metric geometry

Peel neighborhoods

arXiv:2603.26645

summary

The paper defines a canonical, parameter‑free notion of peel neighborhoods in finite metric spaces of strict negative type and shows how they can be computed efficiently to estimate local dimension and detect singularities in stratified manifolds.

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.

Addresses downstream issues with corrected theorem from previous work. No changes in thrust, but examples redone from scratch. Some typo and minor bug fixes besides

Topics & keywords

#metric spaces#negative type#peel neighborhoods#local dimension estimation#stratified manifolds#topologypeel neighborhoodsstrict negative typesoft thresholdlocal dimensionsingularity detectionstratified manifolds
Peel neighborhoods · wovepaper