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Microsystems, Electronics and Acoustics
ISSN 2523-4447 · e‑ISSN 2523-4455 Open Access · CC BY-SA 4.0
Vol. 30 · Issue 3 · 2025 Dec 23, 2025 Electronic Systems and Signals

Clustering Method Using Cardinal Number Vectors

OA
Olena Olehivna Abakumova Corresponding Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського» Ukraine
VZ
Valerii Yakovych Zhuikov Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського» Ukraine
ML
Mykola O. Lukianov Політехніка Гданська Poland
Pages344933.1-344933.7 PublishedDec 23, 2025
PDF (Ukrainian)
VOL 30 · ISS 3 · 2025 View issue

Abstract

In modern technical systems, clustering serves as a key procedure for structuring, analyzing, and interpreting large volumes of data, which in turn enhances decision-making efficiency and the optimization of system processes. This study presents a comparative analysis of the main groups of clustering methods and proposes a novel approach based on the powerful mathematical framework of cardinal numbers. The theoretical foundations for constructing cardinal number vectors are revealed, positioning them as a mathematical tool for data representation in clustering tasks. The proposed approach defines object distances within a selected orthogonal basis using the calculated cardinalities of abstract set sequences represented as vectors of cardinal numbers. The study explores the formation of these vectors and the computation of corresponding similarity metrics, followed by the generation of a distance matrix. A practical example illustrates the calculation of distances between three functions and a reference function based on their respective cardinal number vectors. It is demonstrated that altering the basis or projections according to the technical problem allows for the formation of different clusters, reflecting the flexibility and adaptability of the proposed method. The calculations are formalized, straightforward, and easily algorithmized, which enables the implementation of dynamic clustering. This approach holds significant promise for use in intelligent data analysis systems and information processing in electronic devices.

Keywords

#clustering #vectors #cardinal numbers #similarity metric #local object #orthonormal basis

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