eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-07
28:1
28:12
10.4230/LIPIcs.ISAAC.2017.28
article
Temporal Hierarchical Clustering
Dey, Tamal K.
Rossi, Alfred
Sidiropoulos, Anastasios
We study hierarchical clusterings of metric spaces that change over time. This is a natural geo- metric 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 ultrametric space, which naturally induces a hierarchical clustering of the set of points. We enforce 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol092-isaac2017/LIPIcs.ISAAC.2017.28/LIPIcs.ISAAC.2017.28.pdf
clustering
hierarchical clustering
multi-objective optimization
dynamic metric spaces
moving point sets
approximation algorithms