Time Series Modeling with Fuzzy Cognitive Maps: Simplification Strategies

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 graph-based 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 $\frac{1}{3}$ of nodes and up to $\frac{1}{6}$ of weights for real-world time series. For regular data sets, like the synthetic time series, FCM-based models can be simplified even more.
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Khalid Saeed; Václav Snášel. 13th IFIP International Conference on Computer Information Systems and Industrial Management (CISIM), Nov 2014, Ho Chi Minh City, Vietnam. Springer, Lecture Notes in Computer Science, LNCS-8838, pp.409-420, 2014, Computer Information Systems and Industrial Management. 〈10.1007/978-3-662-45237-0_38〉
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Wladyslaw Homenda, Agnieszka Jastrzebska, Witold Pedrycz. Time Series Modeling with Fuzzy Cognitive Maps: Simplification Strategies. Khalid Saeed; Václav Snášel. 13th IFIP International Conference on Computer Information Systems and Industrial Management (CISIM), Nov 2014, Ho Chi Minh City, Vietnam. Springer, Lecture Notes in Computer Science, LNCS-8838, pp.409-420, 2014, Computer Information Systems and Industrial Management. 〈10.1007/978-3-662-45237-0_38〉. 〈hal-01405614〉

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