Fun with Flags: Robust Principal Directions via Flag Manifolds

arXiv:2401.04071v2 Announce Type: replace-cross
Abstract: Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its variants, and introduce a framework based on the flags of linear subspaces, ie a hierarchy of nested linear subspaces of increasing dimension, which not only allows for a common implementation but also yields novel variants, not explored previously. We begin …

abstract analysis arxiv computer computer vision cs.cv cs.lg data extensions framework fun linear machine machine learning math.dg math.oc outlier pca robust stat.ml type variants via vision work