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Formation of Machine Learning Features Based on the Construction of Tropical Functions Научная публикация

Журнал

Моделирование и анализ информационных систем
ISSN: 1818-1015 , E-ISSN: 2313-5417

Вых. Данные

Год: 2022, Том: 29, Номер: 3, Страницы: 200-209 Страниц : 10 DOI: 10.18255/1818-1015-2022-3-200-209

Ключевые слова

persistent homology, persistent landscape, machine learning, Hilbert space, tropical functions

Авторы

Chukanov Sergey N. ¹ , Chukanov Ilya S. ²

Организации

1	Sobolev Institute of Mathematics, SB RAS, Omsk branch, 13 Pevtsova str., Omsk, 644043, Russia
2	Ural Federal University named after the First President of Russia B. N. Yeltsin, st. Mira, 19, Yekaterinburg, Sverdlovsk Oblast, Russia

Информация о финансировании (2)

1	Российский научный фонд	22-21-00035
2	Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН».	0314-2019-0020

One of the main methods of computational topology and topological data analysis is persistent homology, which combines geometric and topological information about an object using persistent diagrams and barcodes. The persistent homology method from computational topology provides a balance between reducing the data dimension and characterizing the internal structure of an object. Combining machine learning and persistent homology is hampered by topological representations of data, distance metrics, and representation of data objects. The paper considers mathematical models and functions for representing persistent landscape objects based on the persistent homology method. The persistent landscape functions allow you to map persistent diagrams to Hilbert space. The representations of topological functions in various machine learning models are considered. An example of finding the distance between images based on the construction of persistent landscape functions is given. Based on the algebra of polynomials in the barcode space, which are used as coordinates, the distances in the barcode space are determined by comparing intervals from one barcode to another and calculating penalties. For these purposes, tropical functions are used that take into account the basic structure of the barcode space. Methods for constructing rational tropical functions are considered. An example of finding the distance between images based on the construction of tropical functions is given. To increase the variety of parameters (machine learning features), filtering of object scanning by rows from left to right and scanning by columns from bottom to top are built. This adds spatial information to topological information. The method of constructing persistent landscapes is compatible with the approach of constructing tropical rational functions when obtaining persistent homologies.

Chukanov S.N. , Chukanov I.S.
Formation of Machine Learning Features Based on the Construction of Tropical Functions
Моделирование и анализ информационных систем. 2022. V.29. N3. P.200-209. DOI: 10.18255/1818-1015-2022-3-200-209 РИНЦ OpenAlex

Поступила в редакцию:	5 июн. 2022 г.
Опубликована в печати:	24 сент. 2022 г.
Опубликована online:	24 сент. 2022 г.

РИНЦ:	49448407
OpenAlex:	W4297145332

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