English

Injectivity, stability, and positive definiteness of max filtering

Functional Analysis 2025-04-25 v2 Information Theory math.IT

Abstract

Given a real inner product space V and a group G of linear isometries, max filtering offers a rich class of G-invariant maps. In this paper, we identify nearly sharp conditions under which these maps injectively embed the orbit space V/G into Euclidean space, and when G is finite, we estimate the map's distortion of the quotient metric. We also characterize when max filtering is a positive definite kernel.

Keywords

Cite

@article{arxiv.2212.11156,
  title  = {Injectivity, stability, and positive definiteness of max filtering},
  author = {Dustin G. Mixon and Yousef Qaddura},
  journal= {arXiv preprint arXiv:2212.11156},
  year   = {2025}
}