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.