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Foundations of Computational Mathematics

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30-06-2016

Multidimensional Persistence and Noise

Authors: Martina Scolamiero, Wojciech Chachólski, Anders Lundman, Ryan Ramanujam, Sebastian Öberg

Published in: Foundations of Computational Mathematics | Issue 6/2017

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Abstract

In this paper, we study multidimensional persistence modules (Carlsson and Zomorodian in Discrete Comput Geom 42(1):71–93, 2009; Lesnick in Found Comput Math 15(3):613–650, 2015) via what we call tame functors and noise systems. A noise system leads to a pseudometric topology on the category of tame functors. We show how this pseudometric can be used to identify persistent features of compact multidimensional persistence modules. To count such features, we introduce the feature counting invariant and prove that assigning this invariant to compact tame functors is a 1-Lipschitz operation. For one-dimensional persistence, we explain how, by choosing an appropriate noise system, the feature counting invariant identifies the same persistent features as the classical barcode construction.

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Title: Multidimensional Persistence and Noise
Authors: Martina Scolamiero
Wojciech Chachólski
Anders Lundman
Ryan Ramanujam
Sebastian Öberg
Publication date: 30-06-2016
Publisher: Springer US
Published in: Foundations of Computational Mathematics / Issue 6/2017
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI: https://doi.org/10.1007/s10208-016-9323-y

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