Electrical and Computer Engineering
Dean of Engineering
University of Wisconsin-Madison
ECE Seminar Series: "Learning Subspaces by Pieces," Daniel Pimentel Alarcon, Wisconsin (698/699)
Wednesday, February 8, 2017
to 5:00 PM
1064 Duncan Hall
6100 Main St
Houston, Texas, USA
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 piecesof 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 drug discovery, networks estimation, computer vision, rigidity theory, tensors, recommender systems, phylogenetics, wood classification and deep learning.
Biography of Daniel Pimentel-Alarcon:
Daniel Pimentel-Alarcon is a postdoctoral researcher at the Wisconsin Institute for Discovery. He received his Ph.D. in ECE in 2016 at the University of Wisconsin-Madison, under the supervision of Robert Nowak. His research stems from the fact that many engineering problems involve estimating linear subspaces from high-dimensional data that is severely corrupted not only by errors but also by missing values. His work aims to understand when and how subspaces can be identified from incomplete data.