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Decomposition of exact pfd persistence bimodules

Cochoy Jérémy 1 Steve Y. Oudot 1
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We identify a certain class of persistence modules indexed over $\mathbb{R}^2$ that are decomposable into direct sums of indecomposable summands called blocks. The conditions on the modules are that they are both pointwise finite-dimensional (pfd) and exact. Our proof follows the same scheme as the one for pfd persistence modules indexed over $\mathbb{R}$, yet it departs from it at key stages due to the product order not being a total order on $\mathbb{R}^2$, which leaves some important gaps open. These gaps are filled in using more direct arguments. Our work is motivated primarily by the study of interlevel-sets persistence, although the proposed results reach beyond that setting.
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Contributor : Steve Oudot <>
Submitted on : Friday, September 2, 2016 - 10:53:22 AM
Last modification on : Tuesday, January 14, 2020 - 4:39:20 PM

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  • HAL Id : hal-01359312, version 1
  • ARXIV : 1605.09726


Cochoy Jérémy, Steve Y. Oudot. Decomposition of exact pfd persistence bimodules. Discrete and Computational Geometry, Springer Verlag, 2019. ⟨hal-01359312⟩



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