The Normalized Graph Cut and Cheeger Constant: from Discrete to Continuous
Statistics Theory
2013-03-05 v3 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1004.5485,
title = {The Normalized Graph Cut and Cheeger Constant: from Discrete to Continuous},
author = {Ery Arias-Castro and Bruno Pelletier and Pierre Pudlo},
journal= {arXiv preprint arXiv:1004.5485},
year = {2013}
}