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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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https://hal.inria.fr/hal-01757092
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Submitted on : Tuesday, April 3, 2018 - 1:44:58 PM
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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, Springer, 2019, ⟨10.1007/s41468-019-00026-x⟩. ⟨hal-01757092⟩

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