Speaker: Eddie Aamari

Abstract: We look at the problem of manifold reconstruction in a semi-asymptotic framework. Under geometrical regularity constraints, we propose a computable estimator of the support of an unknown measure from which we observe a i.i.d. -sample. has the same topology as and we give a rate of convergence for the Hausdorff distance. The method is based on a tangential Delaunay complex. After having reduced the question to estimating the tangent spaces of , the problem is handled with local PCA. A denoising technique with local PCA in a mixture model will be presented as well.