Mathematical Analysis of Large Data Sets

Monday, April 10, 2006, 3:40 p.m. PSA 113

Michael Kirby

Dept. Math. & Comp. Sci., Colorado State University

A Surprising Application of a 25 Pixel Camera

Abstract Geometric ideas for the classification of large high-dimensional data sets will be presented and in particular the challenging problem of face recognition under variations in illumination will be explored. It appears that the manner in which faces reflect light under varying illumination is highly discriminatory. As a result we are led to consider the idea of multi-set to multi-set image recognition. These image sets may then be mapped to points on Grassman manifolds and compared using metrics that arise naturally in this setting. We have shown that this approach leads to error free classification on the illumination problem on the (relatively small) CMU PIE data base. Furthermore, we show that these results persist when we (mathematically) employ a 25 pixel camera! This work is a collaborative effort between researchers in Mathematics and Computer Science at Colorado State University.

For further information please contact: Anne Gelb