# Rank-based persistence

@article{Bergomi2019RankbasedP, title={Rank-based persistence}, author={Mattia G. Bergomi and Pietro Vertechi}, journal={ArXiv}, year={2019}, volume={abs/1905.09151} }

Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other combinatorial, based on arbitrary set-valued functors. To unify the study of topological and combinatorial persistence in a common categorical framework, we give axioms for a generalized rank function on objects in a target category, so that functors to that category…

## 4 Citations

Hochschild homology, and a persistent approach via connectivity digraphs

- Mathematics
- 2022

We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree i ≥ 2. To extend them to higher degrees,…

Topological graph persistence

- Mathematics
- 2017

Abstract Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional…

Beyond Topological Persistence: Starting from Networks

- MathematicsMathematics
- 2021

Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability…

Steady and ranging sets in graph persistence

- MathematicsArXiv
- 2020

In the category of graphs, a standard way of producing gp-functions is proposed: steady and ranging sets for a given feature; their meaning is investigated in three concrete networks.

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