Iterated Integrals and Paths of Persistence Diagrams

Path signatures are a reparametrization-invariant characterization of paths, which are defined via iterated integrals. More generally, path signatures form the 0-cochains of Kuo-Tsai Chen’s iterated integral cochain model of path spaces. By considering multivariate time series as a path through Euclidean space, we can leverage the path signatures as a reparametrization-invariant feature set for time series. In this talk, we will introduce the path signature, consider its application to studying paths of persistence diagrams (persistence vineyards), and briefly discuss how Chen’s perspective can lead to generalizations.