Abstract
Fuzzy cognitive maps (FCMs), characterized by a great deal of abstraction, flexibility, adaptability, and fuzzy reasoning, are widely used tools for modeling dynamic systems and decision support systems. Research on the problem of finding sparse FCMs from observed data is outstanding. Evolutionary algorithms (EAs) play a key role in learning FCMs from time series without expert knowledge. In this paper, we first involve sparsity penalty in the objective function optimized by EAs. To improve the performance of EAs, we develop an effective initialization operator based on the Lasso, a convex optimization approach. Comparative experiments on synthetic data with varying sizes and densities compared with other state-of-the-art methods demonstrate the effectiveness of the proposed approach. Moreover, the proposed initialization operator is able to promote to performance of EAs in learning sparse FCMs from time series.
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References
Kosko, B.: Fuzzy cognitive maps. Int. J. Man Mach. Stud. 24(1), 65–75 (1986)
Song, H., Miao, C., Roel, W., Shen, Z., Catthoor, F.: Implementation of fuzzy cognitive maps based on fuzzy neural network and application in prediction of time series. IEEE Trans. Fuzzy Syst. 18(2), 233–250 (2010)
Stach, W., Kurgan, L.A., Pedrycz, W.: Numerical and linguistic prediction of time series with the use of fuzzy cognitive maps. IEEE Trans. Fuzzy Syst. 16(1), 61–72 (2008)
Stylios, C.D., Groumpos, P.P.: Modeling complex systems using fuzzy cognitive maps. IEEE Trans. Syst. Man Cybern. Part A: Syst. Hum. 34(1), 155–162 (2004)
Andreou, A.S., Mateou, N.H., Zombanakis, G.A.: Soft computing or crisis management and political decision making: the use of genetically evolved fuzzy cognitive maps. Soft. Comput. 9(3), 194–210 (2005)
Wu, K., Liu, J.: Robust learning of large-scale fuzzy cognitive maps via the lasso from noisy time series. Knowl.-Based Syst. 113, 23–38 (2016)
Tsadiras, K.: Comparing the inference capabilities of binary, trivalent and sigmoid fuzzy cognitive maps. Inf. Sci. 178, 3880–3894 (2008)
Salmeron, J.L., Papageorgiou, E.I.: A fuzzy grey cognitive maps-based decision support system for radiotherapy treatment planning. Knowl.-Based Syst. 30, 151–160 (2012)
Chen, Y., Mazlack, L.J., Minai, A.A., Lu, L.J.: Inferring causal networks using fuzzy cognitive maps and evolutionary algorithms with application to gene regulatory network reconstruction. Appl. Soft Comput. 37, 667–679 (2015)
Liu, J., Chi, Y., Zhu, C.: A dynamic multi-agent genetic algorithm for gene regulatory network reconstruction based on fuzzy cognitive maps. IEEE Trans. Fuzzy Syst. 24(2), 419–431 (2016)
Papageorgiou, E.I.: Learning algorithms for fuzzy cognitive maps - a review study. IEEE Trans. Syst. Man Cybern. Part C 42(2), 150–163 (2012)
Papageorgiou, E.I., Stylios, C.D., Groumpos, P.P.: Fuzzy cognitive map learning based on nonlinear Hebbian rule. In: Proceedings of Australian Conference on Artificial Intelligence, pp. 256–268 (2003)
Stach, W., Kurgan, L.A., Pedrycz, W.: Data-driven nonlinear Hebbian learning method for fuzzy cognitive maps. In: Proceedings of 2008 IEEE International Conference on Fuzzy Systems, pp. 1975–1981 (2008)
Stach, W., Kurgan, L., Pedrycz, W.: A divide and conquer method for learning large fuzzy cognitive maps. Fuzzy Sets Syst. 161(19), 2515–2532 (2010)
Wu, K., Liu, J., Chi, Y.: Wavelet fuzzy cognitive maps. Neurocomputing 232, 94–103 (2017)
Stach, W., Kurgan, L., Pedrycz, W., Reformat, M.: Genetic learning of fuzzy cognitive maps. Fuzzy Sets Syst. 153(3), 371–401 (2005)
Chen, Y., Mazlack, L.J., Lu, L.J.: Learning fuzzy cognitive maps from data by ant colony optimization. In: Proceedings of Genetic and Evolutionary Computation Conference, pp. 9–16 (2012)
Neubauer, A.: A theoretical analysis of the non-uniform mutation operator for the modified genetic algorithm. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 93–96 (1997)
Eshellman, L.J.: Real-coded genetic algorithms and interval-schemata. Found. Genet. Algorithms 2, 187–202 (1993)
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9(3), 1–15 (1994)
Acampora, G., Pedrycz, W., Vitiello, A.: A competent memetic algorithm for learning fuzzy cognitive maps. IEEE Trans. Fuzzy Syst. 23(6), 2397–2411 (2015)
Stach, W., Pedrycz, W., Kurgan, L.A.: Learning of fuzzy cognitive maps using density estimate. IEEE Trans. Syst. Man Cybern. Part B 42(3), 900–912 (2012)
Chi, Y., Liu, J.: Learning of fuzzy cognitive maps with varying densities using a multi-objective evolutionary algorithm. IEEE Trans. Fuzzy Syst. 24(1), 71–81 (2016)
Acknowledgements
This work is partially supported by the Outstanding Young Scholar Program of National Natural Science Foundation of China (NSFC) under Grant 61522311, the Overseas, Hong Kong & Macao Scholars Collaborated Research Program of NSFC under Grant 61528205, and the Key Program of Fundamental Research Project of Natural Science of Shaanxi Province, China under Grant 2017JZ017.
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Wu, K., Liu, J. (2017). Learning of Sparse Fuzzy Cognitive Maps Using Evolutionary Algorithm with Lasso Initialization. In: Shi, Y., et al. Simulated Evolution and Learning. SEAL 2017. Lecture Notes in Computer Science(), vol 10593. Springer, Cham. https://doi.org/10.1007/978-3-319-68759-9_32
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DOI: https://doi.org/10.1007/978-3-319-68759-9_32
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