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<p>Quasisymmetric functions have recently been used in time-series analysis as polynomial features that are invariant under, so-called, dynamic time warping. We extend this notion to data indexed by two parameters and thus provide warping invariants for images. We show that two-parameter quasisymmetric functions are complete in a certain sense and provide a two-parameter quasi-shuffle identity. A compatible coproduct is based on diagonal concatenation of the input data, leading to a (weak) form of Chen’s identity.</p>

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Two-parameter sums signatures and corresponding quasisymmetric functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月15日

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  • Joscha Diehl,
  • Leonard Schmitz

摘要

Quasisymmetric functions have recently been used in time-series analysis as polynomial features that are invariant under, so-called, dynamic time warping. We extend this notion to data indexed by two parameters and thus provide warping invariants for images. We show that two-parameter quasisymmetric functions are complete in a certain sense and provide a two-parameter quasi-shuffle identity. A compatible coproduct is based on diagonal concatenation of the input data, leading to a (weak) form of Chen’s identity.