Conditions of the correctness for the algebra of estimates calculation algorithms with μ-operators over a set of binary-data recognition problems
This paper is aimed to show that specialized neural networks can be useful for finding exact solutions of the recognition problems involving binary data. For this purpose, as an original subclass, we take the subclass of estimates calculation algorithms (ECAs) in which all algorithms correspond to t...
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| Published in: | Pattern recognition and image analysis Vol. 27; no. 2; pp. 166 - 174 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Moscow
Pleiades Publishing
01.04.2017
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| ISSN: | 1054-6618, 1555-6212 |
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| Abstract | This paper is aimed to show that specialized neural networks can be useful for finding exact solutions of the recognition problems involving binary data. For this purpose, as an original subclass, we take the subclass of estimates calculation algorithms (ECAs) in which all algorithms correspond to three-level multilayer neural networks (μ-blocks). The correctness conditions are defined that allow a correct algorithm to be constructed in the algebra over this ECA subclass for each Ω-regular recognition problem. This approach does not require additional constraints, except for a trivial one, on the system of ECA support sets. |
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| AbstractList | This paper is aimed to show that specialized neural networks can be useful for finding exact solutions of the recognition problems involving binary data. For this purpose, as an original subclass, we take the subclass of estimates calculation algorithms (ECAs) in which all algorithms correspond to three-level multilayer neural networks (μ-blocks). The correctness conditions are defined that allow a correct algorithm to be constructed in the algebra over this ECA subclass for each Ω-regular recognition problem. This approach does not require additional constraints, except for a trivial one, on the system of ECA support sets. |
| Author | Dyusembaev, A. E. Grishko, M. V. |
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| Keywords | correctness algebra μ-block estimates calculation algorithm neural network |
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| References | Zhuravlev (CR1) 1977; 235 Dyusembaev (CR10) 2001 Rudakov (CR7) 1989 Zhuravlev (CR2) 1978; 2 D’yakonov (CR8) 2005; 45 Zhuravlev (CR5) 1973 Dyusembaev, Kaliazhdarov (CR12) 2015; 91 Dyusembaev (CR11) 1982; 22 Zhuravlev (CR4) 1998 Dyusembaev (CR9) 1993; 323 Matrosov (CR6) 1985 D’yakonov (CR13) 2009; 49 Zhuravlev (CR3) 1979; 19 Yu. I. Zhuravlev (4758_CR2) 1978; 2 A. E. Dyusembaev (4758_CR10) 2001 Yu. I. Zhuravlev (4758_CR4) 1998 A. E. Dyusembaev (4758_CR9) 1993; 323 A. G. D’yakonov (4758_CR13) 2009; 49 Yu. I. Zhuravlev (4758_CR5) 1973 Yu. I. Zhuravlev (4758_CR1) 1977; 235 K. V. Rudakov (4758_CR7) 1989 A. E. Dyusembaev (4758_CR12) 2015; 91 V. L. Matrosov (4758_CR6) 1985 A. E. Dyusembaev (4758_CR11) 1982; 22 A. G. D’yakonov (4758_CR8) 2005; 45 Yu. I. Zhuravlev (4758_CR3) 1979; 19 |
| References_xml | – year: 1985 ident: CR6 article-title: Correct algebras for recognition algorithms with limited capacity publication-title: Doctoral Dissertation in Mathematical Physics – volume: 45 start-page: 1134 issue: 6 year: 2005 end-page: 1145 ident: CR8 article-title: Algebras for estimation calculation algorithms: minimal degree for correct algorithm publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 2 start-page: 37 year: 1978 end-page: 45 ident: CR2 article-title: Correct algebras for sets of incorrect (heuristic) algorithms publication-title: Kibernetika – volume: 235 start-page: 761 issue: 4 year: 1977 end-page: 763 ident: CR1 article-title: Algebras for sets of incorrect (heuristic) algorithms publication-title: Dokl. Akad. Nauk SSSR – volume: 19 start-page: 200 issue: 3 year: 1979 end-page: 208 ident: CR3 article-title: The way to generate recognition algorithms being correct for the given reference sample publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 22 start-page: 1491 issue: 6 year: 1982 end-page: 1499 ident: CR11 article-title: Correctness of algebraic closure for test recognition algorithms publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 91 start-page: 236 issue: 2 year: 2015 end-page: 239 ident: CR12 article-title: On Exact Solutions of Recognition Problems Based on the Neural Network Approach publication-title: Dokl. Mathematics doi: 10.1134/S1064562415020143 – year: 2001 ident: CR10 publication-title: Mathematical Models for Program Segmentation – start-page: 3 year: 1998 end-page: 413 ident: CR4 publication-title: Selected Papers – volume: 323 start-page: 711 issue: 6 year: 1993 end-page: 714 ident: CR9 article-title: On one approach to a segmentation program publication-title: Dokl. Akad. Nauk – year: 1973 ident: CR5 article-title: Recognition algorithms based on estimations calculation. Conceptual meaning for parameters setting algorithms publication-title: Proc. Int. Symp. on Practical Application of Pattern Recognition – volume: 49 start-page: 200 issue: 1 year: 2009 end-page: 208 ident: CR13 article-title: Algebra for estimation calculation algorithms: normalizing with respect to segment publication-title: Zh. Vychisl. Mat. Mat. Fiz. – start-page: 176 year: 1989 end-page: 201 ident: CR7 article-title: On algebraic theory of universal and local limitations for recognition and classification problems publication-title: Recognition, Classification, Prediction – start-page: 176 volume-title: Recognition, Classification, Prediction year: 1989 ident: 4758_CR7 – volume: 323 start-page: 711 issue: 6 year: 1993 ident: 4758_CR9 publication-title: Dokl. Akad. Nauk – volume: 22 start-page: 1491 issue: 6 year: 1982 ident: 4758_CR11 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume-title: Doctoral Dissertation in Mathematical Physics year: 1985 ident: 4758_CR6 – volume-title: Mathematical Models for Program Segmentation year: 2001 ident: 4758_CR10 – volume: 49 start-page: 200 issue: 1 year: 2009 ident: 4758_CR13 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 235 start-page: 761 issue: 4 year: 1977 ident: 4758_CR1 publication-title: Dokl. Akad. Nauk SSSR – volume-title: Proc. Int. Symp. on Practical Application of Pattern Recognition year: 1973 ident: 4758_CR5 – start-page: 3 volume-title: Selected Papers year: 1998 ident: 4758_CR4 – volume: 45 start-page: 1134 issue: 6 year: 2005 ident: 4758_CR8 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 2 start-page: 37 year: 1978 ident: 4758_CR2 publication-title: Kibernetika – volume: 91 start-page: 236 issue: 2 year: 2015 ident: 4758_CR12 publication-title: Dokl. Mathematics doi: 10.1134/S1064562415020143 – volume: 19 start-page: 200 issue: 3 year: 1979 ident: 4758_CR3 publication-title: Zh. Vychisl. Mat. Mat. Fiz. |
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| SubjectTerms | Computer Science Image Processing and Computer Vision Mathematical Method in Pattern Recognition Pattern Recognition |
| Title | Conditions of the correctness for the algebra of estimates calculation algorithms with μ-operators over a set of binary-data recognition problems |
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