Multiscale Geometric Methods for Noisy Point Clouds in High Dimensions

We discuss techniques for the geometric multiscale analysis of intrinsically low-dimensional point clouds. We first show how such techniques may be used to estimate the intrinsic dimension of data sets, then discuss a novel geometric multiscale transform, based on what we call geometric wavelets, that leads to novel approximation schemes for point clouds, and dictionary learning methods for data sets. Finally, we apply similar techniques to model estimation when points are sampled from a measure supported on a union of an unknown number of unknown planes of unknown dimension.

Dr. Mauro Maggioni

Assistant Professor in Mathematics and Computer Science, Duke University on March 18, 2011 at 1:00 PM in Engineering Building III, Room 2213

Dr. Mauro Maggioni received the Ph.D. in Mathematics from the Washington University, St. Louis, in 2002. He then was a Gibbs Assistant Professor in Mathematics at Yale University, till 2006 when he moved to Duke University as an Assistant Professor in Mathematics and Computer Science. He works at the intersection between harmonic analysis, machine learning, graph theory, and signal processing.

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