Two-parameter sums signatures and corresponding quasisymmetric functions
Combinatorics
2024-10-10 v3
Abstract
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.
Cite
@article{arxiv.2210.14247,
title = {Two-parameter sums signatures and corresponding quasisymmetric functions},
author = {Joscha Diehl and Leonard Schmitz},
journal= {arXiv preprint arXiv:2210.14247},
year = {2024}
}