Weighted persistent homology
Copyright policy )Weighted persistent homology
We introduce weighted versions of the classical ��ech and Vietoris-Rips complexes. We show that a version of the Vietoris-Rips Lemma holds for these weighted complexes and that they enjoy appropriate stability properties. We also give some preliminary applications of these weighted complexes.
11 pages, 5 figures
- University of North Carolina at Chapel Hill United States
- University of North Carolina at Greensboro United States
Applied homological algebra and category theory in algebraic topology, bottleneck distance, Vietoris–Rips complex, persistence diagram, 68U10, interleaving, stability, Computing methodologies for image processing, Other homology theories in algebraic topology, persistent homology, Čech complex, 55N99, 55U10, 55U99, 55N35, weighted persistent homology, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, 55U99, Vietoris-Rips complex
Applied homological algebra and category theory in algebraic topology, bottleneck distance, Vietoris–Rips complex, persistence diagram, 68U10, interleaving, stability, Computing methodologies for image processing, Other homology theories in algebraic topology, persistent homology, Čech complex, 55N99, 55U10, 55U99, 55N35, weighted persistent homology, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, 55U99, Vietoris-Rips complex
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