Developing the path signature methodology and its application to landmark-based human action recognition
Landmark-based human action recognition in videos is a challenging task in computer
vision. One key step is to design a generic approach that generates discriminative features …
vision. One key step is to design a generic approach that generates discriminative features …
Path signatures for diversity in probabilistic trajectory optimisation
Motion planning can be cast as a trajectory optimisation problem where a cost is minimised
as a function of the trajectory being generated. In complex environments with several …
as a function of the trajectory being generated. In complex environments with several …
Time-warping invariants of multidimensional time series
In data science, one is often confronted with a time series representing measurements of
some quantity of interest. Usually, in a first step, features of the time series need to be …
some quantity of interest. Usually, in a first step, features of the time series need to be …
Learning paths from signature tensors
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor
decomposition, algebraic geometry, and numerical optimization to this group action. Given a …
decomposition, algebraic geometry, and numerical optimization to this group action. Given a …
Smooth rough paths, their geometry and algebraic renormalization
We introduce the class of “smooth rough paths” and study their main properties. Working in a
smooth setting allows us to discard sewing arguments and focus on algebraic and geometric …
smooth setting allows us to discard sewing arguments and focus on algebraic and geometric …
Rank and symmetries of signature tensors
F Galuppi, P Santarsiero - arXiv preprint arXiv:2407.20405, 2024 - arxiv.org
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the
path. In this paper we propose a systematic study of basic properties of signature tensors …
path. In this paper we propose a systematic study of basic properties of signature tensors …
The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures
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). We provide two …
every integrable measure on the free nilpotent Lie group of step (over). We provide two …
Tropical time series, iterated-sums signatures, and quasisymmetric functions
Aiming for a systematic feature extraction from time series, we introduce the iterated-sums
signature over arbitrary commutative semirings. The case of the tropical semiring is a …
signature over arbitrary commutative semirings. The case of the tropical semiring is a …
Rectifiable paths with polynomial log‐signature are straight lines
The signature of a rectifiable path is a tensor series in the tensor algebra whose coefficients
are definite iterated integrals of the path. The signature characterizes the path up to a …
are definite iterated integrals of the path. The signature characterizes the path up to a …