Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 44, Number 4 (2012), 907-937.
The normalized graph cut and Cheeger constant: from discrete to continuous
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.
Adv. in Appl. Probab. Volume 44, Number 4 (2012), 907-937.
First available in Project Euclid: 5 December 2012
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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.