Informatics and Applications
2024, Volume 18, Issue 1, pp 71-77
ON THE GENERATION OF SYNTHETIC FEATURES BASED ON SUPPORT CHAINS AND ARBITRARY METRICS WITHIN A TOPOLOGICAL APPROACH TO DATA ANALYSIS.
PART 1. INCLUSION OF EMPIRICAL DISTANCE FUNCTIONS INTO THE FORMALISM
Abstract
The analysis of the formalism of topological recognition theory based on the fundamental concepts of functional analysis made it possible to propose previously unexplored approaches to determining lattice estimates. In particular, the use of support chains for the analysis of Boolean lattices formed over Zhuravlev-regular sets of precedents has pointed to a new direction of research which consists in replacing estimates of lattice elements with certain types of functions and/or vectors. This extension of the formalism also allows for a systematic study of semiempirical distance functionals known in the literature to solve applied problems. Promising directions for further development of the formalism are substantiated including the functionals reducing descriptions of sets of a Boolean lattice to scalars and the development of a mathematical apparatus for the analysis of lattices where operations on the corresponding functions are involved. The latter direction is interesting as it allows defining lattice metrics without using lattice estimates.
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[+] About this article
Title
ON THE GENERATION OF SYNTHETIC FEATURES BASED ON SUPPORT CHAINS AND ARBITRARY METRICS WITHIN A TOPOLOGICAL APPROACH TO DATA ANALYSIS. PART 1. INCLUSION OF EMPIRICAL DISTANCE FUNCTIONS INTO THE FORMALISM
Journal
Informatics and Applications
2024, Volume 18, Issue 1, pp 71-77
Cover Date
2024-04-10
DOI
10.14357/19922264240110
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
topological data analysis; lattice theory; algebraic approach by Yu. I. Zhuravlev; functional analysis
Authors
I. Yu. Torshin 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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