Aspects of topological approaches for data science
Jelena Grbić, Jie Wu, Kelin Xia, Guo‐Wei Wei
Abstract
We establish a new theory which unifies various aspects of topological approaches for 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.
Topics & Concepts
Topological data analysisTopology (electrical circuits)Data scienceComputer scienceMathematicsAlgorithmCombinatoricsTopological and Geometric Data AnalysisBioinformatics and Genomic NetworksCell Image Analysis Techniques