License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2012.486
URN: urn:nbn:de:0030-drops-38830
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3883/
Go to the corresponding LIPIcs Volume Portal

Varadarajan, Kasturi ; Xiao, Xin

On the Sensitivity of Shape Fitting Problems

pdf-format:
44.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{varadarajan_et_al:LIPIcs:2012:3883,
  author =	{Kasturi Varadarajan and Xin Xiao},
  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 =	{Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2012/3883},
  URN =		{urn:nbn:de:0030-drops-38830},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.486},
  annote =	{Keywords: Coresets, shape fitting, k-means, subspace approximation}
}

Keywords: Coresets, shape fitting, k-means, subspace approximation
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Issue Date: 2012
Date of publication: 14.12.2012

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI