License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.38
URN: urn:nbn:de:0030-drops-163793
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16379/
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Charikar, Moses ; Waingarten, Erik

Polylogarithmic Sketches for Clustering

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LIPIcs-ICALP-2022-38.pdf (0.8 MB)

Abstract

Given n points in ?_p^d, we consider the problem of partitioning points into k clusters with associated centers. The cost of a clustering is the sum of p-th powers of distances of points to their cluster centers. For p ∈ [1,2], we design sketches of size poly(log(nd),k,1/ε) such that the cost of the optimal clustering can be estimated to within factor 1+ε, despite the fact that the compressed representation does not contain enough information to recover the cluster centers or the partition into clusters. This leads to a streaming algorithm for estimating the clustering cost with space poly(log(nd),k,1/ε). We also obtain a distributed memory algorithm, where the n points are arbitrarily partitioned amongst m machines, each of which sends information to a central party who then computes an approximation of the clustering cost. Prior to this work, no such streaming or distributed-memory algorithm was known with sublinear dependence on d for p ∈ [1,2).

BibTeX - Entry

@InProceedings{charikar_et_al:LIPIcs.ICALP.2022.38,
  author =	{Charikar, Moses and Waingarten, Erik},
  title =	{{Polylogarithmic Sketches for Clustering}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{38:1--38:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16379},
  URN =		{urn:nbn:de:0030-drops-163793},
  doi =		{10.4230/LIPIcs.ICALP.2022.38},
  annote =	{Keywords: sketching, clustering}
}

Keywords: sketching, clustering
Collection: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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