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An Exact Solution Approach for Hierarchical Clustering

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  • Rick Willemsen

    (Econometric Institute, Erasmus University, 3062 PA Rotterdam, Netherlands)

  • Carlo Cavicchia

    (Econometric Institute, Erasmus University, 3062 PA Rotterdam, Netherlands)

  • Wilco van den Heuvel

    (Econometric Institute, Erasmus University, 3062 PA Rotterdam, Netherlands)

  • Michel van de Velden

    (Econometric Institute, Erasmus University, 3062 PA Rotterdam, Netherlands)

Abstract

In hierarchical clustering, a hierarchy of nested data partitions is obtained. Commonly used agglomerative and divisive heuristics do not optimize over a global objective function. Although several objective functions and approximation algorithms have been proposed, exact methods that find optimal solutions based on these objective functions have received little attention. In this paper, we consider an objective function involving a sum of partitional clustering objectives over each level. We introduce two compact mixed-integer linear programming formulations as well as a set-covering formulation that can handle various objective functions. In addition, we provide a branch-and-price framework to solve the set-covering formulation. We apply our branch-and-price approach to real-world data instances containing up to 200 observations compared with 15 in the literature.

Suggested Citation

  • Rick Willemsen & Carlo Cavicchia & Wilco van den Heuvel & Michel van de Velden, 2026. "An Exact Solution Approach for Hierarchical Clustering," INFORMS Journal on Computing, INFORMS, vol. 38(2), pages 447-462, March.
    • Handle: RePEc:inm:orijoc:v:38:y:2026:i:2:p:447-462
    DOI: 10.1287/ijoc.2024.0903
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