A. Martínez-Pérez

A. Martínez-Pérez

In the election of a hierarchical clustering method, theoretic properties may give some insight to determine which method is the most suitable to treat a clustering problem. Herein, we study some basic properties of two hierarchical clustering methods: $α$-unchaining single linkage or $SL(α)$ and a modified version of this one, $SL^*(α)$. We compare the results with the properties satisfied by the classical linkage-based hierarchical clustering methods.

A. Martínez-Pérez

A hierarchical clustering method is stable if small perturbations on the data set produce small perturbations in the result. These perturbations are measured using the Gromov-Hausdorff metric. We study the problem of stability on linkage-based hierarchical clustering methods. We obtain that, under some basic conditions, standard linkage-based methods are semi-stable. This means that they are stable if the input data is close enough to an ultrametric space. We prove that, apart from exotic examples, introducing any unchaining condition in the algorithm always produces unstable methods.