🤖 AI Summary
This work addresses the lack of a unified optimization foundation and quality evaluation mechanism in hierarchical clustering methods based on minimum-distance merging. It proposes a class of hierarchical agglomerative clustering algorithms derived from a bipartite objective function. By reinterpreting classical hierarchical clustering procedures as optimization processes of this objective, the study establishes, for the first time, a general connection between hierarchical clustering and an explicit optimization goal. This framework not only provides a unified theoretical interpretation for several existing algorithms but also naturally yields cluster quality metrics and stopping criteria, thereby enhancing both the interpretability and practical utility of hierarchical clustering.
📝 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.