Hierarchical Aggregation Clustering Algorithms Derived from the Bi-partial Objective Function

Abstract: The paper outlines the principles of construction of a broad class of hierarchical aggregation algorithms of cluster analysis, essentially based on minimum distance mergers, which are derived from the general bi-partial objective function. It is shown how the algorithms arise from the bi-partial objective function, their affinity with the classical hierarchical aggregation algorithms is demonstrated, and the examples of such algorithms for the concrete forms of the bi-partial objective function are provided. This amounts to the first explicit and, at the same time, quite general, connection between optimization in clustering and the hierarchical aggregation algorithms. Thereby, the respective hierarchical algorithms gain a deeper justification, the means for evaluating the quality of clustering is provided, along with the criterion of stopping the cluster mergers.