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

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Injectivity, Stability, and Positive Definiteness of Max Filtering

  • 期刊论文

  • 发表日期：

    2025年4月23日

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  • Dustin G. Mixon,
  • Yousef Qaddura

摘要

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.