The shift-dimension of multipersistence modules-Reference-Cited by-同舟云学术

The shift-dimension of multipersistence modules

Published:2024-06-15 Issue: Volume: Page:
ISSN:2367-1726
Container-title:Journal of Applied and Computational Topology
language:en
Short-container-title:J Appl. and Comput. Topology

Author:

Chachólski Wojciech,Corbet René^ORCID,Sattelberger Anna-Laura^ORCID

Abstract

AbstractWe present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate polynomial ring arising from the hierarchical stabilization of the zeroth total multigraded Betti number. We give a fast algorithm for the computation of the shift-dimension of interval modules in the bivariate case. We construct multipersistence contours that are parameterized by multivariate functions and hence provide a large class of feature maps for machine learning tasks.

Funder

Knut och Alice Wallenbergs Stiftelse

Horizon 2020 Framework Programme

digital futures at KTH

Brummer & Partners MathDataLab

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s41468-024-00169-6.pdf

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