PDE and Applied Mathematics Seminar[ Edit ]
Estimating a manifold from (possibly noisy) samples appears to be a difficult problem. Indeed, even after decades of research, there are no (computationally tractable) manifold learning methods that actually "learn" the manifold. Most of the methods try, instead, to embed the manifold into a low-dimensional Euclidean space. This process inevitably introduces distortions and cannot guarantee a robust estimate of the manifold.
In this talk, we will discuss a new method to estimate a manifold in the ambient space, which is efficient even in the case of an ambient space of high dimension. The method gives a robust estimate to the manifold and its tangent, without introducing distortions. Moreover, we will show statistical convergence guarantees.
It is on a work in progress, joint with Barak Sober.