Advances in Applied Probability

The normalized graph cut and Cheeger constant: from discrete to continuous


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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.

Article information

Adv. in Appl. Probab., Volume 44, Number 4 (2012), 907-937.

First available in Project Euclid: 5 December 2012

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Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties

Cheeger isoperimetric constant of a manifold conductance of a graph; neighborhood graph spectral clustering U-process empirical process


ARIAS-CASTRO, ERY; PELLETIER, BRUNO; PUDLO, PIERRE. The normalized graph cut and Cheeger constant: from discrete to continuous. Adv. in Appl. Probab. 44 (2012), no. 4, 907--937. doi:10.1239/aap/1354716583.

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