Temporal Hierarchical Clustering * †

Tamal Dey, Alfred Rossi, Anastasios Sidiropoulos
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent sequence of hierarchical clusterings from a sequence of unlabeled point sets. We encode the clustering objective by embedding each point set into an ul-trametric space, which naturally induces a hierarchical clustering of the set of points. We enforce temporal
more » ... orce temporal coherence among the embeddings by finding correspondences between successive pairs of ultrametric spaces which exhibit small distortion in the Gromov-Hausdorff sense. We present both upper and lower bounds on the approximability of the resulting optimization problems.