Numeric invariants from multidimensional persistence

Journal Article · Fri May 19 04:00:00 EDT 2017 · Journal of Applied and Computational Topology

DOI:https://doi.org/10.1007/s41468-017-0003-z· OSTI ID:1335203

Skryzalin, Jacek ^[1]; Carlsson, Gunnar ^[2]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2. Stanford Univ., Stanford, CA (United States)

In this paper, we analyze the space of multidimensional persistence modules from the perspectives of algebraic geometry. We first build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence over one-dimensional persistence. We argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Lastly, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 1335203
• Report Number(s): SAND--2016-8670J; 647142
• Journal Information: Journal of Applied and Computational Topology, Journal Name: Journal of Applied and Computational Topology Journal Issue: 1 Vol. 1; ISSN 2367-1726
• Publisher: Springer
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
applies topology
multidimensional persistent homology
numeric invariants