Name of Speaker: Dr. Daniel Pimentel Alarcon
Conference Room, 755 in 25 PP Building
Time: 11:00 am – noon on Wednesday, February 15
Title: Learning Subspaces by Pieces
Abstract: Subspaces lie at the heart of data analysis. As soon as we get our hands on some data, finding a subspace that explains it is one of the first things we try, for example, using Principal Component Analysis (PCA) or linear regression.
Many applications have missing data and gross errors. For example, in computer vision, occlusions produce missing data, and foreground can be modeled as gross errors; in surveys and recommender systems, subjects do not know or do not want to provide all information; in networked systems it is impossible or impractical to measure all components.
In this talk I will present our recent results on when and how subspaces can be identified from highly incomplete and corrupted data. The main idea is to analyze the algebraic structure of small pieces of subspaces to then stitch them together. This gives rise to new algorithms and theoretical insights regarding low-rank matrix completion, robust PCA, coherence, arbitrary (non-uniform) samplings, lower bounds, and computational complexity, among others. This also opens the door to study more complex data structures, like unions of subspaces and manifolds.
I will discuss applications of our results in areas as diverse as astronomy, drug discovery, networks estimation, computer vision, rigidity theory, tensors, recommender systems, phylogenetics, wood classification and deep learning.
-- Rajshekhar Sunderraman Professor and Acting Chair Computer Science Department Georgia State University P.O. Box 5060 Atlanta, GA 30302-5060 www: http://tinman.cs.gsu.edu/~raj phone: (404)413-5726 fax: (404)413-5717