Department of Mathematics
University of Southern California
“Efficient Representation of Data on Smooth Manifolds: Non-Asymptotic Bounds and Robustness”
It has been empirically observed that many high-dimensional datasets are well approximated by low-dimensional structures. Over the past decade, this fact has motivated the investigation of modeling techniques which exploit these low-dimensional intrinsic structures, along with applications to high-dimensional statistics, machine learning, and signal processing. One particularly interesting example is the situation when the “low-dimensional structure” is a smooth submanifold of a high-dimensional Euclidean space. We study sparse multiscale representations and associated compression schemes for such data, and provide non-asymptotic probabilistic performance guarantees that depend only on the “intrinsic dimension” of the underlying submanifold.
This talk is based on a joint work with M. Maggioni and N. Strawn.