A Unified Topological Approach to Data Science
arXiv:2103.16926
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.
arXiv comment46 pages, 8 fingures
References in corpus (9)
- TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions
- Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening
- Persistent homology analysis of protein structure, flexibility and folding
- Discrete differential calculus, graphs, topologies and gauge theory
- Analysis of Kolmogorov Flow and Rayleigh-Bénard Convection using Persistent Homology
- Differential calculus and gauge theory on finite sets
- Homologies of path complexes and digraphs
- Simple homotopy types of Hom-complexes, neighborhood complexes, Lovász complexes, and atom crosscut complexes
- The stability of persistent homology of hypergraphs