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Home | Seminars and Symposia | Past seminars/symposia: Friday, October 17, 2014

DTC Seminar Series

Data Analysis with Low-dimensional Structures

by

Yi (Grace) Wang
Department of Mathematics
Duke University

Friday, October 17, 2014
1:00 p.m. reception
1:25 p.m. seminar

402 Walter Library

Yi (Grace) Wang

Analyzing data collected from different fields is a challenge facing scientists and engineers. The property of being high-dimensional makes these data sets hard to investigate. Fortunately, in many cases, data locally concentrate along a low-dimensional subspace, which makes it possible to analyze. This talk will demonstrate different objectives where low-dimensional structures can be utilized for various data analysis purposes.

A major part of the talk will introduce a solution to the high-dimensional regression problem. More precisely, given a set of high-dimensional predictors {xi} and the corresponding high-dimensional responses {yi}, the high-dimensional regression problem seeks a function f such that f(xi) is sufficiently close to yi for all i. An algorithm with piecewise linear mappings built on a tree structure is proposed. It is designed to handle high-dimensional predictors and responses, and in particular, cases where closeness of predictors is inconsistent with closeness of responses. Experimental results demonstrate the excellent performance of our method.

Additional problems in the area will be discussed briefly, including the consistency analysis of a subspace-based classification algorithm and forgery detection in paintings.

 

Yi (Grace) Wang received her Diploma in Mathematics from Huazhong University of Science and Technology, Wuhan, China, 2005. From 2006 to 2012, she was with the University of Minnesota, where she received her M.S. in Statistics and Ph.D. in Mathematics, under the supervision of Dr. Hui Zou and Dr. Gilad Lerman, respectively. Since 2012, she has been a postdoctoral researcher at the Statistical and Applied Mathematical Sciences Institute (SAMSI) and a visiting assistant professor at the Mathematics Department, Duke University, Durham, NC. Her general research interests lie in modeling high-dimensional data clouds with appropriate (locally) low-dimensional structures, as well as relevant applications to real data. Currently, she focuses on the development and justification of general algorithms that reveal the underlying low-dimensional structures under different challenges. She also works with real-world data, including light curves in astronomy, medical signals, images in art as well as hyperspectral images and videos of chemical plumes.