1. Partial matchings induced by morphisms between persistence modules
- Author
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R. Gonzalez-Diaz, M. Soriano-Trigueros, A. Torras-Casas, and Universidad de Sevilla. Departamento de Matemática Aplicada I
- Subjects
Computational Geometry (cs.CG) ,FOS: Computer and information sciences ,Control and Optimization ,Block functions ,Topological data analysis ,Computer Science Applications ,Computational Mathematics ,55N31, 13P20 ,Computational Theory and Mathematics ,Partial matchings ,FOS: Mathematics ,Algebraic Topology (math.AT) ,Computer Science - Computational Geometry ,Persistence modules ,Mathematics - Algebraic Topology ,Geometry and Topology - Abstract
We study how to obtain partial matchings using the block function $\mathcal{M}_f$, induced by a morphism $f$ between persistence modules. $\mathcal{M}_f$ is defined algebraically and is linear with respect to direct sums of morphisms. We study some interesting properties of $\mathcal{M}_f$, and provide a way to obtain $\mathcal{M}_f$ using matrix operations.
- Published
- 2023
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