Date:
-
Location:
POT 745
Speaker(s) / Presenter(s):
Zhaojun Bai, University of California, Davis
Title: Some Modified Matrix Eigenvalue Problems
Abstract:
This is the title of a well-known numerical linear algebra
survey article by Gene Golub published in 1973. The article
covers a range of matrix eigenvalue problems which require some
manipulations before the standard algorithms may be used.
I am using the same title to consider a new set of modified
matrix eigenvalue problems. This includes constrained and
bi-level optimizations arising from algorithms for fairness in machine
learning, such as spectral clustering with group fairness
and fair principal component analysis. We also consider
eigenvalue optimization via 2D eigenvalue problem with applications
to the calculation of the distance to instability among others,
and stationary values of a quadratic form subject to non-homogeneous
linear constraints for applications such as image segmentation with
constraints. I will discuss how to explore the underlying
structures of these problems to turn them into our familiar
eigenvalue problems and algorithms.