Linear Binary Classification of Data with Interval Uncertainty
- 作者: Erokhin V.I.1, Kadochnikov A.P.1, Sotnikov S.V.1
-
隶属关系:
- A. F. Mozhaisky Military-Space Academy of Ministry of Defence of the Russian Federation
- 期: 编号 3 (2023)
- 页面: 76-83
- 栏目: Optimal and Rational Choice
- URL: https://bakhtiniada.ru/2071-8594/article/view/270345
- DOI: https://doi.org/10.14357/20718594230308
- ID: 270345
如何引用文章
全文:
详细
The problem of linear binary separation of finite interval sets (classes) is considered. Using the theory of interval systems of linear inequalities, the problem is reduced to the problem of finding a solution to a system of linear inequalities of a special form. In turn, the problem of finding a quasioptimal solution to the specified system (or a pseudo-solution in the case of its incompatibility and linear inseparability of classes) is reduced to problems of unconditional minimization. Illustrative numerical examples are given.
全文:

作者简介
Vladimir Erokhin
A. F. Mozhaisky Military-Space Academy of Ministry of Defence of the Russian Federation
编辑信件的主要联系方式.
Email: erohin_v_i@mail.ru
Doctor of physical and mathematical sciences, professor. Senior researcher
俄罗斯联邦, St. PetersburgAndrey Kadochnikov
A. F. Mozhaisky Military-Space Academy of Ministry of Defence of the Russian Federation
Email: kado162@mail.ru
Candidate of technical sciences. Head of laboratory
俄罗斯联邦, St. PetersburgSergey Sotnikov
A. F. Mozhaisky Military-Space Academy of Ministry of Defence of the Russian Federation
Email: svsotnikov@gmail.com
Candidate of technical sciences. Senior researcher
St. Petersburg参考
- Vapnik V.N., Chervonenkis A.Ya. 1974. Teoriya raspoznavaniya obrazov (statisticheskie problemy obucheniya) [Pattern recognition theory (statistical learning problems)]. Moscow: Nauka. 416 p.
- Vorontsov K.V. Lektsii po linejnym algoritmam klassifikatsii [Lectures on linear classification algorithms]. 2009. URL: http://www. machinelearning. ru/wiki/images/6/68/voron-ML-Lin.pdf (accessed January 20, 2023).
- Deisenroth M. P., Faisal A. A., Ong C. S. 2020. Mathematics for machine learning. Cambridge University Press. URL: https://mml-book.com (accessed January 20, 2023).
- Voshchinin A.P. Zadachi analiza s neopredelennyi dannymi – interval'nost' i/ili sluchajnost'? [Problems of analysis with uncertain data – interval and/or randomness?] // Proceedings of International Conference on Computational Mathematics IICM-2004. Workshops / Eds.: Yu. I. Shokin, A.M. Fedotov, S.P. Kovalyov, et al. – Novosibirsk: ICM&MG Publ., 2004.
- Utkin L.V., Zhuk Yu.A., Selikhovkin I.A. Model' klassifikatsii na osnove nepolnoj informatsii o priznakakh v vide ikh srednikh znachenij [Classification model based on incomplete information about signs in the form of their average values] // Iskusstvennyj intellekt i prinyatie reshenij [Artificial intelligence and decision making]. 2012. V. 2. P. 16-26.
- Fiedler M., Nedoma J., Ramnik J. et al. Linear Optimization Problems with Inexact Data. N.Y.: Springer Science+Business Media, Inc. 2006.
- Bennett K.P., Campbell C. Support vector machines: hype or hallelujah? ACM SIGKDD explorations newsletter. 2000. V. 2. No 2. P. 1-13.
- Moguerza J.M., Muñoz A. Support vector machines with applications. Statistical Science. 2006. V. 21. No 3. P. 322-336.
- Carrizosa E., Morales D.R. Supervised classification and mathematical optimization. Computers & Operations Research. 2013. V. 40. No 1. P. 150-165.
- Silva A.P.D. Optimization approaches to supervised classification. European Journal of Operational Research. 2017. V. 261. No 2. P. 772-788.
- Nueda M.J., Gandí, C, Molina M.D. LPDA: A new classification method based on linear programming // PLoS ONE. 2022. V. 17. No 7. P. 1-13.
- Sevakula R.K., Verma N.K. Improving Classifier Generalization: Real-Time Machine Learning based Applications // Studies in Computational Intelligence. Springer Nature. 2022. V. 989. 166 p.
- Lankaster P. Theory of matrices. New York-London: Academic Press. 1969.
- Gorelik V.A., Murav'eva O.V. Postroenie razdelyayushchej giperploskosti, ustojchivoj k korrektsii dannykh [Construction of a separating hyperplane, resistant to data correction] // Modelirovanie, dekompozitsiya i optimizatsiya slozhnykh dinamicheskikh protsessov [Modeling, Decomposition and Optimization of Complex Dynamic Processes] 2013. V.28. No 1. P. 42-49.
- Murav'eva O.V. Studying the stability of solutions to systems of linear inequalities and constructing separating hyperplanes. // Journal of applied and industrial mathematics. 2014. V. 8. No 3. P. 349-356.
- Murav'eva O.V. Parametricheskaya ustojchivost' sistem linejnykh neravenstv [Parametric stability of systems of linear inequalities] // Tavricheskij vestnik informatiki i matematiki [Tauride Bulletin of Informatics and Mathematics] 2015. V.2. No 27. P. 101-109.
补充文件
