Abstract
In this paper, we consider the problem of constructing a correction algorithm with the aim of increasing the adaptive properties of the ΣΠ-neuron, relying solely on the structure of the ΣΠ-neuron itself. To build the corrector, the logical-algebraic method of data analysis is used. Comparison of the advantages of the neural network approach and the logical-algebraic method suggests that a combined approach to the organization of the neural network improves its efficiency and allows one to build a set of rules that reveal hidden patterns in a given subject area, thus improving the quality of the recognition system.
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References
- 1.
V. N. Gridin and V. I. Solodovnikov, “Sharing neural network technologies and decision trees to search for logical patterns,” in: Information Technology and Nanotechnology [in Russian], Proc. III Int. Conf., Samara (2017), pp. 1763–1769.
- 2.
L. A. Lyutikova, Modeling and minimization of knowledge bases in terms of multivalued predicate logic [in Russian], preprint, Nalchik (2006).
- 3.
L. A. Lyutikova, “Use of mathematical logic with the significance variable in modeling knowledge systems,” Vestn. Samar. Univ., No. 6 (65), 20–27 (2008).
- 4.
L. A. Lyutikova and E. V. Shmatova, “Analysis and synthesis of pattern recognition algorithms using variable-valued logic,” Inform. Tekhnol., 22, No. 4, 292–297 (2016).
- 5.
E. Pap, “Pseudo-analysis as a mathematical base for soft computing,” Soft Comput., 1, 61–68 (1997).
- 6.
Z. M. Shibzukhov, “On some constructive and correct classes of algebraic ΣΠ-algorithms,” Dokl. Ross. Akad. Nauk, 432, No. 4, 465–468 (2010).
- 7.
Z. M. Shibzukhov, “Correct aggregation operations with algorithms,” Pattern Recogn. Image Anal., 24, No. 3, 377–382 (2014).
- 8.
A. V. Timofeev and L. A. Lyutikova, “Development and application of multivalued logic and network flows in intelligent systems,” Tr. SPIIRAN, No. 2, 114–126 (2005).
- 9.
A. V. Timofeev and V. Kh. Pshibikhov, “Algorithms for learning and minimizing the complexity of polynomial recognition systems,” Izv. Akad. Nauk SSSR. Tekhn. Kibern., No. 7, 214–217 (1974).
- 10.
K. V. Vorontsov, “Optimization methods of linear and monotone correction in the algebraic approach to the problem of recognition,” Zh. Vychisl. Mat. Mat. Fiz., 40, No. 1, 166–176 (2000).
- 11.
Yu. I. Zhuravlev, “On the algebraic approach to the solution of recognition or classification problems,” Probl. Kibern., 33, 5–68 (1978).
- 12.
Yu. I. Zhuravlev and K. V. Rudakov, “On algebraic correction of information processing (transformation) procedures,” in: Problems of Applied Mathematics and Computer Science [in Russian] (1987), pp. 187–198.
- 13.
S. V. Yablonsky, Introduction to Discrete Mathematics, Nauka, Moscow (2001).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 154, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, 2018.
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Lyutikova, L.A. Construction of a Logical-Algebraic Corrector to Increase the Adaptive Properties of the ΣΠ-Neuron. J Math Sci 253, 539–546 (2021). https://doi.org/10.1007/s10958-021-05251-3
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Keywords and phrases
- ΣΠ-neuron
- algorithm
- corrector
- classifier
- predicate
- disjunctive normal form
- logical function
AMS Subject Classification
- 68T05
- 68T27