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.

Spaces of Clusterings

We propose two algorithms to cluster a set of clusterings of a fixed dataset, such as sets of clusterings produced by running a clustering algorithm with a range of parameters, or with many initializations. We use these to study the effects of varying the parameters of HDBSCAN, and to study methods for initializing $k$-means.