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Let M be a bounded domain of a Euclidian space with smooth boundary. Werelate the Cheeger constant of M and the conductance of a neighborhood graphdefined on a random sample from M. By restricting the minimization defining thelatter over a particular class of subsets, we obtain consistency (afternormalization) as the sample size increases, and show that any minimizingsequence of subsets has a subsequence converging to a Cheeger set of M.

The Normalized Graph Cut and Cheeger Constant: from Discrete to Continuous