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The Normalized Graph Cut and Cheeger Constant: From Discrete to Continuous
- Part of
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- Journal:
- Advances in Applied Probability / Volume 44 / Issue 4 / December 2012
- Published online by Cambridge University Press:
- 04 January 2016, pp. 907-937
- Print publication:
- December 2012
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- Article
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Let M be a bounded domain of
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.
with a smooth boundary. We relate the Cheeger constant of 