Persistent Homology of Geospatial Data: A Case Study with Voting

A crucial step in the analysis of persistent homology is transformation data into an appropriate topological object (which, our case, a simplicial complex). Software packages for computing typically construct Vietoris--Rips or other distance-based complexes on point clouds because they are relatively easy to compute. We investigate alternative methods constructing and effects making associated choices during simplicial-complex construction output persistent-homology algorithms. present two new from two-dimensional geospatial (such as maps). apply these California precinct-level voting set, we thereby demonstrate that constructions can capture geometric characteristics missed by constructions. Our thus yield more interpretable persistence modules barcodes data. In particular, able distinguish short-persistence features occur only narrow range distance scales (e.g., patterns densely populated cities) noise incorporating information about spatial relationships between regions.