A version of cluster analysis that eliminates cluster as an inexact concept (Q1380255)

As is well known, so-called cluster analysis, or the method of pattern recognition ``without training'', is a fairly miscellaneous collection of mathematical and algorithmic methods for classifying objects of a set. Its character, for the most part prescribed, is stipulated by a lack of rigor in the very concept of a cluster, i.e., of an accumulation of points selected by certain criteria in a set of points. To choose a concrete mathematical formalism, one invokes intuitive arguments; only in some cases is this choice justified more or less rigorously. We consider cluster analysis as a problem of constructing planar gradual mappings of some properties of a multivariate finite distribution of points. We show that this approach allows one to define a version of cluster analysis in which the concept of a cluster is not essential.