36 citations · 208 across the 26 of their papers we have counts for
10 papers · 1 filter
Conjugation, loop and closure invariants of the iterated-integrals signature
Joscha Diehl, Rosa Preiß, Jeremy Reizenstein
Given a feature set for the shape of a closed loop, it is natural to ask which features in that set do not change when the starting point of the path is moved. For example, in two…
A multiplicative surface signature through its Magnus expansion
Ilya Chevyrev, Joscha Diehl, Kurusch Ebrahimi-Fard +1
In the last decade, the concept of path signature has achieved significant success in data science applications. It offers a powerful set of features that effectively capture and d…
Hopf Algebra on Vincular Permutation Patterns
Joscha Diehl, Emanuele Verri
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specif…
The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures
Marianne Clausel, Joscha Diehl, Raphael Mignot +3
We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step (over $\mathbb{R}^d…
Signatures of graphs for bicommutative Hopf algebras
Diego Caudillo, Joscha Diehl, Kurusch Ebrahimi-Fard +1
This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that a…
Generalized iterated-sums signatures
Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia
We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F.~Király and H.~Oberhauser. In particular, we show how to…