DPS Clustering: New Results

Abstract

The results presented in this paper are obtained as part of the continued development and research of clustering algorithms based on the discrete mathematical analysis. The article briefly describes the theory of Discrete Perfect Sets (DPS-sets) that is the basis for the construction of DPS-clustering algorithms. The main task of the previously constructed DPS-algorithms is to search for clusters in multidimensional arrays with noise. DPS-algorithms have two stages: the first stage is the recognition of the maximum perfect set of a given density level from the initial array, the second stage is the partitioning of the result of the first stage into connected components, which are considered to be clusters. Study of qualities of DPS-algorithms showed that, in a number of situations in the first stage, the result does not include all clusters which have practical sense. In the second stage, partitioning into connected components can lead to unnecessarily small clusters. Simple variation of parameters in DPS-algorithms does not allow for eliminating these drawbacks. The present paper is devoted to the construction on the basis of DPS-algorithms of their new versions, more free from these drawbacks.