Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values

Asilata Bapat; Robyn Brooks; Celia Hacker; Claudia Landi; Barbara I. Mahler; Elizabeth R. Stephenson

doi:10.48550/arXiv.2210.12868

Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values

Asilata Bapat, Robyn Brooks, Celia Hacker, Claudia Landi, Barbara I. Mahler, Elizabeth R. Stephenson

Mathematical Sciences Institute

Research output: Contribution to journal › Article

Abstract

The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would allow multi-parameter persistent homology to be a viable option for data analysis. In this paper, we provide theoretical results for the computation of the matching distance in two dimensions along with a geometric interpretation of the lines through parameter space realizing this distance. The crucial point of the method we propose is that it can be easily implemented.

Original language	English
Article number	2210.12868
Number of pages	28
Journal	arXiv e-prints
DOIs	https://doi.org/10.48550/arXiv.2210.12868
Publication status	Published - 23 Oct 2022

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10.48550/arXiv.2210.12868

https://arxiv.org/abs/2210.12868

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title = "Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values",

abstract = "The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would allow multi-parameter persistent homology to be a viable option for data analysis. In this paper, we provide theoretical results for the computation of the matching distance in two dimensions along with a geometric interpretation of the lines through parameter space realizing this distance. The crucial point of the method we propose is that it can be easily implemented.",

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AU - Mahler, Barbara I.

AU - Stephenson, Elizabeth R.

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AB - The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would allow multi-parameter persistent homology to be a viable option for data analysis. In this paper, we provide theoretical results for the computation of the matching distance in two dimensions along with a geometric interpretation of the lines through parameter space realizing this distance. The crucial point of the method we propose is that it can be easily implemented.

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M3 - Article

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JF - arXiv e-prints

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Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values

Abstract

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