Henry Adams, Baris Coskunuzer
Published 2021-03-11Version 1
We introduce several geometric notions, including thick-thin decompositions and the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "size" or "persistence" of a homology class. As a case study, we analyze the power filtration on unweighted graphs, and provide explicit bounds for the life spans of homology classes in persistence diagrams in all dimensions.
Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem
On the Bootstrap for Persistence Diagrams and Landscapes
Universality of persistence diagrams and the bottleneck and Wasserstein distances
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