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The Cluster Algorithms for Solving Problems with Asymmetric Proximity Measures

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Abstract

Cluster analysis is used in various scientific and applied fields and is a topical subject of research. In contrast to the existing methods, the algorithms offered in this paper are intended for clustering objects described by feature vectors in a space in which the symmetry axiom is not satisfied. In this case, the clustering problem is solved using an asymmetric proximity measure. The essence of the first of the proposed clustering algorithms consists in sequential generation of clusters with simultaneous transfer of the objects clustered from previously created clusters into a current cluster if this reduces the quality criterion. In comparison with the existing algorithms of non-hierarchical clustering, such an approach to cluster generation makes it possible to reduce the computational costs. The second algorithmis a modified version of the first one andmakes it possible to reassign the main objects of clusters to further decrease the value of the proposed quality criterion.

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Acknowledgments

This work was supported by the Russian Science Foundation, project no. 14-11-0083.

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Authors and Affiliations

  1. Don State Technical University, pl. Gagarina 1, Rostov-on-Don, 344000, Russia

    A. R. Aidinyan & O. L. Tsvetkova

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  1. A. R. Aidinyan
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  2. O. L. Tsvetkova
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Correspondence to A. R. Aidinyan.

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Original Russian Text © A.R. Aidinyan, O.L. Tsvetkova, 2018, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2018, Vol. 21, No. 2, pp. 127–138.

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Aidinyan, A.R., Tsvetkova, O.L. The Cluster Algorithms for Solving Problems with Asymmetric Proximity Measures. Numer. Analys. Appl. 11, 99–107 (2018). https://doi.org/10.1134/S1995423918020015

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  • DOI: https://doi.org/10.1134/S1995423918020015

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