Fractional signature: a generalisation of the signature inspired by fractional calculus
This work addresses a theoretical extension in mathematical analysis with potential applications in machine learning, though it appears incremental as it builds on existing signature methods.
The paper tackles the problem of generalizing the signature of a path using fractional calculus to describe solutions of linear Caputo controlled fractional differential equations, and tests a machine-learning-friendly version in handwritten digit recognition, achieving significant accuracy improvements.
In this paper, we propose a novel generalisation of the signature of a path, motivated by fractional calculus, which is able to describe the solutions of linear Caputo controlled FDEs. We also propose another generalisation of the signature, inspired by the previous one, but more convenient to use in machine learning. Finally, we test this last signature in a toy application to the problem of handwritten digit recognition, where significant improvements in accuracy rates are observed compared to those of the original signature.