Scientific Part
Computer Sciences

Dendrograms of electroencephalograms and their characterization based on metrics

L. B. Tyapaev^a, V. S. Anashin<sup>bc

a</sup> Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia
^b Lomonosov Moscow State University, GSP-1 Leninskie Gory, Moscow 119991, Russia
^c Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44, bldg. 2 Vavilova St., Moscow 119333, Russia

Abstract: Dendrograms obtained from electroencephalograms are studied as maximal prefix codes. A dendrogram defines a distribution on the space of 2-adic integers and represents a partition, up to the set of zero Haar measure, into balls of nonzero radii. Non-Archimedean and Archimedean metrics are proposed for the characterization of dendrograms associated with the electroencephalograms of given mental classes. To more reliably distinguish one mental class from another, it is proposed to use the Gromov – Hausdorff distance between disconnected compact spaces: non-Archimedean in the form of a union of 2-adic balls represented by branches of a dedrogram, on the one hand, and Archimedean in the form of a (fat) Cantor set, on the other hand.

Key words: EEG dendrogram, maximal prefix code, 2-adic integers, ultrametric, metric space of dendrograms, characteristic distribution function, 2-adic ball, Gromov – Hausdorff distance.

UDC: 519.237.8

Received: 12.02.2025
Revised: 19.03.2025

DOI: 10.18500/1816-9791-2025-25-3-434-441