*Name of Speaker*: Dr. Daniel Pimentel Alarcon
*Place: *CS 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.
Professor and Acting Chair
Computer Science Department
Georgia State University
P.O. Box 5060
Atlanta, GA 30302-5060
phone: (404)413-5726 fax: (404)413-5717