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Topological Persistence and Simplification

Abstract

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.

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Edelsbrunner, Letscher & Zomorodian Topological Persistence and Simplification. Discrete Comput Geom 28, 511–533 (2002). https://doi.org/10.1007/s00454-002-2885-2

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