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.
"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