Functional Data and Holonomy

In machine learning, a fundamental problem is to construct good feature maps for data. Such feature maps should allow us to approximate functions and characterise probability measures on the data space. In many applications, the data themselves come in the form of functions, equipped with additional structure, and the feature map should preserve this structure. For instance, time series data are viewed as maps from an interval into a vector space, while images can be interpreted as maps from a square into a vector space. In this talk, we discuss how (higher) holonomy provides a computable way to build effective feature maps for functional data. This is joint work with Harald Oberhauser.