Generalized iterated-sums signatures

Joscha Diehl; Kurusch Ebrahimi-Fard; Nikolas Tapia

doi:10.1016/j.jalgebra.2023.06.007

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arXiv · 2012.04597

Generalized iterated-sums signatures

Joscha Diehl·Kurusch Ebrahimi-Fard·Nikolas Tapia

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Abstract

We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F.~Kir\'aly and H.~Oberhauser. In particular, we show how to recover the character property of the associated linear map over the tensor algebra by considering a deformed quasi-shuffle product of words on the latter. We introduce three non-linear transformations on iterated-sums signatures, close in spirit to Machine Learning applications, and show some of their properties.

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Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia. 2020-12-08. Generalized iterated-sums signatures. https://doi.org/10.1016/j.jalgebra.2023.06.007

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