Towards balanced clustering - part 1 (preliminaries)
This is an incremental work that provides foundational definitions and examples for balanced clustering problems.
The paper introduces preliminary concepts for balanced clustering, describing various balance indices and optimization formulations, with illustrative examples including student team design.
The article contains a preliminary glance at balanced clustering problems. Basic balanced structures and combinatorial balanced problems are briefly described. A special attention is targeted to various balance/unbalance indices (including some new versions of the indices): by cluster cardinality, by cluster weights, by inter-cluster edge/arc weights, by cluster element structure (for element multi-type clustering). Further, versions of optimization clustering problems are suggested (including multicriteria problem formulations). Illustrative numerical examples describe calculation of balance indices and element multi-type balance clustering problems (including example for design of student teams).