Homology Groups of High-Resolution Temporal Rainfall

Abstract:

Using high-resolution temporal rainfall intensities from Iowa City, IA (IIHR, U of Iowa), we perform an analysis of the homology groups generated by data connectivity in state space, and attempt a qualitative interpretation of the first and second homology groups. Let us note that homology groups are generated, in the context of topological data analysis (TDA), by representing the data in n-dimensional state space and building a connectivity diagram according to the respective distances between the data points. Subsequently, the topological invariants of the resulting connected structures are being analyzed.