Persistent Homology of Geospatial Data: A Case Study with Voting

Understand

A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (in our case, a simplicial complex).

• Modern packages for persistent homology often construct Vietoris--Rips or other distance-based simplicial complexes on point clouds because they are relatively easy to compute.
• We investigate alternative methods of constructing these complexes and the effects of making associated choices during simplicial-complex construction on the output of persistent-homology algorithms.
• We present two new methods for constructing simplicial complexes from two-dimensional geospatial data (such as maps).