colony algorithm and nearest-better clustering: Applications on multivariate time series prediction

As an effective soft computing method, fuzzy cognitive maps (FCMs) have been successfully utilized to process time series prediction problems. However, FCM-based time series prediction models face some challenges including the complicated spatial–temporal dependencies, the complex causal relations among different variables, the low convergence speed, the immersing local minimization, and the non-convex optimization problems. To address these challenges, we propose a multivariate time series prediction model combining niching-based artificial bee colony algorithm and high-order fuzzy cognitive maps (HFCMs), termed NABC-HFCM. Firstly, the learning of the HFCM is divided into multiple multimodal optimization problems (MMOPs). Secondly, a complete mathematical frame via multimodal artificial bee colony algorithm and nearest-better clustering is established to solve all decomposed MMOPs. Finally, the learned HFCM can be employed to predict the time series evolution trend. Experimental results on eight multi-variate datasets have demonstrated better prediction and generalization performance of NABC-HFCM by comparison with several representative baseline algorithms as a whole.