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Hierarchical Means Clustering

Author

Listed:
  • Maurizio Vichi

    (University of Rome La Sapienza)

  • Carlo Cavicchia

    (Erasmus University Rotterdam)

  • Patrick J. F. Groenen

    (Erasmus University Rotterdam)

Abstract

In the cluster analysis literature, there are several partitioning (non-hierarchical) methods for clustering multivariate objects based on model estimation. Distinct to these methods is the use of a system of n nested statistical models and the optimization of a loss function to best-fit a clustering model to observed data. Many hierarchical clustering methods are not model-based where hierarchy is obtained using a divisive or agglomerative greedy procedure. This paper aims to fill this gap by proposing a novel hierarchical cluster analysis methodology called Hierarchical Means Clustering. HMC produces a set of nested partitions with a centroid-based model estimated via least-squares by minimizing the total within-cluster deviance of the n partitions in the hierarchy. Hierarchical Means Clustering produces a hierarchy formed by n-1 nested partitions from 2 to n clusters with minimal total cluster deviance. Six real data examples are featured, and key links to k-means, Ward’s method, Bisecting k-means and model-based hierarchical agglomerative clustering methods are discussed.

Suggested Citation

  • Maurizio Vichi & Carlo Cavicchia & Patrick J. F. Groenen, 2022. "Hierarchical Means Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 553-577, November.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:3:d:10.1007_s00357-022-09419-7
    DOI: 10.1007/s00357-022-09419-7
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    References listed on IDEAS

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    2. N. Sriram, 1990. "Clique optimization: A method to construct parsimonious ultrametric trees from similarity data," Journal of Classification, Springer;The Classification Society, vol. 7(1), pages 33-52, March.
    3. Fionn Murtagh & Pierre Legendre, 2014. "Ward’s Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward’s Criterion?," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 274-295, October.
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