Codes and Expansions (CodEx) Seminar
Keaton Hamm (The University of Texas at Arlington)
Column Selection and You
This talk is an invitation to the world of column subset selection and related ideas. We will discuss the original NP-hard column subset selection problem and theme and variations therof including column-row matrix factorizations (which also go by the names (pseudo)skeleton decomposition, cross approximation, interpolative decomposition, Nyström method, and CUR decomposition). These ideas have found utility in a wide array of applications from natural language processing to astronomy to image processing. We will illustrate several applications and discuss recent work on how column selection can be used to speed up Robust PCA as well as provide a Robust CUR decomposition, which can allow one to extract canonical background frames from videos. Time permitting, we will discuss tensor analogues of these ideas and give some future directions. Aspects of this work are joint with HanQin Cai, Longxiu Huang, Jiaqi Li, Deanna Needell, and Tao Wang.