Work

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

Year: 2012

Type: article

Abstract: 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 .

Source: Advances in Applied Probability

DOI: 10.1017/s000186780000598x

Authors: Ery Arias-Castro, Bruno Pelletier, Pierre Pudlo

Institutions: University of California System, Université Rennes 2, Université Montpellier 2

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Agence Nationale de la Recherche

Award: Classification non-supervisée en grande dimension : algorithmes et applications