![Algorithmic Spectral Graph Theory_hi-res logo](/sites/default/files/styles/workshop_banner_sm_1x/public/2023-01/Algorithmic%20Spectral%20Graph%20Theory_hi-res.jpg?h=bc58dfd7&itok=8NAdfoPF)
Abstract
Let M be a bounded domain of R^d with smooth boundary. We relate the Cheeger constant of M and the Cheeger constant 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.
Joint work with Bruno Pelletier and Pierre Pudlo.