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arXiv · 1004.5485

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

Ery Arias-Castro·Bruno Pelletier·Pierre Pudlo
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Abstract

Let M be a bounded domain of a Euclidian space with 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.

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Ery Arias-Castro, Bruno Pelletier, Pierre Pudlo. 2010-04-30. The Normalized Graph Cut and Cheeger Constant: from Discrete to Continuous. https://doi.org/10.1239/aap/1354716583

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