Topological persistence and simplification
Herbert Edelsbrunner, David Letscher, Afra Zomorodian · 2002
We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise, depending on its life-time or persistence within the filtration. We give fast algorithms for completing persistence and experimental evidence for their speed and utility.