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On the Sensitivity of Shape Fitting Problems
Conference proceeding   Open access

On the Sensitivity of Shape Fitting Problems

Kasturi Varadarajan and Xin Xiao
IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012), Vol.18, pp.486-497
12/14/2012
DOI: 10.4230/LIPIcs.FSTTCS.2012.486
url
https://doi.org/10.4230/LIPIcs.FSTTCS.2012.486View
Published (Version of record) Open Access

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.
Coresets shape fitting k-means subspace approximation

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