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Journal Articles Journal of Applied and Computational Topology Year : 2019

A Comparison Framework for Interleaved Persistence Modules

Abstract

We present a generalization of the induced matching theorem of [1] and use it to prove a generalization of the algebraic stability theorem for R-indexed pointwise finite-dimensional persistence modules. Via numerous examples, we show how the generalized algebraic stability theorem enables the computation of rigorous error bounds in the space of persistence diagrams that go beyond the typical formulation in terms of bottleneck (or log bottleneck) distance.
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Dates and versions

hal-01757092 , version 1 (03-04-2018)

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Shaun Harker, Miroslav Kramár, Rachel Levanger, Konstantin Mischaikow. A Comparison Framework for Interleaved Persistence Modules. Journal of Applied and Computational Topology, 2019, ⟨10.1007/s41468-019-00026-x⟩. ⟨hal-01757092⟩
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