On Balanced Clustering (Indices, Models, Examples)

Abstract

The paper describes and approach to balanced clustering problems. The list of balanced structures includes balanced partitioning of a set, balanced trees, balanced decomposition of a graph, and balanced multilevel structures. Balance indices (characteristics) for balanced structures (clustering solutions) are based on the difference between the cluster parameters: cardinality of a cluster, the total cluster weight, the total weight of edges/arcs of a cluster, and the structure of a cluster in terms of the types of its elements. The proposed balance indices are used as components for optimization models of balanced clustering: objective functions and constraints. Three numerical examples are presented: (1) calculating the balance indices for clustering based on the structure of a cluster in terms of the types of its elements; (2) calculating the balance indices for a clustering solution for a sample network; (3) balanced clustering for forming several student teams.

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Correspondence to M. Sh. Levin.

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Original Russian Text © M.Sh. Levin, 2017, published in Informatsionnye Protsessy, 2017, Vol. 17, No. 2, pp. 146–158.

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Levin, M.S. On Balanced Clustering (Indices, Models, Examples). J. Commun. Technol. Electron. 62, 1506–1515 (2017). https://doi.org/10.1134/S1064226917120105

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Keywords

  • balanced clustering
  • balance indices
  • combinatorial optimization
  • heuristic