Detecting spatial dependence with persistent homology

Abstract

We propose and demonstrate a topological test for spatial dependence based on the framework of persistent homology. We compare our method to Moran's I, a classical measure of spatial auto-correlation, on synthetic datasets as well as on election and COVID data. We find about 65-75% agreement between the main variant of our method and Moran's I on real datasets. While the Moran's I test is more sensitive overall on these datasets, there are instructive instances (synthetic and real) where our method detects a spatial pattern that the Moran's I test does not.