Abstract
The article provides information on the historical development of the scientific direction of inductive modeling, originated by Ukrainian scholar Professor Oleksiy Ivakhnenko in 1968 with creation of his Group Method of Data Handling, as well as characterizes the basic fundamental, applied and technological achievements. The term inductive modeling can be defined as a self-organizing process of evolutional transition from initial data to mathematical models reflecting some patterns of functioning objects and systems implicitly contained in available experimental, trial or statistical data.
The structured information is presented on the development of GMDH-based inductive modeling in Ukraine and abroad, main fundamental, technological and applied achievements are characterized, as well as the most prospective ways of further research are formulated. The performed survey of the research state in the field of inductive modeling shows that GMDH is one of the most powerful methods of data mining and a promising basis for creating modern information technologies for discovering knowledge from observation data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ivakhnenko, A.G.: The group method of data handling – a rival of the method of stochastic approximation. Sov. Autom. Control 1(3), 43–55 (1968)
Ivakhnenko, A.G.: Heuristic self-organization in problems of automatic control. Automatica (IFAC) 3, 207–219 (1970)
Ivakhnenko, A.G.: Polynomial theory of complex systems. IEEE Trans. Syst. Man Cybern. 1(4), 364–378 (1971)
Ivakhnenko, A.G.: Systems of Heuristic Self-Organization in Technical Cybernetics. Technika, Kiev (1971). (in Russian)
Ivakhnenko, A.G.: Long-Term Forecasting and Control of Complex Systems. Technika, Kiev (1975). (in Russian)
Ivakhnenko, A.G.: Inductive Method for Self-Organizing Models of Complex Systems. Naukova Dumka, Kiev (1982). (in Russian)
Madala, H.R., Ivakhnenko, A.G.: Inductive Learning Algorithms for Complex Systems Modeling. CRC Press, New York (1994)
Ivakhnenko, A.G., Müller, J.-A.: Recent developments of self-organising modeling in prediction and analysis of stock market. Microelectron. Reliab. 37, 1053–1072 (1997)
Anastasakis, L., Mort, N.: The development of self-organization techniques in modelling: a review of the Group Method of Data Handling (GMDH). ACSE research report, vol. 813, 39 p. The University of Sheffield (2001)
Snorek, M., Kordik, P.: Inductive modelling world wide the state of the art. In: Proceedings of 2nd International Workshop on Inductive Modelling, pp. 302–304. CTU, Prague (2007)
Stepashko, V.: Ideas of Academician O.H. Ivakhnenko in the inductive modelling field from historical perspective. In: Proceedings of the 4th International Conference on Inductive Modelling, ICIM-2013, pp. 30–37. IRTC ITS NASU, Kyiv (2013)
Farlow, S.J. (ed.): Self-Organizing Methods in Modeling: GMDH Type Algorithms. Marcel Decker Inc., New York, Basel (1984)
Iwachnenko, A.G., Müller, J.-A.: Selbstorganisation von Vorhersagemodellen. VEB Verlag Technik, Berlin (1984)
Ivakhnenko, A.G., Karpinsky, A.M.: Computer-aided self-organization of models in terms of the general communication theory (information theory). Sov. Autom. Control 15(4), 7–15 (1982)
Ivakhnenko, A.G., Stepashko, V.S.: Noise Immunity of Modelling. Naukova Dumka, Kiev (1985). (in Russian)
Stepashko, V.S., Kostenko, Y.: A GMDH algorithm for two-level modeling of multidimensional cyclic processes. Sov. Autom. Control 20(4), 49–57 (1987)
Ivakhnenko, A.G., Kostenko, Y.: System analysis and long-term prediction on the basis of model self-organisation (OSA algorithm). Sov. Autom. Control 15(3), 11–17 (1982)
Ivakhnenko, A.G.: Objective computer clasterization based on self-organisation theory. Sov. Autom. Control 20(6), 1–7 (1987)
Ivakhnenko, A.G., Osipenko, V.V., Strokova, T.I.: Prediction of two-dimensional physical fields using inverse transition matrix transformation. Sov. Autom. Control 16(4), 10–15 (1983)
Ivakhnenko, A.G.: Inductive sorting method for the forecasting of multidimensional random processes and events with the help of analogs forecast complexing. Pattern Recogn. Image Anal. 1(1), 99–108 (1991)
Oh, S.K., Pedrycz, W.: The design of self-organizing polynomial neural networks. Inf. Sci. 141, 237–258 (2002)
Ivakhnenko, A.G., Ivakhnenko, G.A., Mueller, J.-A.: Self-organization of neuronets with active neurons. Pattern Recogn. Image Anal. 4(4), 177–188 (1994)
Ivakhnenko, A.G., Wunsh, D., Ivakhnenko, G.A.: Inductive sorting-out GMDH algorithms with polynomial complexity for active neurons of neural networks. In: Proceedings of the International Joint Conference on Neural Networks, pp. 1169–1173. IEEE, Piscataway (1999)
Muller, J.-A., Lemke, F.: Self-Organizing Data Mining: An Intelligent Approach to Extract Knowledge from Data. Trafford Publishing Press, Berlin (1999)
Vysotskiy, V.N., Ivakhnenko, A.G., Cheberkus, V.I.: Long term prediction of oscillatory processes by finding a harmonic trend of optimum complexity by the balance-of-variables criterion. Sov. Autom. Control 8(1), 18–24 (1975)
Ivakhnenko, A.G., Krotov, G.I.: A multiplicative-additive nonlinear GMDH algorithm with optimization of the power of factors. Sov. Autom. Control 17(3), 10–15 (1984)
Ivakhnenko, A.G., Peka, PYu., Vostrov, N.P.: Combined Method for Modeling Water and Oil Fields. Naukova dumka, Kiev (1984). (In Russian)
Ivakhnenko, A.G., Yurachkovsky, Y.: Complex Systems Modeling after Experimental Data, Radio and Communication. Radio i Swiaz, Moscow (1987). (in Russian)
Ivakhnenko, A.G., Kovalchuk, P.I., Todua, M.M., Shelud’ko, O.I., Dubrovin, O.F.: Unique construction of regression curve using a small number of points. Sov. Autom. Control 6(5), 29–41 (1973)
Yurachkovsky, Y.: Convergence of multilayer algorithms of the group method of data handling. Sov. Autom. Control 14(3), 29–34 (1981)
Kovalchuk, P.L.: Internal convergence of GMDH algorithms. Sov. Autom. Control 16(2), 88–91 (1983)
Stepashko, V.S.: Potential noise stability of modelling using a combinatorial GMDH algorithm without information regarding the noise. Sov. Autom. Control 16(3), 15–25 (1983)
Kocherga, Y.L.: J-optimal reduction of model structure in the Gauss-Markov scheme. Sov. J. Autom. Inf. Sci. 21(4), 21–23 (1988)
Aksenova, T.I., Yurachkovsky, Y.P.: Characterization of unbiased structure and condition of its J-optimality. Sov. J. Autom. Inf. Sci. 21(4), 24–32 (1988)
Stepashko, V.S.: Noise immunity of choice of model using the criterion of balance of predictions. Sov. Autom. Control 17(5), 27–36 (1984)
Stepashko, V.S.: Investigation of the predicting properties of a recurrent structural-parametric identifier. Sov. J. Autom. Inf. Sci. 24(3), 31–40 (1991)
Stepashko, V.S.: Structural identification of predicting models for planned experiment. J. Autom. Inf. Sci. 25(1), 23–31 (1992)
Stepashko, V.S.: Analysis of criteria effectiveness for structural identification of forecasting models. J. Autom. Inf. Sci. 27(3–4), 13–20 (1994)
Stepashko, V.S.: Method of critical variances as analytical tool of theory of inductive modeling. J. Autom. Inf. Sci. 40(3), 4–22 (2008)
Stepashko, V.S.: Asymptotic Properties of External Criteria for Model Selection. Sov. J. Autom. Inf. Sci. 21(6), 84–92 (1988)
Aksenova, T.I.: Sufficient conditions and convergence rate using different criteria for model selection. Syst. Anal. Model. Simul. 20(1–2), 69–78 (1995)
Sarychev, A.P.: System criterion of regularity in the group method of data handling. J. Autom. Inf. Sci. 38(1), 22–35 (2006)
Sarychev, A.P.: Modelling in the class of regression equations systems in conditions of structural uncertainty. In: Proceedings of 2nd International Workshop on Inductive Modelling, IWIM-2007, pp. 193–203. Czech Technical University, Prague (2007)
Stepashko, V.S., Yefimenko, S.M., Savchenko, Y.A.: Computerized Experiment in Inductive Modeling. Naukova Dumka, Kyiv (2014). (in Ukrainian)
Stepashko, V.S.: A combinatorial algorithm of the group method of data handling with optimal model scanning scheme. Sov. Autom. Control 14(3), 24–28 (1981)
Stepashko, V.S.: A finite selection procedure for pruning an exhaustive search of models. Sov. Autom. Control 16(4), 84–88 (1983)
Moroz, O.G., Stepashko, V.S.: Comparative analysis of model structures generators in sorting-out GMDH algorithm. Inductive Model. Complex Syst. 8, 173–191 (2016). IRTC ITS NASU, Kyiv (in Ukrainian)
Sheludko, O.I.: GMDH algorithm with orthogonalized complete description for synthesis of models by the results of a planned experiment. Sov. Autom. Control 7(5), 24–33 (1974)
Tamura, H., Kondo, T.: Large-spatial pattern identification of air pollution by a combined model of source-receptor matrix and revised GMDH. In: Proceedings of IFAC Symposium on Environmental Systems Planning, Design and Control, pp. 373–380. Elsevier, Oxford (1977)
Yurachkovsky, Y.: Restoration of polynomial dependencies using self-organization. Sov. Autom. Control 14(4), 17–22 (1981)
Pavlov, A.V., Stepashko, V.S., Kondrashova, N.V.: Effective Methods of Models Self-Organization. Akademperiodika, Kyiv (2014). (in Russian)
Stepashko, V., Bulgakova, O.: Generalized iterative algorithm GIA GMDH. In: Proceedings of the 4th International Conference on Inductive Modelling, ICIM-2013, Kyiv, Ukraine, September 2013, pp. 119–123. IRTC ITS NASU, Kyiv
Kondo, T., Ueno, J.: Feedback GMDH-type neural network self-selecting optimum neural network architecture and its application to 3-dimensional medical image recognition of the lungs. In: Proceedings of II International Workshop on Inductive Modelling, September 2007, pp. 63–70. Czech Technical University, Prague. ISBN 978-80-01-03881-9
Kordik, P.: Fully automated knowledge extraction using group of adaptive model evolution. Ph.D. thesis, Department of Computer Science and Computers, FEE, CTU in Prague, 150 p. (2006)
Sarychev, A.P.: The solution of the discriminant analysis task in conditions of structural uncertainty on basis of the group method of data handling. J. Autom. Inf. Sci. 40(6), 27–40 (2008)
Sarycheva, L.: Quality criteria for GMDH-based clustering. In: Proceedings of the II International Conference on Inductive Modelling, ICIM-2008, pp. 84–90. IRTC ITS NASU, Kyiv (2008)
Borisova, I.A.: Calculation of FRiS-function over mixed dataset in the task of generalized classification. In: Proceedings of the III International Conference on Inductive Modelling, ICIM-2010, pp. 44–50. KNTU, Kherson, Ukraine (2010)
Cepek, M., Snorek, M., Chudacek, V.: ECG signal classification using GAME neural network and its comparison to other classifiers. In: Proceedings of International Conference on Artificial Neural Networks, ICANN 2008, pp. 768–777. Springer, Heidelberg (2008)
Voss, M.S., Feng, X.: A new methodology for emergent system identification using particle swarm optimization (PSO) and the group method of data handling (GMDH). In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1227–1232. Morgan Kaufmann Publishers, New York (2002)
Onwubolu, G., Sharma, A., Dayal A. et al.: Hybrid particle swarm optimization and group method of data handling for inductive modeling. In: Proceedings of 2nd International Conference on Inductive Modelling, pp. 95–103. IRTC ITS NASU, Kyiv (2008)
Jirina, M., Jirina Jr., M.: Genetic selection and cloning in GMDH MIA method. In: Proceedings of the II International Workshop on Inductive Modelling, IWIM 2007, pp. 165–171. CTU, Prague (2007)
Lytvynenko, V., Bidyuk, P., Myrgorod, V.: Application of the method and combined algorithm on the basis of immune network and negative selection for identification of turbine engine surging. In: Proceedings of the II International Conference on Inductive Modelling, ICIM-2008, pp. 116–123. IRTC ITS NASU, Kyiv (2008)
Lytvynenko, V.: Hybrid GMDH cooperative immune network for time series forecasting. In: Proceedigns of the 4th International Conference on Inductive Modelling, pp. 179–187. IRTC ITS NASU, Kyiv (2013)
Oh, S.K., Pedrycz, W., Park, H.S.: Multi-layer hybrid fuzzy polynomial neural networks: a design in the framework of computational intelligence. Neurocomputing 64, 397–431 (2005)
Zaychenko, Y.: The investigations of fuzzy group method of data handling with fuzzy inputs in the problem of forecasting in financial sphere. In: Proceedings of the II International Conference on Inductive Modelling, ICIM-2008, pp. 129–133. IRTC ITS NASU, Kyiv (2008)
Bodyanskiy, Y.V., Zaychenko, Y.P., Pavlikovskaya, E.: The neo-fuzzy neural network structure optimization using the GMDH for the solving forecasting and classification problems. In: Proceedings of the 3rd International Workshop on Inductive Modelling, IWIM-2009, Krynica, Poland, pp. 10–17. Czech Technical University, Prague (2009)
Bodyanskiy, Y., Vynokurova, O., Teslenko, N.: Cascade GMDH-wavelet-neuro-fuzzy network. In: Proceedings of the IV International Workshop on Inductive Modelling, IWIM-2011, pp. 16–21. IRTC ITS NASU, Kyiv (2011)
Dyvak, M., Manzhula, V., Pukas, A., Stakhiv, P.: Structural identification of interval models of the static systems. In: Proceedings of 2nd International Workshop on Inductive Modelling, pp. 132–139. Czech Technical University, Prague (2007)
Voytyuk, I., Dyvak, M., Spilchuk, V.: The method of structure identification of macromodels as difference operators based on the analysis of interval data and genetic algorithm. In: Proceedings of the IV International Workshop on Inductive Modelling, IWIM-2011, pp. 114–118. IRTC ITS NASU, Kyiv (2011)
Lemke, F.: Parallel self-organizing modeling. In: Proceedings of the II International Conference on Inductive Modelling, ICIM-2008, pp. 176–183. IRTC ITS NASU, Kyiv (2008)
Koshulko, O.A., Koshulko, A.I.: Multistage combinatorial GMDH algorithm for parallel processing of high-dimensional data. In: Proceedings of III International Workshop on Inductive Modelling, IWIM-2009, pp. 114–116. CTU, Prague (2009)
Stepashko, V., Yefimenko, S.: Parallel algorithms for solving combinatorial macromodelling problems. Przegląd Elektrotechniczny (Electr. Rev.) 85(4), 98–99 (2009)
ÄŒepek, M., KordÃk, P., Å norek, M.: The effect of modelling method to the inductive preprocessing algorithm. In: Proceedings of the III International Conference on Inductive Modelling, ICIM-2010, pp. 131–138. KNTU, Kherson (2010)
KordÃk, P., ÄŒerný, J.: Advanced ensemble strategies for polynomial models. In: Proceedings of the III International Conference on Inductive Modelling, ICIM-2010, pp. 77–82. KNTU, Kherson (2010)
http://knowledgeminer.eu. Accessed 17 May 2017
Lemke, F.: Insights v.2.0, self-organizing knowledge mining and forecasting tool (2013). http://www.knowledgeminer.eu. Accessed 21 May 2017
https://www.gmdhshell.com. Accessed 12 Apr 2017
www.gmdh.net. Accessed 15 Apr 2017
www.mgua.irtc.org.ua. Accessed 11 May 2017
Ivakhnenko, A.G., Ivakhnenko, G.A., Savchenko, E.A.: GMDH algorithm for optimal model choice by the external error criterion with the extension of definition by model bias and its applications to the committees and neural networks. Pattern Recogn. Image Anal. 12(4), 347–353 (2002)
Ivakhnenko, A.G., Savchenko, E.A.: Investigation of efficiency of additional determination method of the model selection in the modeling problems by application of GMDH algorithm. J. Autom. Inf. Sci. 40(3), 47–58 (2008)
Samoilenko, O., Stepashko, V.: A method of successive elimination of spurious arguments for effective solution of the search-based modelling tasks. In: Proceedings of the II International Conference on Inductive Modelling, pp. 36–39. IRTC ITS NASU, Kyiv (2008)
Yefimenko, S., Stepashko, V.: Intelligent recurrent-and-parallel computing for solving inductive modeling problems. In: Proceedings of 16th International Conference on Computational Problems of Electrical Engineering, pp. 236–238. LNPU, Lviv, Ukraine (2015)
Stepashko, V.S.: Conceptual fundamentals of intelligent modeling. Control Syst. Mach. (USiM) 4, 3–15 (2016). (in Russian)
Yefimenko, S.N.: Construction of systems of predictive models for multidimensional interrelated processes. Control Syst. Mach. (USiM) 4, 80–86 (2016). (in Russian)
Stepashko, V.S.: GMDH algorithms as basis of modeling process automation after experimental data. Sov. J. Autom. Inf. Sci. 21(4), 33–41 (1988)
Yefimenko, S., Stepashko, V.: Technologies of numerical investigation and applying of data-based modeling methods. In: Proceedings of the II International Conference on Inductive Modelling, ICIM-2008, pp. 236–240. IRTC ITS NASU, Kyiv (2008)
Shcherbakova, N., Stepashko, V.: Integrated environment for storing and handling information in tasks of inductive modelling for business intelligence systems. In: Setlak, G., Alexandrov, M., Markov, K. (eds.) Artificial Intelligence Methods and Techniques for Business and Engineering Applications, pp. 210–219. ITHEA, Rzeszow, Poland, Sofia, Bulgaria (2012)
Samoilenko, O.A.: Designing new GMDH algorithms as basic components of a modeling subsystem. Inductive Model. Complex Syst. 3, 191–208. IRTC ITS NASU, Kyiv (2011). (in Ukrainian)
Bulgakova, O., Zosimov, V., Stepashko, V.: Software package for modeling of complex systems based on iterative GMDH algorithms with the network access capability. Syst. Res. Inf. Technol. 1, 43–55 (2014). (in Ukrainian)
Pavlov, A.: Design patterns of automated structure-parametric identification system. In: Proceedings of 6th International Workshop on Inductive Modelling, pp. 31–35. IRTC ITS NASU, Kyiv (2015)
Stepashko, V., Samoilenko, O., Voloschuk, R:. Informational support of managerial decisions as a new kind of business intelligence systems. In: Setlak, G., Markov, K. (eds.) Computational Models for Business and Engineering Domains, pp. 269–279. ITHEA, Rzeszow, Poland, Sofia, Bulgaria (2014)
Iutynska, G., Stepashko, V.: Mathematical modeling in the microbial monitoring of heavy metals polluted soils. In: Book of Proceedings of IX ESA Congress, Part 2, pp. 659–660. Institute of Soil Science and Plant Cultivation, Warsaw (2006)
Kalavrouziotis, I.K., Vissikirsky, V.A., Stepashko, V.S., Koukoulakis, P.H.: Application of qualitative analysis techniques to the environmental modeling of plant species cultivation. Glob. NEST J. 12(2), 161–174 (2010)
Alyomov, S.V., Bulgakova, O.S., Stepashko, V.S.: Modeling of the Black Sea pollution impact on the total number of benthic organisms species. Collected Art. SNUNE&I Sevastopol 3(39), 54–62 (2011). (in Ukrainian)
Stepashko, V., Moroz, O.: Hybrid searching GMDH-GA algorithm for solving inductive modeling tasks. In: IEEE International Conference on Data Stream Mining & Processing, pp. 350–355, Lviv, Ukraine (2016)
Zosimov, V., Stepashko, V. Bulgakova, O.: Inductive building of search results ranking models to enhance the relevance of the text information retrieval. In: Spies, M., et al. (ed.) Proceedings of the 26th International Workshop on Database and Expert Systems Applications, Valencia, Spain, pp. 291–295. IEEE Computer Society, Los Alamitos (2015)
Schmidhuber, J.: Deep learning in neural networks: an overview. Neural Netw. 61, 85–117 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Stepashko, V. (2018). Developments and Prospects of GMDH-Based Inductive Modeling. In: Shakhovska, N., Stepashko, V. (eds) Advances in Intelligent Systems and Computing II. CSIT 2017. Advances in Intelligent Systems and Computing, vol 689. Springer, Cham. https://doi.org/10.1007/978-3-319-70581-1_34
Download citation
DOI: https://doi.org/10.1007/978-3-319-70581-1_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-70580-4
Online ISBN: 978-3-319-70581-1
eBook Packages: EngineeringEngineering (R0)