Stable and consistent density-based clustering

We present a consistent approach to density-based clustering, which satisfies a stability theorem that holds without any distributional assumptions. We also show that the algorithm can be combined with standard procedures to extract a flat clustering from a hierarchical clustering, and that the resulting flat clustering algorithms satisfy stability theorems. The algorithms and proofs are inspired by topological data analysis.

@article{rolle2025_2005.09048,
  title={ Stable and consistent density-based clustering via multiparameter persistence },
  author={ Alexander Rolle and Luis Scoccola },
  journal={arXiv preprint arXiv:2005.09048},
  year={ 2025 }
}