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arXiv · 1805.11190

The reflection distance between zigzag persistence modules

Alexander Elchesen·Facundo Mémoli
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Abstract

By invoking the reflection functors introduced by Bernstein, Gelfand, and Ponomarev in 1973, in this paper we define a metric on the space of all zigzag modules of a given length, which we call the reflection distance. We show that the reflection distance between two given zigzag modules of the same length is an upper bound for the $\ell^1$-bottleneck distance between their respective persistence diagrams.

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Alexander Elchesen, Facundo Mémoli. 2018-05-28. The reflection distance between zigzag persistence modules. https://arxiv.org/abs/1805.11190

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