Alexander Rolle (6/1/20): Stable and consistent density-based clustering
Title: Stable and consistent density-based clustering
Abstract: We present a consistent approach to density-based clustering, which satisfies a stability theorem that holds without any distributional assumptions. We first define a 3-parameter hierarchical clustering of a metric probability space, and show that this construction is stable. Several well-known hierarchical clustering methods can be obtained as "horizontal" or "vertical" slices of this construction. We obtain a stable and consistent hierarchical clustering algorithm by taking 1-parameter slices that are not horizontal or vertical.