AUTHOR=Bois Alexandre , Tervil Brian , Oudre Laurent 

TITLE=Persistence-based clustering with outlier-removing filtration

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

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=<p>This article describes a non-parametric clustering algorithm with an outlier removal step. Our method is based on tools from topological data analysis: we define 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 evaluate our method on point cloud and graph datasets, showing that it can compete with state-of-the-art methods while being non-parametric.</p>