chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2022-23-5-227-240cheb-1420Research ArticleИстория математики и приложенийСomputer scienceРаспознавание аномалий неизвестного заранее типаRecognition of anomalies of an a priori unknown typeИвановАлександр ОлеговичIvanovAlexander Olegovich

доктор физико-математических наук, профессор

doctor of physical and mathematical sciences, professor

aoiva@mech.math.msu.suНосовскийГлеб ВладимировичNosovskyGleb Vladimirovich

кандидат физико-математических наук, доцент

candidate of physical and mathematical sciences, associateprofessor

gleb_nosovskiy@mail.ruКибкалоВладислав АлександровичKibkaloVladislav Alexandrovich

кандидат физико-математических наук

candidate of physical and mathematical sciences

slava.kibkalo@gmail.comНикулинМихаил АлександровичNikulinMikhail Alexandrovich

аспирант

postgraduate student

nikmihale@gmail.comПопеленскийФедор ЮрьевичPopelenskyFyodor Yurievich

кандидат физико-математических наук

candidate of physical and mathematical sciences

popelens@mech.math.msu.suФедосеевДенис АлександровичFedoseevDenis Alexandrovich

кандидат физико-математических наук

candidate of physical and mathematical sciences

denfedex@yandex.ruГрибушинИван ВладимировичGribushinIvan Vladimirovich

ведущий инженер

lead engineer

ivangribushin@yandex.ruЗлобинВалерий ВалерьевичZlobinValery Valerievich

ведущий инженер ключевых проектов

leading engineer of key projects

hello.valera@gmail.comКузинСергей СергеевичKuzinSergey Sergeevich

ведущий инженер

leading engineer

serkuz23@ya.ruМазуренкоИван ЛеонидовичMazurenkoIvan Leonidovich

кандидат физико-математических наук, заведующий лабораторией интеллектуальных систем и науки о данных HUAWEI

candidate of physical and mathematical sciences, Head of the Laboratory of Intelligent Systems and Data Science HUAWEI

ivan@mazurenko.ruМосковский государственный университет им. М. В. ЛомоносоваРоссияLomonosov Moscow State UniversityRussian FederationМосковский государственный университет им. М. В. Ломоносова; Московский центр фундаментальной и прикладной математикиРоссияLomonosov Moscow State University; Moscow Center for Fundamental and Applied MathematicsRussian FederationООО «Техкомпания Хуавей»РоссияLLC «Huawei Tech Company»Russian FederationМосковский государственный университет им. М. В. Ломоносова; , ООО «Техкомпания Хуавей»РоссияLomonosov Moscow State University; LLC «Huawei Tech Company»Russian Federation202217012023235227240Copyright © Иванов А.О., Носовский Г.В., Кибкало В.А., Никулин М.А., Попеленский Ф.Ю., Федосеев Д.А., Грибушин И.В., Злобин В.В., Кузин С.С., Мазуренко И.Л., 20232023Иванов А.О., Носовский Г.В., Кибкало В.А., Никулин М.А., Попеленский Ф.Ю., Федосеев Д.А., Грибушин И.В., Злобин В.В., Кузин С.С., Мазуренко И.Л.Ivanov A.O., Nosovsky G.V., Kibkalo V.A., Nikulin M.A., Popelensky F.Y., Fedoseev D.A., Gribushin I.V., Zlobin V.V., Kuzin S.S., Mazurenko I.L.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/1420

В работе предложена модификация метода PaDiM детекции аномалий, сопоставляющему изображению вектор и вычисляющему расстояние Махаланобиса от такого векторадо распределения векторов обучающего множенства. Выделяется подмножество тех координатных осей векторов, распределение вдоль которых наименее близко к нормальному в сравнении с остальными по выбранному статистическому критерию. Применение к этим координатам векторов процедуры выпрямления (униформизации) перед вычислением расстояния Махаланобиса повышает значение ROCAUC метода PaDiM.

In the present article we propose a modification of the PaDiM anomaly detection method which maps images to vectors and then calculates the Mahalanobis distance between such vectors and the distribution of the vectors of the training set. Of the coordinate axes of the vectors we choose a subset of such that the distribution along them is close to normal according to the chosen statistical criterion. The uniformization procedure is then applied to those coordinates and the Mahalanobis distance is calculated. This approach is shown to increase the ROCAUC value in comparison with the PaDiM method.

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The authors declare that there are no conflicts of interest present.