Path signatures are powerful nonparametric tools for time series analysis, shown to form a universal and characteristic feature map for Euclidean valued time series data. The theory of path signatures can be lifted to the setting of Lie group valued time series while retaining their universal and characteristic properties. This talk will introduce these generalized path signatures on Lie groups and discuss their topological origins in Chen’s cochain model for path spaces. We will then consider these signatures in the context of kernel methods in machine learning, and demonstrate an application to the human action recognition problem in computer vision.

Website: https://www.math.upenn.edu/~ldarrick/

Organizer: iakogan@ncsu.edu Contact for Zoom link