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| HAL: hal-00473264, version 2 |
| arXiv: 1004.5485 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-04-30) | v2 (2010-05-31) | v3 (2011-06-09) |
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| The Cheeger Constant: from Discrete to Continuous |
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| Ery Arias-Castro 1Bruno Pelletier 2 |
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| (2010-04-14) |
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| 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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| 1: | Department of Mathematics, University of California, San Diego (Math Dept, UCSD) |
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University of California, San Diego |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3: | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
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CNRS : UMR5149 – Université Montpellier II - Sciences et techniques |
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| Subject | : | Mathematics/Statistics Statistics/Statistics Theory |
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| Cheeger isoperimetric constant of a manifold – conductance of a graph – neighborhood graph – spectral clustering – U-processes – empirical processes |
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| hal-00473264, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00473264 | |
| oai:hal.archives-ouvertes.fr:hal-00473264 | |
| From: Pierre Pudlo | |
| Submitted on: Wednesday, 12 May 2010 11:05:18 | |
| Updated on: Monday, 31 May 2010 09:05:29 | |
