Peel neighborhoods

Abstract

We introduce the canonical, parameter-free, and efficiently computable notion of peel neighborhoods in a finite metric space of strict negative type. Using a soft threshold to upper bound their radius or cardinality allows peel neighborhoods to be computed at scale, enabling useful microscopic descriptions of geometry and topology. As an example of their utility, peel neighborhoods enable efficient and performant estimates of local dimension and detections of singularities in samples from stratified manifolds.