A Unified Topological Approach to Data Science

Abstract

We establish a new theory which gives a unified topological approach to data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.

46 pages, 8 fingures

References in corpus (2)

• Persistent homology analysis of protein structure, flexibility and folding
• Simple homotopy types of Hom-complexes, neighborhood complexes, Lovász complexes, and atom crosscut complexes