In topological data analysis, one often builds a filtered space from data and uses its persistent homology to describe properties of the data. One-parameter filtrations like the Vietoris-Rips complex or the offset filtration work well in many situations, but they are overly sensitive to outliers. A more robust approach is to add an additional density parameter to the filtration, leading to multiparameter persistence. We introduce the core bifiltration given as the union of balls centered at data points in sufficiently dense areas, namely we consider balls that contain at least k data points for some density parameter k. By intersecting the balls with Voronoi cells, we obtain the Delaunay core bifiltration, which is smaller and for which we have a computationally efficient implementation for lower dimensions. Both bifiltrations share similar (Prohorov) stability properties.

Based on the article Core Bifiltration: https://doi.org/10.1007/s41468-025-00226-8