Flag manifolds for robust averaging, principal directions, and hierarchical data representation

Data Science Seminar

Nathan Mankovich
University of Valencia

Abstract

A flag is a sequence of nested subspaces of a finite-dimensional vector space and the flag manifold is the collection of all flags with the same sequence of subspace dimensions. Flag manifolds are used in computer vision, communications, bioinformatics, and remote sensing. For example, flags have improved video clustering, motion averaging, and outlier detection in computer vision datasets. This talk will introduce the robust subspace averages that result in flags (flag mean and flag median), the robust averages of flags (chordal flag mean and the chordal flag median), find flags of robust principal directions, and finally, present a method for representing data with feature hierarchies using flag manifolds.