The Shift-Dimension of Multipersistence Modules
Commutative Algebra
2025-05-27 v4 Algebraic Topology
Abstract
We 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.
Keywords
Cite
@article{arxiv.2112.06509,
title = {The Shift-Dimension of Multipersistence Modules},
author = {Wojciech Chachólski and René Corbet and Anna-Laura Sattelberger},
journal= {arXiv preprint arXiv:2112.06509},
year = {2025}
}
Comments
20 pages, 4 figures