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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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Rebecca Willett is an associate professor in the Electrical and Computer Engineering Department and Fellow of the Wisconsin Institute of Discovery at the University of Wisconsin-Madison. Previously she held assistant and associate professor positions at Duke University. She completed her PhD in Electrical and Computer Engineering at Rice University in 2005. Prof. Willett received the National Science Foundation CAREER Award in 2007, was a member of the DARPA Computer Science Study Group 2007-2011, and received an Air Force Office of Scientific Research Young Investigator Program award in 2010. Her research interests include network and imaging science with applications in medical imaging, wireless sensor networks, astronomy, and social networks.
Title: “Nonlinear Models for Matrix Completion"
The past decade of research on matrix completion has shown it is possible to leverage linear dependencies to impute missing values in a low-rank matrix. However, the corresponding assumption that the data lies in or near a low-dimensional linear subspace is not always met in practice. Extending matrix completion theory and algorithms to exploit low-dimensional nonlinear structure in data will allow missing data imputation in a far richer class of problems. In this talk, I will describe how models of low-dimensional nonlinear structure can be used for matrix completion. In particular, we will explore matrix completion in the context of unions of subspaces, in which data points lie in or near one of several subspaces, and nonlinear algebraic varieties, a polynomial generalization of classical linear subspaces.
Low Algebraic-Dimension Matrix Completion (LADMC) is a novel and efficient method for imputing missing values and admits new bounds on the amount of missing data that can be accurately imputed. The proposed algorithms are able to recover synthetically generated data up to predicted sample complexity bounds and outperform standard low-rank matrix completion in experiments with real motion capture data.
This is joint work with Daniel Pimentel-Alarcon, Gregory Ongie, Laura Balzano, and Robert Nowak.
