Advances in Applied Probability

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

ERY ARIAS-CASTRO, BRUNO PELLETIER, and PIERRE PUDLO

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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.

Article information

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

Dates
First available in Project Euclid: 5 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1354716583

Digital Object Identifier
doi:10.1239/aap/1354716583

Mathematical Reviews number (MathSciNet)
MR3052843

Zentralblatt MATH identifier
1318.62105

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties

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

Citation

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. https://projecteuclid.org/euclid.aap/1354716583.


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