Exterior Critical Series of Persistence Modules
Rings and Algebras
2014-05-13 v2 Commutative Algebra
Algebraic Topology
Abstract
The persistence barcode is a well-established complete discrete invariant for finitely generated persistence modules [5] [1]. Its definition, however, does not extend to multi- dimensional persistence modules. In this paper, we introduce a new discrete invariant: the exterior critical series. This invariant is complete in the one-dimensional case and can be defined for multi-dimensional persistence modules, like the rank invariant [2]. However, the exterior critical series can detect some features that are not captured by the rank invariant.
Keywords
Cite
@article{arxiv.1305.4780,
title = {Exterior Critical Series of Persistence Modules},
author = {Pawin Vongmasa and Gunnar Carlsson},
journal= {arXiv preprint arXiv:1305.4780},
year = {2014}
}
Comments
16 pages, 1 figure