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arXiv · 1305.4780

Exterior Critical Series of Persistence Modules

Pawin Vongmasa·Gunnar Carlsson
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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.

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Pawin Vongmasa, Gunnar Carlsson. 2013-05-21. Exterior Critical Series of Persistence Modules. https://arxiv.org/abs/1305.4780

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