MATH Seminar
| Title: Analysis and recovery of high-dimensional data with low-dimensional structures |
|---|
| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Wenjing Liao of Georgia Institute of Technology |
| Contact: Yuanzhe Xi, yxi26@emory.edu |
| Date: 2018-12-07 at 2:00PM |
| Venue: MSC N302 |
| Download Flyer |
| Abstract: High-dimensional data arise in many fields of contemporary science and introduce new challenges in statistical learning and data recovery. Many datasets in image analysis and signal processing are in a high-dimensional space but exhibit a low-dimensional structure. We are interested in building efficient representations of these data for the purpose of compression and inference, and giving performance guarantees depending on the intrinsic dimension of data. I will present two sets of problems: one is related with manifold learning; the other arises from imaging and signal processing where we want to recover a high-dimensional, sparse vector from few linear measurements. In the first problem, we model a data set in $R^D$ as samples from a probability measure concentrated on or near an unknown $d$-dimensional manifold with $d$ much smaller than $D$. We develop a multiscale adaptive scheme to build low-dimensional geometric approximations of the manifold, as well as approximating functions on the manifold. The second problem arises from source localization in signal processing where a uniform array of sensors is set to collect propagating waves from a small number of sources. I will present some theory and algorithms for the recovery of the point sources with high precision. |
See All Seminars