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

TL;DR

This paper develops a general framework for hierarchical clustering algorithms based on the bi-partial objective function, linking optimization principles with classical methods and providing tools for evaluation and stopping criteria.

Contribution

It introduces a broad class of hierarchical aggregation algorithms derived from the bi-partial objective function, establishing a formal connection between optimization and clustering.

Findings

Algorithms are derived from the bi-partial objective function.

The connection between optimization and hierarchical clustering is explicitly established.

Provides criteria for evaluating and stopping cluster mergers.

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.