Geodesic
The algebraic stability for persistent Laplacians
Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 297-323.

Voir la notice de l'article provenant de la source International Press of Boston

The stability of topological persistence is one of the fundamental issues in topological data analysis. Numerous methods have been proposed to address the stability of persistent modules or persistence diagrams. Recently, the concept of persistent Laplacians has emerged as a novel approach to topological persistence, attracting significant attention and finding applications in various fields. In this paper, we investigate the stability of persistent Laplacians. We introduce the notion of “Laplacian trees”, which captures the collection of persistent Laplacians that persist from a given parameter. To formalize our study, we construct the category of Laplacian trees and establish an algebraic stability theorem for persistent Laplacian trees. Notably, our stability theorem is applied to the real-valued functions on simplicial complexes and digraphs.
DOI : 10.4310/HHA.2024.v26.n2.a15
Classification : 55N31, 15A63, 18A25
Keywords: persistent homology, persistent Laplacian, algebraic stability, inner product space, persistence harmonic space 
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Jian Liu; Jingyan Li; Jie Wu. The algebraic stability for persistent Laplacians. Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 297-323. doi : 10.4310/HHA.2024.v26.n2.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a15/

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