Informacionnye TehnologiiInformacionnye TehnologiiИнформационные технологии1684-6400New Technologies Publishing House70838610.17587/it.32.294-299Modeling and optimizationМоделирование и оптимизацияResearch ArticleApplication of codes in modular metrics for searching for k-neighborsПрименение кодов в модульной метрике для поиска k ближайших соседейSharapovA. R.ШараповА. Р.
Russian Federation

Postgradient Student

аспирант

arsharapov@hse.ruDavydovV. A.ДавыдовВ. А.
Russian Federation

Cand. of Tech. Sc., Cand. of Econ. Sc., Associate Professor

канд. техн. наук, канд. экон. наук, доц.

v.davydov@hse.ruNational Research University Higher School of EconomicsНациональный исследовательский университет "Высшая школа экономики"090620263262942990806202608062026Copyright ©; 2026, Informacionnye TehnologiiCopyright ©; 2026, Информационные технологии2026Informacionnye TehnologiiИнформационные технологииhttps://journals.eco-vector.com/1684-6400/article/view/708386

This paper examines the application of error-correcting codes in the modular metric to solving the problem of object identification on a set of D-dimensional vectors in a base-Q number system using the k-neighbor method. The training set is preprocessed using a clustering method that decodes all training set vectors with a selected code in the modular metric.

Рассматривается применение кодов, исправляющих ошибки в модульной метрике, для решения задачи идентификации объекта на множестве системы исчисления с основанием Q векторов размерности D методом k ближайших соседей. В качестве предварительной обработки обучающей выборки используется метод кластеризации, использующий процедуру декодирования всех векторов обучающей выборки выбранным кодом в модульной метрике.

k-nearest neighbors methodmetricsclusteringcodes in modular metricvectorметод k ближайших соседейметрикикластеризациякоды в модульной метрикевекторFix E., Hodges J. L. Discriminatory analysis. Nonparametric discrimination; consistency properties, Technical Report 4, USAF School of Aviation Medicine, 1951.Fix E., Hodges J. L. Discriminatory analysis. Nonparametric discrimination; consistency properties // Technical Report 4. USAF School of Aviation Medicine. 1951.Cover T., Hart P. Nearest neighbor pattern classification, IEEE Transactions on Information Theory, 1967, vol. 13, no. 1, pp. 21—27, DOI: 10.1109/tit.1967.1053964.Cover T., Hart P. Nearest neighbor pattern classification // IEEE Transactions on Information Theory. 1967. Vol. 13, N. 1. P. 21—27. DOI: 10.1109/tit.1967.1053964.Wu X., Kumar V., Quinlan J. R., Ghosh J., Yang Q., Motoda Н. Top 10 algorithms in data mining, Knowledge and Information Systems, 2008, vol. 14, no. 1, pp. 1—37, DOI: 10.1007/s10115-007-0114-2.Wu X., Kumar V., Quinlan J. R., Ghosh J., Yang Q., Motoda Н. Top 10 algorithms in data mining // Knowledge and Information Systems. 2008. Vol. 14, N. 1. P. 1—37. DOI: 10.1007/s10115-007-0114-2.Mulak P., Talhar N. Analysis of Distance Measures Using K-Nearest Neighbor Algorithm on KDD Dataset, International Journal of Science and Research (IJSR), 2015, vol. 4, no. 7, pp. 2101—2104.Mulak P., Talhar N. Analysis of Distance Measures Using K-Nearest Neighbor Algorithm on KDD Dataset // International Journal of Science and Research (IJSR). 2015. Vol. 4, N. 7. P. 2101—2104.Aggarwal C. C., Hinneburg A., Keim D. A. On the Surprising Behavior of Distance Metrics in High Dimensional Space, Database Theory — ICDT, Lecture Notes in Computer Science, 2001, vol. 1973, DOI: 10.1007/3-540-44503-X_27.Aggarwal C. C., Hinneburg A., Keim D. A. On the Surprising Behavior of Distance Metrics in High Dimensional Space // Database Theory — ICDT. Lecture Notes in Computer Science. 2001. Vol. 1973. DOI: 10.1007/3-540-44503-X_27.Kataria A., Singh M. D. А Review of Data Classification Using K-Nearest Neighbor Algorithm, International Journal of Emerging Technology and Advanced Engineering, 2013, vol. 3, no. 6, pp. 354—360.Kataria A., Singh M. D. А Review of Data Classification Using K-Nearest Neighbor Algorithm // International Journal of Emerging Technology and Advanced Engineering. 2013. Vol. 3, N. 6. P. 354—360.Xu S., Wu Y. An algorithm for remote sensing image classification based on artificial immune В-cell network, The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2008, vol. 37, pp. 107—112.Xu S., Wu Y. An algorithm for remote sensing image classification based on artificial immune В-cell network // The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. 2008. Vol. 37. P. 107—112.Manne S., Kotha S., Fatima S. S. Text categorization with K-nearest neighbor approach, Proceedings of the International Conference on Information Systems Design and Intelligent Applications, 2012, vol. 132, pp. 413—420, DOI: 10.1007/978-3-642-27443-5_47.Manne S., Kotha S., Fatima S. S. Text categorization with K-nearest neighbor approach // Proceedings of the International Conference on Information Systems Design and Intelligent Applications. 2012. Vol. 132. P. 413—420. DOI: 10.1007/978-3-642-27443-5_47.Xiubo G., Tie-Yan L., Qin T., Andrew A., Li H., Shum H.-Y. Query dependent ranking using k-nearest neighbor, Proceedings of the 31st Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, 2008, pp. 115—122, DOI: 10.1145/1390334.1390356.Xiubo G., Tie-Yan L., Qin T., Andrew A., Li H., Shum H.-Y. Query dependent ranking using k-nearest neighbor // Proceedings of the 31st Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. 2008. P. 115—122. DOI: 10.1145/1390334.1390356.Bajramovic F., Mattern F., Butko N., Denzler J. А comparison of nearest neighbor search algorithms for generic object recognition, Advanced Concepts for Intelligent Vision Systems, 2006, pp. 1186—1197, DOI: 10.1007/11864349_108.Bajramovic F., Mattern F., Butko N., Denzler J. А comparison of nearest neighbor search algorithms for generic object recognition // Advanced Concepts for Intelligent Vision Systems. 2006. P. 1186—1197. DOI: 10.1007/11864349_108.Yang Y., Ault T., Pierce T., Lattimer C. W. Improving text categorization methods for event tracking, Proceedings of the 23rd Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, 2000, pp. 65—72, DOI: 10.1145/345508.345550.Yang Y., Ault T., Pierce T., Lattimer C. W. Improving text categorization methods for event tracking // Proceedings of the 23rd Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. 2000. P. 65—72. DOI: 10.1145/345508.345550.Davydov V. A. Codes that correct errors in the modular metric, the Lee metric, and operator errors, Problemy peredachi informatsii, 1993, vol. 29, no. 3, pp. 10—20 (in Russian).Давыдов В. А. Коды, исправляющие ошибки в модульной метрике, метрике Ли и ошибки оператора // Проблемы передачи информации. 1993. Т. 29, № 3. С. 10—20.Davydov V., Zeulin N., Pastushok I., Turlikov А. Coding Scheme for High-Order QAM Modulations in the Manhattan Metric, IEEE Communications Letters, 2020, vol. 24, no. 11, pp. 2387—2391, DOI: 10.1109/lcomm.2020.3010474.Davydov V., Zeulin N., Pastushok I., Turlikov А. Coding Scheme for High-Order QAM Modulations in the Manhattan Metric // IEEE Communications Letters. 2020. Vol. 24, N. 11. P. 2387—2391. DOI: 10.1109/lcomm.2020.3010474.