Multi-output time series forecasting with randomized multivariate Fuzzy Cognitive Maps

• Published in: Chaos, solitons and fractals solitons and fractals, 2023-11, Vol.176, p.114077, Article 114077
• Main Authors: Orang, Omid, de Lima e Silva, Petrônio Cândido, Guimarães, Frederico Gadelha
• Format: Article
• Language: English
• Subjects: Echo state network; Fuzzy Cognitive Maps; Least squares; Multiple-input multiple-output; Multivariate fuzzy time series
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2023.114077

Fuzzy Cognitive Maps (FCMs) have become a relevant technique for modeling and forecasting time series due to their advantages in dealing with uncertainty and simulating the dynamics of complex systems. Although numerous univariate and multivariate FCM-based forecasting models have been presented in the literature, one of the still open questions is how to enable FCMs to forecast multivariate time series for multiple-input, multiple-output (MIMO) systems with an efficient learning mechanism. from a computational point of view. This paper suggests a randomized MIMO FCM-based forecasting approach called MO-RHFCM to predict low-dimensional multivariate time series. More specifically, MO-RHFCM is a hybrid model merging the concepts of multivariate fuzzy time series, high order FCM (HFCM), and Echo State Networks (ESN). The structure of MO-RHFCM consists of three layers: input layer, reservoir (internal) layer, and output layer. Only the output layer is trainable using the Least Squares minimization algorithm; hence training the proposed MO-RHFCM method is fast and simple. The weights inside each sub-reservoir are selected randomly and remain fixed during the training process. The obtained results indicate the efficacy and validity of the proposed MO-RHFCM technique compared with some machine learning and deep learning baseline models. •Introducing a new randomized multivariate FCM model as a reservoir computing.•The first introduction of FCM-based forecasting method for multiple outputs systems.•The superior performance of the proposed model in comparison to other baselines.•Less complexity of our proposed model compared to baseline deep learning models.