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December 2012 The normalized graph cut and Cheeger constant: from discrete to continuous
ERY ARIAS-CASTRO, BRUNO PELLETIER, PIERRE PUDLO
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Adv. in Appl. Probab. 44(4): 907-937 (December 2012). DOI: 10.1239/aap/1354716583

Abstract

Let M be a bounded domain of ∝d with a smooth boundary. We relate the Cheeger constant of M and the conductance of a neighborhood graph defined on a random sample from M. By restricting the minimization defining the latter over a particular class of subsets, we obtain consistency (after normalization) as the sample size increases, and show that any minimizing sequence of subsets has a subsequence converging to a Cheeger set of M.

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ERY ARIAS-CASTRO. BRUNO PELLETIER. PIERRE PUDLO. "The normalized graph cut and Cheeger constant: from discrete to continuous." Adv. in Appl. Probab. 44 (4) 907 - 937, December 2012. https://doi.org/10.1239/aap/1354716583

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1318.62105
MathSciNet: MR3052843
Digital Object Identifier: 10.1239/aap/1354716583

Subjects:
Primary: 62G05, 62G20

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 4 • December 2012
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