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DOI: 10.4230/LIPIcs.FSTTCS.2012.486

On the Sensitivity of Shape Fitting Problems

Authors: Kasturi Varadarajan and Xin Xiao

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract

In this article, we study shape fitting problems, epsilon-coresets, and total sensitivity. We focus on the (j,k)-projective clustering problems, including k-median/k-means, k-line clustering, j-subspace approximation, and the integer (j,k)-projective clustering problem. We derive upper bounds of total sensitivities for these problems, and obtain epsilon-coresets using these upper bounds. Using a dimension-reduction type argument, we are able to greatly simplify earlier results on total sensitivity for the k-median/k-means clustering problems, and obtain positively-weighted epsilon-coresets for several variants of the (j,k)-projective clustering problem. We also extend an earlier result on epsilon-coresets for the integer (j,k)-projective clustering problem in fixed dimension to the case of high dimension.

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Kasturi Varadarajan and Xin Xiao. On the Sensitivity of Shape Fitting Problems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 486-497, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{varadarajan_et_al:LIPIcs.FSTTCS.2012.486,
  author =	{Varadarajan, Kasturi and Xiao, Xin},
  title =	{{On the Sensitivity of Shape Fitting Problems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{486--497},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.486},
  URN =		{urn:nbn:de:0030-drops-38830},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.486},
  annote =	{Keywords: Coresets, shape fitting, k-means, subspace approximation}
}

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On the Sensitivity of Shape Fitting Problems

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