Persistence-based clustering with outlier-removing filtration - Bois, Alexandre; Tervil, Brian; Oudre, Laurent (Frontiers in Applied Mathematics and Statistics, 2024)
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.