Functional data such as time series and images are equipped with natural concatenation operations. This algebraic structure allows us to make sense of streaming time series in online applications (concatenating the new incoming data at the end of our existing time series), or gluing together a partitioned image (perhaps processed in parallel). In this talk, we discuss mathematical tools to construct feature maps for such functional data which preserve this underlying concatenation structure. For time series, we provide an overview of existing composable feature maps such as parallel transport into matrix groups and the path signature which have recently been used in a variety of machine learning problems. For images, the concatenation structure is much more complicated as there exist two natural operations: horizontal and vertical concatenation. We will discuss recent work on using tools from higher category theory to construct composable feature maps for 2-dimensional functional data such as images. (No prior knowledge of category theory will be assumed.)

Refreshments will be served preceding the talk, starting at 2:45.