Persistence-based clustering with outlier-removing filtration

Abstract

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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.

Keywords

• hierarchical clustering
• topological data analysis
• filtration
• stability
• outlier removal