The architecture is quite compact compared to most models of pattern recognition that require very large computing power. It lacks logical relationships and aggregation of conditions in fuzzy systems.
Its practical value is in its high flexibility, ease of implementation and time efficiency of the method. High learning speed and universal approximating properties of the proposed network will be especially useful when processing multidimensional vector argument functions.
Listed in what follows are the main results obtained in this chapter.
- The classification problem of the multidimensional overlapping of objects reduces to a fuzzy modification of pattern recognition tasks.
- Based on the promising developments in the field of cellular self-organizing neural networks and fuzzy clustering procedures, the author proposed a deep fuzzy neural network for pattern recognition and algorithms for training, characterized by a high degree of neuronal self-organization, the absence of heuristic training parameters, the ability to control selectively individual connections between neurons to solve the problem of “dead” neurons, the high convergence rate and improvement of the separation properties of the network in the case of overlapping clusters and classes.
- The proposed FCNN-SOM can be effectively used not only for multidimensional clustering of semi-structured data in the form of generalized patterns but also for the automatic configuration of parameters and the type of membership functions (fuzzification) in adaptive fuzzy inference systems.
- The network can operate in the mode of exact and fuzzy clustering, depending on the nature of the data being processed.
- To improve the accuracy of the intersecting features, a deep neuro-fuzzy classifier that combines FCNN-SOM and RBFN through a layer of fuzzy clustering is proposed.
- An experimental study on test data on the qualitative and quantitative evaluation of the solution demonstrated the model’s computational efficiency and capability for fuzzy separation of overlapping clusters.
- The practical importance of the developed methodology of multicriteria neural network analysis of global TED was demonstrated on a set of quantitative and qualitative indicators, including technological and social dimensions of TED. Based on that, we constructed a flexible neuro-fuzzy model of the trajectory of global TED as a dynamic range of FCNN, differing in having a quite simple but powerful strategy for increasing the accuracy of clustering, without compromising interpretability, the assessment of the TED level, TED characteristics of individual countries and prediction of future values of a multidimensional process. Comparison of these parameters to leadership and national TED trajectories makes it possible to obtain a reliable estimate not only of the speed but also of the level of TED of each country.
- To build a predictive model on a neural network is not a requirement of stationarity of the process. The neural network is a universal tool that can accurately identify non-linear patterns and relationships between the components of multivariate random processes. The use of fuzzy clustering allows a more accurate separation of overlapping clusters.
In conclusion, perspectives for future research in the field of mining multidimensional semi-structured data, describing complex intersecting objects, are associated with the development of effective models of deep fuzzy neural networks based on different principles concerning the introduction of fuzziness in the structure and on the basis of modification of teaching strategies.
Acknowledgment: This chapter was prepared within the framework of the Competitiveness Enhancement Programme of National Research, Tomsk State University, with the financial support of the Russian Foundation for Basic Research (grant 16-29-12858).
Bibliography
[1]Kohonen T. Self-organizing maps. Moscow, Russia: BINOM. Knowledge laboratory, 2008.
[2]Duke VA. Computer psychodiagnostics. Saint Petersburg, Russia: Brotherhood, 1994.
[3]Pospelov DA. Artificial intelligence. Reference. Book 2. Models and methods. Moscow, Russia: Radio and communication, 1990.
[4]Lutsenko EV. Theoretical bases and technology of adaptive semantic analysis to support decision-making. Krasnodar, Russia: CUI MVD RF, 1996.
[5]Lutsenko EV. Automated system-cognitive analysis in the management of active objects. Krasnodar, Russia: KubSAU, 2002.
[6]Bohr N. Atomic physics and human knowledge. Moscow, Russia: Mir, 1961.
[7]Gorbachev SV. Intelligent mapping system “, Informeo”: the experience of using neuroinformation technologies. In Proceedings of VIII all-Russian seminar “Neuroinformatics and its applications”, pages 146–148. Krasnoyarsk, Russia: Publishing house Krasnoyarsk state University, 2000.
[8]Gorbachev SV. Building neural network control system to solve the problem of the identification of geological bodies 3-D. In Proceedings of the IX all-Russian seminar “Neuroinformatics and its applications”, pages 113–114. Krasnoyarsk, Russia: Publishing house Krasnoyarsk state University, 2001.
[9]Gorbachev SV and Syryamkin VI. Neuro-fuzzy techniques in intelligent systems of processing and analysis of multidimensional information. Tomsk, Russia: Publishing house Tomsk state University, 2014.
[10]Bodyanskiy Y, Gorshkov Y, Kolodyaznhiy V, and Stephan A. Combined learning algorithm for a selforginizing map with fuzzy inference. In Proceedings of Computational intelligence, theory and applications: International Conference 8th Fuzzy Days in Dortmund, volume 33, pages 641–650, 2005.
[11]Borisov VV, Kruglov VV, and Fedulov AS. Fuzzy models and networks. Moscow, Russia: Telecom, 2012.
[12]Hoeppner F, Klawonn F, Kruse R, and Runkler T. Fuzzy Clustering Analysis: Methods for Classification, Data Analysis and Image Recognition. Chichester: John Wiley & Sons, 1999.
[13]Keller JM and Hunt DJ. Incorporating fuzzy membership function into the perceptron algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7:693–699, 1985.
[14]Mitra S and Pal SK. Fuzzy multi-layer perceptron, inferencing and rule generation. IEEE Transactions on Neural Networks, 6:51–63, 1995.
[15]Bezdek JC. Pattern Recognition with Fuzzy Objective Function Algorithms. New York, USA: Plenum Press, 1981.
[16]Bodyansky EV and Rudenko OG. Artificial neural networks: architectures, learning, applications. Kharkov, Ukraine: TELETECH, 2004.
[17]Xu R and Wunsch DC. Clustering. In IEEE Press Series on Computational Intelligence. Hoboken, USA: John Wiley & Sons, 2009.
[18]Gorban AN. Training of neural networks. Moscow, Russia: Paragraf, 1990.
[19]Vuorimaa P. Fuzzy self-organizing map. Fuzzy Sets and Systems, 66:223–231, 1994.
[20]Vuorimaa P. Use of the fuzzy self-orginizing map in pattern self-recognition. In Proceedings of 3-rd IEEE Int. Conf. Fuzzy Systems “FUZZ-IEEE’94”, pages 798–801, Orlando, USA, 1994.
[21]Tsao ECK, Bezdek JC, and Pal NR. Fuzzy Kohonen clustering networks. Pattern Recognition, 27:757–764, 1994.
[22]Pascual-Marqui RD. Smoothly Distributed Fuzzy cMeans: a New Self-Organizing map. Pattern Recognition, 34:2395–2402, 2001. R. D. Pascual-Marqui, A. D. Pascual-Montano, K. Kochi, J. M. Caraso.
[23]Anikin VI and Karmanov AA. The training of the artificial neural network Kohonen’s self-organizing cellular automaton. Information technologies,, 11:73–80, 2014.
[24]Chua LO and Yang L. Cellular neural networks. Theory. IEEE Transactions on Circuits and Systems CAS-35, 10:1257–1272, 1988.
[25]Chua LO and Yang L. Cellular neural networks. Applications. IEEE Transactions on Circuits and Systems CAS-35, 10:1273–1290, 1988.
[26]Dvoretzky A. On stochastic approximation. In Proceedings 3-rd Berkley Symp. Math. Statistics and Probability, pages 39–55, 1956.
[27]Dawod M, Hasan M, and Daood A. Experimental Study: Comparison of clustering algorithms. Int. Journal of Engineering Research and Application, 7(8):23–34, 2017.
[28]Bezdek JC, Tsao ECK, and Pal NR. Fuzzy Kohonen Clustering Networks. IEEE Transactions on Fuzzy Systems, pages 1035–1043, 1992.
[29]Karayiannis NB and Pai PI. Fuzzy algorithm for learning vector quantization. IEEE Trans. on Neural Network., 5:1196–1211, 1996.
[30]Wu KL and Yang MS. A fuzzy-soft learning vector quantization. Neurocomputing is, 55:681–697, 2003.
[31]Kondratiev ND, Yakovets YV, and Abalkin LI. Large cycles of conjuncture and theory of foresight: Selected works. Moscow: Economy, 2002.
[32]Glazyev S and Kharitonov V. Nanotechnology as a key factor in the new technological order in the economy. Moscow: Twent, 2009.
[33]Gorbachev SV and Syryamkin VI. Cognitive neural network modeling of the trajectory of global technical and economic development. In Proceedings of International Conference on Cognitive Computing and Information Processing CCIP-2015, pages 341–346. NOIDA, India, 2015.