Simplicial Manifold Reconstruction via Tangent Space Estimation

September 16 (Wednesday) at 1:30 pm
BH 232M

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 $\hat{\mathcal{M}}$ of the support $\mathcal{M}$ of an unknown measure from which we observe a i.i.d. $n$-sample. $\mathcal{M}$ has the same topology as $\mathcal{M}$ 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 $\mathcal{M}$, the problem is handled with local PCA. A denoising technique with local PCA in a mixture model will be presented as well.