Resumen

BATYRSHIN, Ildar Z.. Correlation Functions over Sets with Involutions. Comp. y Sist. [online]. 2024, vol.28, n.4, pp.1955-1960.  Epub 25-Mar-2025. ISSN 2007-9737.  https://doi.org/10.13053/cys-28-4-5218.

In recent years, it has been shown that many correlation and association coefficients used in statistics can be viewed as functions defined on a set with an involution operation. In this case, the involution can be thought of as a mapping of elements of a set into “opposite” elements, with the correlation between mutually opposite elements being -1. The methods constructing such correlation functions using similarity and dissimilarity functions defined over a set with involution have been proposed, and many known in statistics correlation and association coefficients have been constructed in such a way. It was shown that these correlation functions can be obtained by rescaling bipolar similarity functions; for this reason, they are referred to as similarity correlation functions. The paper reconsiders and summarizes some basic results on methods of constructing correlation functions on sets with involution called here involutive sets. The considered methods can be used for constructing new correlation functions on sets with involution if a suitable similarity or dissimilarity function is defined.

Palabras llave : Correlation; association; similarity; distance; involution.