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.

翻译：本文研究了受F. Király与H. Oberhauser先前工作启发的广义迭代和签名之代数性质。特别地，我们通过考虑张量代数上词汇的变形拟混积，展示了如何恢复其关联线性映射的特征性质。我们引入三种与机器学习应用精神相近的迭代和签名非线性变换，并论证了它们的若干性质。