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Applicability and Interpretability of Ward’s Hierarchical Agglomerative Clustering With or Without Contiguity Constraints

Author

Listed:
  • Nathanaël Randriamihamison

    (INRAE, UR875 Mathématiques et Informatique Appliquées Toulouse
    Université de Toulouse, CNRS UPS)

  • Nathalie Vialaneix

    (INRAE, UR875 Mathématiques et Informatique Appliquées Toulouse)

  • Pierre Neuvial

    (Université de Toulouse, CNRS UPS)

Abstract

Hierarchical agglomerative clustering (HAC) with Ward’s linkage has been widely used since its introduction by Ward (Journal of the American Statistical Association, 58(301), 236–244, 1963). This article reviews extensions of HAC to various input data and contiguity-constrained HAC, and provides applicability conditions. In addition, different versions of the graphical representation of the results as a dendrogram are also presented and their properties are clarified. We clarify and complete the results already available in an heterogeneous literature using a uniform background. In particular, this study reveals an important distinction between a consistency property of the dendrogram and the absence of crossover within it. Finally, a simulation study shows that the constrained version of HAC can sometimes provide more relevant results than its unconstrained version despite the fact that the constraint leads to optimize the objective criterion on a reduced set of solutions at each step. Overall, this article provides comprehensive recommendations, both for the use of HAC and constrained HAC depending on the input data, and for the representation of the results.

Suggested Citation

  • Nathanaël Randriamihamison & Nathalie Vialaneix & Pierre Neuvial, 2021. "Applicability and Interpretability of Ward’s Hierarchical Agglomerative Clustering With or Without Contiguity Constraints," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 363-389, July.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:2:d:10.1007_s00357-020-09377-y
    DOI: 10.1007/s00357-020-09377-y
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    References listed on IDEAS

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    1. Gordon, A. D., 1996. "A survey of constrained classification," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 17-29, January.
    2. Marie Chavent & Vanessa Kuentz-Simonet & Amaury Labenne & Jérôme Saracco, 2018. "ClustGeo: an R package for hierarchical clustering with spatial constraints," Computational Statistics, Springer, vol. 33(4), pages 1799-1822, December.
    3. Anuška Ferligoj & Vladimir Batagelj, 1982. "Clustering with relational constraint," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 413-426, December.
    4. Gale Young & A. Householder, 1938. "Discussion of a set of points in terms of their mutual distances," Psychometrika, Springer;The Psychometric Society, vol. 3(1), pages 19-22, March.
    5. 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.
    6. Jesse R. Dixon & Siddarth Selvaraj & Feng Yue & Audrey Kim & Yan Li & Yin Shen & Ming Hu & Jun S. Liu & Bing Ren, 2012. "Topological domains in mammalian genomes identified by analysis of chromatin interactions," Nature, Nature, vol. 485(7398), pages 376-380, May.
    7. Vladimir Batagelj, 1981. "Note on ultrametric hierarchical clustering algorithms," Psychometrika, Springer;The Psychometric Society, vol. 46(3), pages 351-352, September.
    8. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    9. Stephen Johnson, 1967. "Hierarchical clustering schemes," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 241-254, September.
    10. Gabor J. Szekely & Maria L. Rizzo, 2005. "Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 151-183, September.
    11. Nathan Krislock & Henry Wolkowicz, 2012. "Euclidean Distance Matrices and Applications," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 879-914, Springer.
    12. Douglas Steinley & Lawrence Hubert, 2008. "Order-Constrained Solutions in K-Means Clustering: Even Better Than Being Globally Optimal," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 647-664, December.
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