36 citations · 208 across the 26 of their papers we have counts for
29 papers
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…
On the signature of an image
Joscha Diehl, Kurusch Ebrahimi-Fard, Fabian Harang +1
Over the past decade, the importance of the 1D signature which can be seen as a functional defined along a path, has been pivotal in both path-wise stochastic calculus and the anal…
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…
A structure theorem for streamed information
Cristopher Salvi, Joscha Diehl, Terry Lyons +2
We identify the free half shuffle algebra of Schützenberger (1958) with an algebra of real-valued functionals on paths, where the half shuffle emulates integration of a functional…