The reflection distance between zigzag persistence modules

05/28/2018

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by   Alexander Elchesen, et al.

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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 ℓ^p-bottleneck distance between their respective persistence diagrams.