The cluster algorithms for solving problems with asymmetric proximity measures
A.R. Aydinyan, O.L. Tsvetkova
Don State Technical University, Russian Federation, Rostov-on-Don, Gagarin sq., 1, 344000
Keywords: кластеризация, кластерный анализ, алгоритмы кластеризации, асимметричная мера близости, аксиома симметрии, clustering, cluster analysis, cluster algorithms, asymmetric proximity measure, the axiom of symmetry
Abstract
The cluster analysis is used in various fundamental and applied fields and is a current topic of research. Unlike conventional methods, the proposed algorithms are used for clustering objects represented by vectors in space with the non-observance of the axiom of symmetry. In this case, the feature of solving the clustering problem is the use of an asymmetric proximity measures. The first one among the proposed clustering algorithms sequentially forms clusters with a simultaneous generalization to clustered objects from previously created clusters to a current cluster if this reduces the quality criterion. This approach to the formation of clusters allows reducing the computational costs as compared with existing non-hierarchical cluster algorithms. The second algorithm is a modified version of the first algorithm. The second algorithm allows reassigning the main objects of clusters to further reduce the proposed quality criterion.
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