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Theory of equivalence systems for describing the algebraic closures of a generalized estimation model

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Abstract

The recognition problem is considered in which the initial information is given by the values of similarity functions on pairs of objects. A generalization of the estimation algorithm model for this problem is proposed. A theory for the description and analysis of algebraic closures of the generalized and classical models is developed.

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References

  1. Yu. I. Zhuravlev and V. V. Nikiforov, “Recognition Algorithms Based on Estimate Evaluation,” Kibernetika, No. 3, 1–11 (1971).

  2. Yu. I. Zhuravlev, M. M. Kamilov, and Sh. E. Tulyaganov, Estimation Algorithms and Their Applications (FAN, Tashkent, 1974) [in Russian].

    Google Scholar 

  3. Yu. I. Zhuravlev, “Correct Algorithms over Sets of Incorrect (Heuristic) Algorithms: Part I,” Kibernetika, No. 4, 5–17 (1977).

  4. Yu. I. Zhuravlev, “Correct Algorithms over Sets of Incorrect (Heuristic) Algorithms: Part II,” Kibernetika, No. 6, 21–27 (1977).

  5. V. L. Matrosov, “On the Completeness Criteria for the Model of Estimation Algorithms and Its Algebraic Closure,” Dokl. Akad. Nauk SSSR 258, 791–796 (1981).

    MathSciNet  Google Scholar 

  6. V. L. Matrosov, “Synthesis of Optimal Algorithms in Algebraic Closures of Recognition Algorithm Models,” in Recognition, Classification, and Forecast: Mathematical Methods and Applications (Nauka, Moscow, 1989), No. 1, pp. 149–176 [in Russian].

    Google Scholar 

  7. A. G. D’yakonov, “An Algebra over Estimation Algorithms: The Minimal Degree of Correct Algorithms,” Zh. Vychisl. Mat. Mat. Fiz. 45, 1134–1145 (2005) [Comput. Math. Math. Phys. 45, 1095–1106 (2005)].

    MATH  MathSciNet  Google Scholar 

  8. A. G. D’yakonov, “Analysis of Algebraic Closures of Recognition Algoriths: Markup Operators,” Tavricheskii Vestnik Informatiki Mat., No. 1, 199–203 (2008).

  9. A. G. D’yakonov, “Correctness Criteria for Algebraic Closures of the Estimate-Calculating Algorithm Model,” Dokl. Akad. Nauk 423, 461–464 (2008) [Dokl. Math. 77, 453–456 (2008)].

    MATH  MathSciNet  Google Scholar 

  10. Yu. I. Zhuravlev, “An Algebraic Approach to Recognition and Classification Problems,” in Mathematical Methods in Recognition and Classification Problems (Hafner Press, 1986; Nauka, Moscow, 1978).

  11. J. T. Tou and R. C. Gonzalez, Pattern recognition principles (Addison-Wesley, Reading, Mass., 1974; Mir, Moscow, 1978).

    MATH  Google Scholar 

  12. A. A. Dokukin, “Synthesis of Polynomials over Extreme Estimation Algorithms,” Candidate’s Dissertation in Mathematics (Computing Centre, Russian Academy of Sciences, Moscow, 2008) [in Russian].

    Google Scholar 

  13. M. A. Aizerman, E. M. Bravermann, and L. I. Rozonoer, Metod potentsial’nykh funktsii v teorii obucheniya mashin (Nauka, Moscow, 1970) [in Russian].

    Google Scholar 

  14. T. V. Plokhonina, “Correctness of Algebraic Finite-Degree Closures of a Family of Estimation Algorithms for Regular Problems,” Zh. Vychisl. Mat. Mat. Fiz. 27, 763–770 (1987).

    MATH  MathSciNet  Google Scholar 

  15. K. V. Rudakov, “On the Algebraic Theory of Universal and Local Constraints for Classification Problems,” in Recognition, Classification, and Forecast: Mathematical Methods and Applications (Nauka, Moscow, 1989), No. 1, pp. 176–201 [in Russian].

    Google Scholar 

  16. A. A. Dokukin, “The Construction of a Recognition Algorithm in the Algebraic Closure,” Zh. Vychisl. Mat. Mat. Fiz. 41, 1873–1877 (2001) [Comput. Math. Math. Phys. 41, 1811–1815 (2001)].

    MathSciNet  Google Scholar 

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Correspondence to A. G. D’yakonov.

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Original Russian Text © A.G. D’yakonov, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 2, pp. 388–400.

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D’yakonov, A.G. Theory of equivalence systems for describing the algebraic closures of a generalized estimation model. Comput. Math. and Math. Phys. 50, 369–381 (2010). https://doi.org/10.1134/S0965542510020181

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