Time series modeling with fuzzy cognitive maps: simplification strategies the case of a posteriori removal of nodes and weights

Abstract

The article is focused on the issue of complexity of Fuzzy Cognitive Maps designed to model time series. Large Fuzzy Cognitive Maps are impractical to use. Since Fuzzy Cognitive Maps are graphbased models, when we increase the number of nodes, the number of connections grows quadratically. Therefore, we posed a question how to simplify trained FCM without substantial loss in map’s quality. We proposed evaluation of nodes’ and weights’ relevance based on their influence in the map. The article presents the method first on synthetic time series of different complexity, next on several real-world time series. We illustrate how simplification procedure influences MSE. It turned out that with just a small increase of MSE we can remove up to ⅓ of nodes and up to ⅙ of weights for real-world time series. For regular data sets, like the synthetic time series, FCM-based models can be simplified even more.