Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: A hierarchical clustering method is stable if small perturbations on the data set produce small perturbations in the result. This perturbations<lb>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.<lb>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.

GROMOV-HAUSDORFF STABILITY OF LINKAGE-BASED HIERARCHICAL CLUSTERING METHODS