Extended Evolutionary Learning of Fuzzy Cognitive Maps for the Prediction of Multivariate Time-Series
Fuzzy cognitive maps (FCMs) is a knowledge representation tool that can be exploited for predicting multivariate time-series. FCM model represents dependencies among data variables as a directed, weighted graph of fuzzy sets (concepts). This way, FCM can
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Extended Evolutionary Learning of Fuzzy Cognitive Maps for the Prediction of Multivariate Time-Series Wojciech Froelich and Elpiniki I. Papageorgiou
Abstract Fuzzy cognitive maps (FCMs) is a knowledge representation tool that can be exploited for predicting multivariate time-series. FCM model represents dependencies among data variables as a directed, weighted graph of fuzzy sets (concepts). This way, FCM can be easily interpreted or constructed by experts in contrary to black box knowledge representation methods. Since FCM is a parametric model, it can be trained using historical data. So far, the genetic algorithm has been used to solely optimize the weights of FCM leaving the rest of FCM parameters to be adjusted by experts. Previous studies have shown that the genetic algorithm can be also used not only for optimizing the weights but also for optimization of FCM transformation functions. The main idea presented in this chapter is to further extend FCM evolutionary learning process. Special focus is given on fuzzyfication and transformation function optimization, applied in each concept seperately, in order to improve the efficacy of time-series prediction. The proposed extended evolutionary optimization process was evaluated in a number of real medical data gathered from the internal care unit (ICU). Comparing this approach with other known genetic-based learning algorithms, less prediction errors were observed for this dataset.
Electronic supplementary material The online version of this article (doi: 10.1007/978-3642-39739-4_7) contains supplementary material, which is available to authorized users. W. Froelich (B) Institute of Computer Science, University of Silesia, ul.Bedzinska 39, Sosnowiec, Poland e-mail: [email protected] E. I. Papageorgiou Department of Computer Engineering, Technological Educational Institute of Central Greece, 3rd Km Old National Road Lamia-Athens, 35100 Lamia, Greece e-mail: [email protected] E. I. Papageorgiou (ed.), Fuzzy Cognitive Maps for Applied Sciences and Engineering, Intelligent Systems Reference Library 54, DOI: 10.1007/978-3-642-39739-4_7, © Springer-Verlag Berlin Heidelberg 2014
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W. Froelich and E. I. Papageorgiou
1 Introduction The prediction of multivariate time-series is an important issue that emerges in numerous application domains. Many diverse models have been developed for prediction task, e.g. multivariate autoregressive models, artificial neural networks, dynamic Bayesian networks, rule-based fuzzy systems and some others. An alternative prediction model [19, 23] that recently attracted the interest of researchers is fuzzy cognitive maps. FCMs have been proposed as a tool for modeling causal relationships that occur among real-world factors. Similarly as most of other predictive models, FCMs can be constructed by domain experts. Numerous approaches of FCMs that refer to multivariate time-series prediction have been applied in several domains such as medicine [3, 11, 16], geographic information systems [10], economics [7], agricultu
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