Path Signatures on Lie Groups

Understand

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.

• We lift the theory of path signatures to the setting of Lie group valued time series, adapting these tools for time series with underlying geometric constraints.
• We prove that this generalized path signature is universal and characteristic.
• To demonstrate universality, we analyze the human action recognition problem in computer vision, using $SO(3)$ representations for the time series, providing comparable performance to other shallow learning approaches, while offering an easily interpretable feature set.