PerioClust: a simple hierarchical agglomerative clustering approach including constraints

Lise Bellanger (1) , Arthur Coulon (2) , Philippe Husi (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 CITERES - Cités, Territoires, Environnement et Sociétés

PerioClust is a hierarchical agglomerative clustering (HAC) method including temporal (resp. spatial) ordering constraints. This new semi-supervised learning algorithm is designed to consider two potentially error-prone sources of information associated with the same observations. One reflects dissimilarities in the ”feature space” and the other the temporal (resp. spatial) constraint structure between the observations. A distance-based approach is adopted to modify the distance measure in the classical HAC algorithm using a convex combination to take into account the two initial dissimilarity matrices. The choice of the mixing parameter is therefore the key point.We define a criterion based on cophenetic distances, as well as a resampling procedure to ensure the good robustness of the proposed clustering method. The dendrogram associated with this HAC can be interpreted as the result of a compromise between each source of information analysed separately. We illustrate our clustering method on two real data sets: (i) an archaeological one containing temporal information, (ii) a socio-economical one containing geographical information.

Mots clés: Semi-supervised learning algorithm; non-strict constrained approach; hierarchical agglomerative clustering; weighted average distance; cophenetic matrix.

Domaines: Statistiques [math.ST]; Archéologie et Préhistoire; Statistiques [stat]

Lise Bellanger, Arthur Coulon, Philippe Husi. PerioClust: a simple hierarchical agglomerative clustering approach including constraints. Springer. Data Analysis, and Rationality in a Complex World, XXIII, 2020, Springer Series “Studies in Classification, Data Analysis and knowledge Organization", 978-3-030-60104-1. ⟨hal-02952538⟩