Abstract
This review provides an overview of methods for solving recognition problems developed by the eminent Soviet and Russian academic and scientist, Yu.I. Zhuravlev, together with his students and those that followed him. Zhuravlev was the leader of a prominent scientific school associated with the widespread use of various combinatorial-logical and algebraic methods for in the development of methods for solving recognition tasks. The school’s contributions lie in formulating a universal mathematical lexicon for describing recognition algorithms and an algebraic toolkit tailored for the synthesis of effective algorithms for solving learning problems based on precedents. Within the framework of the scientific school, researchers have devised various recognition methodologies, which have been successfully used to solve numerous applied problems.
REFERENCES
L. A. Aslanyan, L. F. Mingo, J. B. Castellanos, F. B. Chelnokov, A. A. Dokukin, and V. V. Ryazanov, “On logical correction of neural network algorithms for pattern recognition,” in Proc. 4th Int. Conf. Information Research & Applications (Foi-commerce, Sofia, 2006).
L. V. Baskalova and Yu. I. Zhuravlev, “A model of recognition algorithms with representative samples and systems of supporting sets,” USSR Comput. Math. Math. Phys. 21, 189–199 (1981). https://doi.org/10.1016/0041-5553(81)90109-9
BigARTM Library. http://bigartm.org/
O. S. Brusov, O. V. Senko, M. S. Kodryan, A. V. Kuznetsova, I. A. Matveev, I. V. Oleichik, N. S. Karpova, M. I. Faktor, A. V. Aleshenko, and S. V. Sizov, “Application of machine learning for predicting the outcome of treatment of patients with schizophrenia according to the indicators of ‘Thrombodynamics’ test,” Zh. Nevrologii Psikhiatrii im. S.S. Korsakova 121 (8), 45–53 (2021). https://doi.org/10.17116/jnevro202112108145
C. J. C. Burges, “A tutorial on support vector machines for pattern recognition,” Data Min. Knowl. Discovery 2, 121–167 (1998). https://doi.org/10.1023/a:1009715923555
I. A. Chegis and S. V. Yablonskii, “Logical methods of control of work of electric schemes,” Tr. Mat. Inst. Steklova 51, 270–360 (1958).
E. V. Djukova, “Discrete (logical) recognition procedures: Principles of construction, complexity of realization and basic modeles,” Pattern Recognit. Image Anal. 13, 417–425 (2003).
E. V. Dyukova, “Asymptotic optimal test algorithms in recognition problems,” Probl. Kibernetiki 39, 165–199 (1982).
E. V. Dyukova, “Recognition algorithms of ‘Bark’ type: Complexity of implementation and metric properties,” Raspoznavanie, Klassifikatsiya, Prognoz. Mat. Metody Ikh Primenenie 2, 99–125 (1989).
E. V. Dyukova, “On the implementation complexity of discrete (logical) recognition procedures,” Comput. Math. Math. Phys. 44, 532–541 (2004).
E. V. Dyukova and N. V. Peskov, “Search for informative fragments in descriptions of objects in discrete recognition procedures,” Comput. Math. Math. Phys. 42, 711–723 (2002).
E. V. Djukova, G. O. Maslyakov, and P. A. Prokofjev, “Dualization problem over the product of chains: Asymptotic estimates for the number of solutions,” Dokl. Math. 98, 564–567 (2018). https://doi.org/10.1134/S1064562418070086
E. V. Djukova, G. O. Masliakov, and P. A. Prokofyev, “On the logical analysis of partially ordered data in the supervised classification problem,” Comput. Math. Math. Phys. 59, 1542–1552 (2019). https://doi.org/10.1134/S0965542519090082
E. V. Djukova, G. O. Maslyakov, and P. A. Prokofyev, “On the number of maximal independent elements of partially ordered sets (the case of chains),” Inf. Ee Primeneniya 13 (1), 25–32 (2019). https://doi.org/10.14357/19922264190104
E. V. Dyukova and Yu. I. Zhuravlev, “Discrete analysis of feature descriptions in recognition problems of high dimensionality,” Comput. Math. Math. Phys. 40 (8), 1214–1227 (2000).
E. V. Djukova, Yu. I. Zhuravlev, N. V. Peskov, and A. A. Sakharov, “Processing of real-valued information by logical recognition procedures,” Iskusstvennyi Intellekt, No. 2, 80–85 (2004).
E. V. Dyukova, Yu. I. Zhuravlev, and K. V. Rudakov, “Algebraic-logic synthesis of correct recognition procedures based on elementary algorithms,” Comput. Math. Math. Phys. 36 (8), 1161–1167 (1996).
E. V. Djukova, Yu. I. Zhuravlev, and R. M. Sotnezov, “Synthesis of corrector family with high recognition ability,” in New Trends in Classification and Data Mining (ITHEA, Sofia, 2010), pp. 32–39.
E. V. Djukova, Yu. I. Zhuravlev, and R. M. Sotnezov, “Construction of an ensemble of logical correctors on the basis of elementary classifiers,” Pattern Recognit. Image Anal. 21, 599–605 (2011). https://doi.org/10.1134/s1054661811040055
E. V. Dyukova, Yu. I. Zhuravlev, and P. A. Prokofjev, “Logical correctors in the problem of classification by precedents,” Comput. Math. Math. Phys. 57, 1866–1886 (2017). https://doi.org/10.1134/S0965542517110057
A. I. Dmitriev, Yu. I. Zhuravlev, and F. P. Krendelev, “On the mathematical principles of classification of items of phenomena,” Diskretnyi Anal., No. 7, 3–17 (1967).
A. A. Dokukin, “A method for constructing an optimal estimate calculation algorithm,” Comput. Math. Math. Phys. 46, 719–725 (2006).
A. A. Dokukin, “On the construction of samples for testing approximate optimization methods for estimate calculation algorithms,” Comput. Math. Math. Phys. 46, 914–918 (2006). https://doi.org/10.1134/S0965542506050149
A. A. Dokukin, “The construction of a recognition algorithm in the algebraic closure,” Comput. Math. Math. Phys. 41, 1811–1815 (2001).
A. G. D’yakonov, “Theory of equivalence systems for describing the algebraic closures of a generalized estimation model,” Comput. Math. Math. Phys. 50, 369–381 (2010). https://doi.org/10.1134/S0965542510020181
A. G. D’yakonov, “Theory of equivalence systems for describing the algebraic closures of a generalized estimation model. II,” Comput. Math. Math. Phys. 51, 490–504 (2010). https://doi.org/10.1134/S0965542511030067
A. G. D’yakonov, “An algebra over estimation algorithms: Monotone decision rules,” Comput. Math. Math. Phys. 45, 1822–1832 (2005).
A. G. D’yakonov, “Algebra over estimation algorithms: Normalization and division,” Comput. Math. Math. Phys. 47, 1050–1060 (2007). https://doi.org/10.1134/S0965542507060140
A. G. D’yakonov, “Algebra over estimation algorithms: Normalization with respect to the interval,” Comput. Math. Math. Phys. 49, 194–202 (2009). https://doi.org/10.1134/S096554250901014X
A. G. D’yakonov, “Forecasting the client’s behavior in supermarkets using weighted schemes of probability and density estimations,” Biznes-Informatika, No. 1, 68–77 (2014).
A. G. D’yakonov, “Algorithms for recommendation systems: LENKOR technology,” Biznes-Informatika, No. 1, 32–39 (2012).
S. V. Gafurov and V. V. Krasnoprshin, “Program technology for designing systems for solving the recognition problems with a complex structure,” Iskusstvennyi Intellekt, No. 1, 30–37 (2008).
H. Ganster, M. Gelautz, A. Pinz, M. Binder, H. Pehamberger, M. Bammer, and J. Krocza, “Initial results of automated melanoma recognition,” in Proc. 9th Scandinavian Conf. on Image Analysis (Uppsala, Sweden, 1995), Vol. 1, pp. 209–218.
V. S. Glushenkov, A. A. Kovalev, O. L. Konovalov, S. B. Kostyukevich, V. V. Krasnoproshin, and B. A. Yukhimenko, “System for representing and editing digital thematic radiation and ecological maps based on personal computers,” Vestsi ANB, Ser. Fiz.-Mat.-Navuk Minsk 5 (6), 102–107 (1992).
R. R. Guliev, O. V. Sen’ko, D. A. Zateishchikov, V. V. Nosikov, I. V. Uporov, A. V. Kuznetsova, M. A. Evdokimova, S. N. Tereshchenko, E. V. Akatova, M. G. Glezer, A. S. Galyavich, N. A. Koziolova, A. V. Yagoda, O. I. Boeva, S. V. Shlyk, S. Yu. Levashov, V. A. Konstantinov, S. D. Brazhnik, I. N. Varfolomeev, and I. N. Kurochkin, “The use of optimal partitionings for multiparameter data analysis in clinical trials,” Mat. Biol. Bioinformatika 11 (1), 46–63 (2016). https://doi.org/10.17537/2016.11.46
I. B. Gurevich and V. V. Yashina, “Operations of descriptive image algebras with one ring,” Pattern Recognit. Image Anal. 16, 298–328 (2006). https://doi.org/10.1134/s1054661806030035
D. Harrison and D. L. Rubinfeld, “Hedonic housing prices and the demand for clean air,” J. Environ. Econ. Manage. 5, 81–102 (1978). https://doi.org/10.1016/0095-0696(78)90006-2
P. Horton and K. Nakai, in A probablistic classification system for predicting the cellular localization sites of proteins (AAAI, 1996), pp. 109–115.
A. Mangal and N. Kumar, “Using big data to enhance the bosch production line performance: A Kaggle challenge,” in 2016 IEEE Int. Conf. on Big Data (Big Data), Washington, D.C., 2016 (IEEE, 2016), pp. 2029–2035. https://doi.org/10.1109/bigdata.2016.7840826
P. Karpovich, “Criteria of the k-singularity and division of 1-singular systems,” Moscow Univ. Comput. Math. Cybern. 34, 164–171 (2010). https://doi.org/10.3103/S0278641910040035
N. N. Kiselyova, V. A. Dudarev, V. V. Ryazanov, O. V. Sen’ko, and A. A. Dokukin, “Predictions of chalcospinels with composition ABCX4 (X–S or Se),” Perspektivnye Mater., No. 7, 5–18 (2020). https://doi.org/10.30791/1028-978x-2020-7-5-18
V.V. Krasnoproshin, “An optimal corrector for a set of recognition algorithms,” USSR Comput. Math. Math. Phys. 19, 209–220 (1979). https://doi.org/10.1016/0041-5553(79)90079-X
D. V. Kochetkov, “Recognition algorithms invariant with respect to transformations of attribute space,” Raspoznavanie, Klassifikatsiya, Prognoz. Mat. metody Ikh Primenenie, No. 1, 178–206 (1989).
N. V. Kovshov, V. L. Moiseev, and V. V. Ryazanov, “Algorithms for finding logical regularities in pattern recognition,” Comput. Math. Math. Phys. 48, 314–328 (2008). https://doi.org/10.1134/S0965542508020140
V. A. Kuznetsov, O. V. Sen’ko, A. V. Kuznetsova, L. P. Semenova, A. V. Aleshchenko, T. B. Gladysheva, and A. V. Ivshina, “Recognition of fuzzy systems by the method of statistically weighed syndromes and its application to immunohematological characterization of the norm and chronical pathology,” Chem. Phys. Rep. 15, 87–107 (1996).
S. B. Larin and V. V. Ryazanov, “The search of precedent-based logical regularities for recognition and data analysis problems,” Pattern Recognit. Image Anal. 7, 322–333 (1997).
Yu. P. Laptin, E. A. Nelyubina, V. V. Ryazanov, and A. P. Vinogradov, “Shape of basic clusters: Using analogues of hough transform in higher dimensions,” Pattern Recognit. Image Anal. 28, 653–658 (2018).
M. Leshno, V. Ya. Lin, A. Pinkus, and S. Schocken, “Multilayer feedforward networks with a nonpolynomial activation function can approximate any function,” Neural Networks 6, 861–867 (1993). https://doi.org/10.1016/s0893-6080(05)80131-5
O. L. Mangasarian and W. H. Wolberg, “Cancer diagnosis via linear programming,” SIAM News 23 (5), 1–18 (1990).
V. L. Matrosov, “Sintez optimal’nykh algoritmov v algebraicheskikh zamykaniyakh modelei algoritmov raspoznavaniya,” Raspoznavanie, Klassifikatsiya, Prognoz, Mat. Metody Ikh Primenenie, No. 1, 149–176 (1989).
V. L. Matrosov, “Correct algebras of recognition algorithms of limited capacity,” Doctoral Dissertation in Physics and Mathematics (Lenin State Pedagogical Inst., Moscow, 1985).
T. V. Plokhonina, “On the ill-posed nature of the algebraic closure of the second power of a set of algorithms for calculating estimates,” USSR Comput. Math. Math. Phys. 25, 74–79 (1985). https://doi.org/10.1016/0041-5553(85)90144-2
Y. F. Robert and E. Schapire, “A short introduction to boosting,” J. Jpn. Soc. Artif. Intell. 14, 771–780 (1999).
M. Yu. Romanov, “A method for constructing a recognition algorithm in algebra over an estimate calculation set,” Comput. Math. Math. Phys. 47, 1368–1372 (2007). https://doi.org/10.1134/S0965542507080143
M. Yu. Romanov, “Implementation of a method for constructing a recognition algorithm in algebra over an estimate calculation set,” Comput. Math. Math. Phys. 48, 1680 (2008). https://doi.org/10.1134/S0965542508090169
K. V. Rudakov, “On algebraic theory of universal and local constraints for classification problems,” Raspoznavanie, Klassifikatsiya, Prognoz. Mat. Metody Ikh Primenenie, No. 1, 176–201 (1989).
V. V. Ryazanov, “Logical regularities in pattern recognition (parametric approach),” Comput. Math. Math. Phys. 47, 1720–1735 (2007). https://doi.org/10.1134/S0965542507100120
V. V. Ryazanov, “On the optimization of a class of recognition models,” Pattern Recognit. Image Anal. 1, 108–118 (1991).
V. V. Ryazanov and V. A. Vorontchikhin, “About some approach for automatic knowledge extraction from precendent data,” in Proc. 7th Int. Conf. Pattern Recognition and Image Processing (2003), Vol. 2, pp. 35–40.
V. V. Ryazanov, “Recognition algorithms based on local optimality criteria,” Pattern Recognit. Image Anal. 4, 98–109 (1994).
V. V. Ryazanov and O. V. Sen’ko, “On some voting models and methods of their optimization,” Raspoznavanie, Klassifikatsiya, Prognoz, Mat. Metody Ikh Primenenie, No. 3, 106–145 (1990).
V. Ryazanov and A. Vinogradov, “Dealing with realizations of hidden regularities in data as independent generalized precedents,” in 2021 Int. Conf. on Information Technology and Nanotechnology (ITNT), Samara, 2021 (IEEE, 2021), Vol. 3, pp. 1–3. https://doi.org/10.1109/itnt52450.2021.9649168
O. V. Sen’ko, “The use of a weighted voting procedure on a system of basis sets in prediction problems,” Comput. Math. Math. Phys. 35, 1249–1257 (1995).
O. V. Senko and A. V. Kuznetsova, “A recognition method based on collective decision making using systems of regularities of various types,” Pattern Recognit. Image Anal. 20, 152–162 (2010). https://doi.org/10.1134/s1054661810020069
O. V. Sen’ko, N. N. Kiselyova, V. A. Dudarev, A. A. Dokukin, and V. V. Ryazanov, “Various machine learning methods efficiency comparison in application to inorganic compounds design,” CEUR Workshop Proc. 2277, 152–156 (2018).
V. V. Sherstnev, M. A. Gruden’, A. V. Kuznetsova, and O. V. Sen’ko, “Predictive risk model for prehypertension,” Byull. Eksp. Biol. Meditsiny 170, 660–664 (2020). https://doi.org/10.47056/0365-9615-2020-170-11-660-664
V. G. Sigillito, S. P. Wing, L. V. Hutton, and K. B. Baker, “Classification of radar returns from the ionosphere using neural networks,” Johns Hopkins APL Tech. Digest 10, 262–266 (1989).
M. N. Vaintsvaig, “Algorithm for learning pattern recognition ‘Bark’,” in Algorithms for Learning Pattern Recognition (Sovetskoe Radio, Moscow, 1973), pp. 8–12.
V. N. Vapnik, A. Ya, and Chervonenkis, Theory of Pattern Recognition (Statistical Learning Problems) (Nauka, Moscow, 1974).
A. M. Veshtort, Yu. A. Zuev, and V. V. Krasnoproshin, “Two-level recognition system with logic corrector,” Raspoznavanie, Klassifikatsiya, Prognoz. Mat. Metody Ikh Primenenie, No. 2, 73–98 (1989).
A. M. Veshtort, S. I. Kashkevich, S. B. Kostyukevich, V. V. Krasnoproshin, and S. G. Sinyakovich, “Principles for constructing the information automated system of aerospace spectrometry data for the purposes of physical-geographic zoning,” Izv. Akad. Nauk SSSR, Ser. Geogr., 89–94 (1988).
K. V. Vorontsov, “Combinatorial bounds for learning performance,” Dokl. Math. 69, 145–148 (2004).
K. V. Vorontsov, “Additive regularization for topic models of text collections,” Dokl. Math. 89, 301–304 (2014). https://doi.org/10.1134/S1064562414020185
Yu. I. Zhuravlev, “On algebraic approach to solving recognition and classification problems,” Probl. Kibernetiki 33, 5–68 (1978).
Yu. I. Zhuravlev and V. V. Nikiforov, “Recognition algorithms based on computing estimates,” Kibernetika, No. 3, 1–11 (1971).
Yu. I. Zhuravlev, “Correct algorithms over sets of ill-posed (heuristic) algorithms. I,” Kibernetika, No. 4, 5–17 (1977).
Yu. I. Zhuravlev, V. V. Ryazanov, and O. V. Sen’ko, Recognition: Mathematical Methods. Program System. Practical Applications (Fazis, Moscow, 2006).
Yu. Zhuravlev, Yu. Laptin, A. Vinogradov, N. Zhurbenko, and A. Likhovid, “Nonsmooth optimization methods in the problems of constructing a linear classifier,” Int. J. Inf. Models Anal. 1 (2), 103–111 (2012).
Yu. I. Zhuravlev, “Correct algorithms over sets of ill-posed (heuristic) algorithms. II,” Kibernetika, No. 6, 21–27 (1977).
Yu. I. Zhuravlev, “Correct algorithms over sets of ill-posed (heuristic) algorithms. III,” Kibernetika, No. 2, 35–43 (1978).
Yu. I. Zhuravlev and I. V. Isaev, “Construction of recognition algorithms correct for a given control sample,” USSR Comput. Math. Math. Phys. 19, 175–189 (1979). https://doi.org/10.1016/0041-5553(79)90138-1
Yu. I. Zhuravlev, G. I. Nazarenko, A. P. Vinogradov, A. A. Dokukin, N. N. Katerinochkina, E. B. Kleimenova, M. V. Konstantinova, V. V. Ryazanov, O. V. Sen’ko, and A. M. Cherkashov, “Methods for discrete analysis of medical data on the basis of recognition theory and some of their applications,” Pattern Recognit. Image Anal. 26, 643–664 (2016). https://doi.org/10.1134/s105466181603024x
Yu. A. Zuev, “A method of improving classification reliability when several classifiers are available, based on the principle of monotonicity,” USSR Comput. Math. Math. Phys. 21, 156–166 (1981). https://doi.org/10.1016/0041-5553(81)90141-5
Funding
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
Aleksandr Petrovich Vinogradov. Born in 1951. MSc degree in physics from the Applied Mathematics and Control Department of Moscow Institute of Physics and Technology, 1974. Doctor in mathematical cybernetics, 1978. Senior Researcher at Dorodnicyn Computing Centre, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences. Author of about 70 scientific papers. Research interests: algebraic and geometrical methods in pattern recognition, image analysis, and processing.
Alexander Gennadjevich D’yakonov. Born in 1979. Doctor of Physical and Mathematical Sciences, Professor of Moscow State University. Multiple winner of international competitions in data science, winner of the first place in the Kaggle ranking of data scientists. Author of three books and more than 80 scientific papers.
Alexander Alexandrovich Dokukin. Born in 1980. Senior researcher at Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences. He graduated with honors from the Faculty of Mathematics and Computer Science at Moscow State University in 2002. In 2005, he completed his postgraduate studies at the same faculty. In 2008, he defended his dissertation for the degree of Candidate of Physical and Mathematical Sciences on the topic “Synthesis of polynomials over extreme algorithms for computing estimates.” Since 2000 he has been working at the Dorodnicyn Research Center of the Russian Academy of Sciences (then the Research Center of the FRC IS RAS). Research interests: pattern recognition and data analysis. He has written and co-authored more than one hundred scientific papers.
Vladimir Vasiljevich Ryazanov. Born in 1950. Graduated from Moscow Institute of Physics and Technology in 1973. He defended his Candidate’s dissertation in 1977 and his Doctoral dissertation in 1994. He has been a full member of the Russian Academy of Natural Sciences since 1998 and a professor since 2008. Since 1976 he has been working at the Computing Center of the Russian Academy of Sciences. Currently, he is the Head of the Department of Data Classification and Analysis Methods at Dorodnicyn Computing Center of the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences. Author of 208 publications. Research interests: methods of optimization of recognition models, algorithms for searching for and processing logical patterns of classes by precedents, mathematical models of recognition based on voting on sets of logical patterns of classes, committee synthesis of collective clustering and construction of stable solutions in clustering problems, restoration of gaps in data, restoration of regressions on sets of recognition algorithms, creation of software classification systems, and solving practical problems in medicine, technology, chemistry, and other fields.
Oleg Valentinovich Senko. Born in 1957. Graduated from Moscow Institute of Physics and Technology in 1981. In 2007 he defended his dissertation on “Empirical forecasting methods based on stable partitions and collective solutions.” His research interests include methods of machine learning and data mining, as well as their practical applications. Currently he is a leading researcher at the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences. He is the author of more than 120 scientific articles.
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Vinogradov, A.P., D’yakonov, A.G., Dokukin, A.A. et al. Recognition Methods in Academician Yu.I. Zhuravlev’s Scientific School. Pattern Recognit. Image Anal. 33, 952–982 (2023). https://doi.org/10.1134/S1054661823040521
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1054661823040521