License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2017.28
URN: urn:nbn:de:0030-drops-82519
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8251/
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Dey, Tamal K. ; Rossi, Alfred ; Sidiropoulos, Anastasios

Temporal Hierarchical Clustering

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LIPIcs-ISAAC-2017-28.pdf (3 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{dey_et_al:LIPIcs:2017:8251,
  author =	{Tamal K. Dey and Alfred Rossi and Anastasios Sidiropoulos},
  title =	{{Temporal Hierarchical Clustering}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{28:1--28:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8251},
  URN =		{urn:nbn:de:0030-drops-82519},
  doi =		{10.4230/LIPIcs.ISAAC.2017.28},
  annote =	{Keywords: clustering, hierarchical clustering, multi-objective optimization, dynamic metric spaces, moving point sets, approximation algorithms}
}

Keywords: clustering, hierarchical clustering, multi-objective optimization, dynamic metric spaces, moving point sets, approximation algorithms
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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