Generalized iterated-sums signatures

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.