Abstract:
We describe similarity measures among objects in metric and competitive spaces. We propose a competitive similarity function as a similarity measure used in classification and pattern recognition problems. This function enables us to construct some efficient algorithms for solving all main data mining problems, to obtain quantitative estimates for the compactness of images and the informativeness of trait spaces, and to construct easily interpretable decision rules. The method applies to problems with arbitrary numbers of images and characters of their distributions, and can also be used for solving poorly conditioned problems.
Citation:
N. G. Zagoruǐko, I. A. Borisova, V. V. Dyubanov, O. A. Kutnenko, “A quantitative measure of compactness and similarity in competitive space”, Sib. Zh. Ind. Mat., 13:1 (2010), 59–71; J. Appl. Industr. Math., 5:1 (2011), 144–154
\Bibitem{ZagBorDyu10}
\by N.~G.~Zagoru{\v\i}ko, I.~A.~Borisova, V.~V.~Dyubanov, O.~A.~Kutnenko
\paper A~quantitative measure of compactness and similarity in competitive space
\jour Sib. Zh. Ind. Mat.
\yr 2010
\vol 13
\issue 1
\pages 59--71
\mathnet{http://mi.mathnet.ru/sjim596}
\transl
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 1
\pages 144--154
\crossref{https://doi.org/10.1134/S1990478911010157}
Linking options:
https://www.mathnet.ru/eng/sjim596
https://www.mathnet.ru/eng/sjim/v13/i1/p59
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O. A. Kutnenko, “Computational Complexity of Two Problems of Cognitive Data Analysis”, J. Appl. Ind. Math., 16:1 (2022), 89
O. A. Kutnenko, A. V. Plyasunov, “NP-hardness of some data cleaning problem”, J. Appl. Industr. Math., 15:2 (2021), 285–291
R. P. Bohush, S. V. Ablameyko, E. R. Adamovskiy, D. Savca, “Image Similarity Estimation Based on Ratio and Distance Calculation between Features”, Pattern Recognit. Image Anal., 30:2 (2020), 147
Ignatyev A.N., Mirzaev I A., “Selection of Features Into the Object'S Own Space Based on the Measure of Its Compactness”, Int. J. Geotech. Earthq., 2019, no. 49, 55–62
Gritsay A.S., Makarov V.V., Khamitov R.N., Tatevosyan A.A., Gritsay S.N., “The Method of Short-Term Forecast Electricity Load With Combined a Sinusoidal Function and An Artificial Neural Network”, Proceedings of the 2019 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (Eiconrus), IEEE Nw Russia Young Researchers in Electrical and Electronic Engineering Conference, IEEE, 2019, 523–526
Aleksandr S. Gritsay, Vladimir V. Makarov, Rustam N. Khamitov, Andrey A. Tatevosyan, Sergey N. Gritsay, 2019 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), 2019, 523
Potapov V., Khamitov R., Makarov V., Gritsay A., Florensov A., Tyunkov D., 2018 12Th International IEEE Scientific and Technical Conference on Dynamics of Systems, Mechanisms and Machines (Dynamics), Dynamics of Systems Mechanisms and Machines, ed. Kosykh A., IEEE, 2018
Viktor Potapov, Rustam Khamitov, Vladimir Makarov, Aleksandr Gritsay, Aleksandr Florensov, Denis Tyunkov, 2018 Dynamics of Systems, Mechanisms and Machines (Dynamics), 2018, 1
Alyamkin S.A., Nikolenko N.A., Pavlovskiy E.N., Dyubanov V.V., “Fris-Censoring of Reference Sample in Face Recognition Task By Deep Neural Networks”, 2017 Siberian Symposium on Data Science and Engineering (Ssdse), IEEE, 2017, 41–43
Maria A. Ivanchuk, Igor V. Malyk, “Building Expert Medical Prognostic Systems Using Voronoi Diagram”, International Journal of Computational Mathematics, 2015 (2015), 1
Volchenko E.V., “Klassifikatsiya ob'ektov v adaptivnykh sistemakh raspoznavaniya na osnove funktsii vzveshennogo konkurentnogo skhodstva”, Vestnik natsionalnogo tekhnicheskogo universiteta kharkovskii politekhnicheskii institut. seriya: informatika i modelirovanie, 2012, no. 62, 18–25
Objects classification based on the function of rival similarity in adaptive recognition systems
S. N. Ganebnykh, M. M. Lange, D. Yu. Stepanov, “Metric classifier using multilevel network of templates”, Pattern Recognit. Image Anal., 22:2 (2012), 265
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