Abstract
In this paper we introduce a class of granular evolving system modeling approach within the framework of interval analysis. Our aim is to present an interval-based learning algorithm which develops both, granular and singular approximations of nonlinear nonstationary functions using singular data. The algorithm is capable of incrementally creating/adapting both model parameters and structure. These are key features in nonlinear systems modeling. In addition, interval analysis provides rigorous bounds on approximation errors, rounding errors, and on uncertainties in data propagated during computations. The learning algorithm is simple and particularly suited to process stream of data in real time. In this paper we focus on the foundations of the approach and on the details of the learning algorithm. An application concerning economic time series forecasting illustrates the usefulness and efficiency of the approach.
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References
Angelov, P., Filev, D.: An approach to online identification of Takagi-Sugeno fuzzy models. IEEE Transactions on SMC - Part B 34(1), 484–498 (2004)
Angelov, P., Zhou, X.: Evolving Fuzzy Rule-Based Classifiers from Data Streams. IEEE Transactions on Fuzzy Systems 16(6), 1462–1475 (2008)
Gabrys, B., Bargiela, A.: General fuzzy min-max neural network for clustering and classification. IEEE Trans. on Neural Networks 11(3), 769–783 (2000)
Kasabov, N.: Evolving Connectionist Systems: The Knowledge Engineering Approach., 2nd edn., 451 p. Springer, Heidelberg (2007)
Pedrycz, W., Gomide, F.: Fuzzy systems engineering: Toward human-centric computing, 526 p. Wiley, Hoboken (2007)
Leite, D.F., Costa Jr., P., Gomide, F.: Evolving Granular Classification Neural Networks. In: IEEE Int. Joint Conference on Neural Networks, pp. 1736–1743 (2009)
Leite, D.F., Costa Jr., P., Gomide, F.: Interval-Based Evolving Modeling. In: IEEE Workshop on Evolving and Self-Developing Intelligent Systems, pp. 1–8 (2009)
Bouchachia, A., Gabrys, B., Sahel, Z.: Overview of Some Incremental Learning Algorithms. In: IEEE International Conference on Fuzzy Systems, pp. 1–6 (2007)
Angelov, P., Filev, D., Kasabov, N.: Guest ed. Evolving Fuzzy Systems - Preface to the Special Sec. IEEE Trans. on Fuzzy Systems 6(6), 1390–1392 (2008)
Hansen, E.R., Walster, G.W.: Global optimization using interval analysis., 2nd edn., 489 p. Marcel Dekker, New York (2004)
Jaulin, L.; Keiffer, M.; Didrit, O.; Walter, E.: Applied Interval Analysis. 379 p. Springer-Verlag, London (2001)
Moore, R.E.: Interval Analysis, 145 p. Prentice Hall, Englewood Cliffs (1966)
Kreinovich, V.: Interval computations and interval-related statistical techniques. In: Adv. in Data Modeling for Meas. in the Metrology, pp. 119–147. Springer, Heidelberg (2008)
Hickey, T., Ju, Q., van Emden, M.H.: Interval Arithmetic: From Principles to Implementation. Journal of the ACM 48(5), 1038–1068 (2001)
Mitchell, T.: Machine Learning, 1st edn., 414 p. McGraw Hill, New York (1997)
Bishop, C.M.: Pattern Recognition and Machine Learning, 738 p. Springer, Heidelberg (2007)
Yao, J.T.: A Ten-year Review of Granular Computing. In: IEEE International Conference on Granular Computing, pp. 734–739 (2007)
Zadeh, L.A.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Sys. 90(2), 111–127 (1997)
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Leite, D., Costa, P., Gomide, F. (2010). Granular Approach for Evolving System Modeling. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_35
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DOI: https://doi.org/10.1007/978-3-642-14049-5_35
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