Clustering models

It is generally accepted that the term “clusterization” (bunch, bundle) was offered by the mathematician R. Trion. Subsequently, a number of terms emerged that are considered synonymous with the term “cluster analysis” or “automatic classification.” Cluster analysis has a very wide range of applications, its methods are used in medicine, chemistry, archeology, marketing, geology, and other disciplines. Clustering consists in grouping similar objects into groups, and this problem is one of the fundamental problems in the field of data analysis. Usually, clustering means the partitioning 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 ones fall into different groups. As will be shown below, this requirement is rather contradictory. Intuitive partitioning “by eye” uses the connectivity of the resulting groups, based on the density of distribution of points. In this paper, we offer a method of clusterization based on this idea.