AUTHOR=Bois Alexandre , Tervil Brian , Oudre Laurent 

TITLE=Persistence-based clustering with outlier-removing filtration

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 10 - 2024

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1260828

DOI=10.3389/fams.2024.1260828

ISSN=2297-4687

ABSTRACT=We describe a non-parametric hierarchical clustering algorithm with an outlier removal step, based on topological data analysis. We use a new filtration on metric spaces which is a variant of the Vietoris-Rips filtration that adds information about the points' nearest neighbor to the persistence diagram. We prove a stability theorem for this filtration, and illustrate our method on point cloud and graph datasets.