Relationship in Metric Classification Algorithms and Analysis of its Properties

Abstract

The relationship between class objects is considered for analyzing the cluster structure of the training dataset. The uniqueness of the solution to the problem of minimal coverage of the training set by prototypes is discussed. Interest in the uniqueness issue is associated with the use of either a base metric as a distance measure for all objects or local metrics derived from the base one. The specific structure of object relationships is reflected in the non-spherical shape of the cluster configurations. For such clusters, no established quality assessments exist. The property of connectivity is explored and its application as a source of new knowledge during the construction of information models in specific subject areas is studied. The connectivity property is proposed to be evaluated through the search for the most distant cluster objects using Dijkstra’s algorithm. The input data is an adjacency matrix constructed based on the intersection information of hyperspheres centered at the cluster objects. The radii of these hyperspheres are defined as the distances to the nearest objects of the opposite classes. Examples of quantitative characteristics of clusters and their possible areas of application are provided. One such characteristic is the cluster curvature coefficient.