The Principle of Class Separation and the Dependence of Clustering Results on the Distance Measure

Abstract

The article considers a methodology for cluster analysis of multidimensional objects based on the calculation of local density, the initial division of objects into two classes K₁ and K₂, the identification of boundary objects, the adjustment of class composition, and subsequent grouping according to the connectivity relation. The influence of the initial partitioning rule and the selected distance measure on the resulting clustering structure is investigated. The partitioning rules used are partitioning based on the mean local density and median partitioning of an ordered sequence of density values. For comparative analysis, the Euclidean, Manhattan, Chebyshev, Canberra, and Hamming distance measures are considered. The main characteristics of the results are the final composition of the classes, the number of objects transferred between classes, the number of groups formed, the composition of the groups, and the group compactness measure Ω(E₀). It is shown that the proposed clustering methodology makes it possible to form groups without specifying their number in advance and to compare the resulting structures obtained using different distance measures. The results confirm that the choice of distance measure and the initial partitioning rule significantly affects the number of groups, their composition, and the group compactness measure. The methodology can be used for the analysis of multidimensional data in tasks involving the identification of hidden relationships, boundary objects, and components of the group structure.