Intrinsic disease maps using persistent cohomology

Abstract

We use persistent cohomology and circular coordinates to investigate three datasets related to infectious diseases. We show that all three datasets exhibit circular coordinates that carry information about the data itself. For one of the datasets we are able to recover time post infection from the circular coordinate itself – for the other datasets, this information was not available, but in one we were able to relate the circular coordinate to red blood cell counts and weight changes in the subjects.