Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Moseley, Benjamin; Pruhs, Kirk; Samadian, Alireza; Wang, Yuyan https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-141668
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Relational Algorithms for k-Means Clustering

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Abstract

This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows represent the data points. The running time is potentially exponentially smaller than N, the number of data points to be clustered that the relational database represents.
Few relational algorithms are known and this paper offers techniques for designing relational algorithms as well as characterizing their limitations. We show that given two data points as cluster centers, if we cluster points according to their closest centers, it is NP-Hard to approximate the number of points in the clusters on a general relational input. This is trivial for conventional data inputs and this result exemplifies that standard algorithmic techniques may not be directly applied when designing an efficient relational algorithm. This paper then introduces a new method that leverages rejection sampling and the k-means++ algorithm to construct a O(1)-approximate k-means solution.

BibTeX - Entry

@InProceedings{moseley_et_al:LIPIcs.ICALP.2021.97,
  author =	{Moseley, Benjamin and Pruhs, Kirk and Samadian, Alireza and Wang, Yuyan},
  title =	{{Relational Algorithms for k-Means Clustering}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{97:1--97:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14166},
  URN =		{urn:nbn:de:0030-drops-141668},
  doi =		{10.4230/LIPIcs.ICALP.2021.97},
  annote =	{Keywords: k-means, clustering, approximation, big-data, databases}
}

Keywords: k-means, clustering, approximation, big-data, databases
Seminar: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue date: 2021
Date of publication: 02.07.2021


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