Bigroup algebras and potter's theorem

Cluster analysis has a very wide range of applications; its methods are used in medicine, chemistry, archeology, marketing, geology and other disciplines. Clustering consists of grouping similar objects together, and this task is one of the fundamental tasks in the field of data mining. Usually, clustering is understood as a partition of a given set of points of a certain metric space into subsets in such a way that close points fall into one group, and distant points fall into different ones. In this paper, we offer a local averaging method for calculating the distribution density of data as points in a metric space. Choosing further sections of the set of points at a certain level of density, we get a partition into clusters. The proposed method offers a stable partitioning into clusters and is free from a number of disadvantages inherent in known clustering methods.