Core Bifiltration

The motivation of this paper is to recognize a geometric shape from a noisy sample in the form of a point cloud. Inspired by the HDBSCAN clustering algorithm and the multicover bifiltration, we introduce the core- and the alpha-core bifiltrations. The multicover-, core- and alpha-core bifiltrations are all interleaved, and they enjoy similar Prohorov stability properties. We have performed experiments with the core and the alpha-core bifiltrations where we have calculated their persistent homology along lines in the two-dimensional persistence parameter space.