Topological Persistence and Simplification
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- Edelsbrunner, Letscher & Zomorodian Discrete Comput Geom (2002) 28: 511. doi:10.1007/s00454-002-2885-2
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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 lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.