Author
Stolz-Pretzer, B
Tanner, J
Harrington, H
Nanda, V
Journal title
Proceedings of the National Academy of Sciences
DOI
10.1073/pnas.2001741117
Issue
33
Volume
117
Last updated
2022-08-05T08:55:35.57+01:00
Page
19664-19669
Abstract
The quest for low-dimensional models which approximate high-dimensional data is pervasive across the physical, natural, and social sciences. The dominant paradigm underlying most standard modeling techniques assumes that the data are concentrated near a single unknown manifold of relatively small intrinsic dimension. Here, we present a systematic framework for detecting interfaces and related anomalies in data which may fail to satisfy the manifold hypothesis. By computing the local topology of small regions around each data point, we are able to partition a given dataset into disjoint classes, each of which can be individually approximated by a single manifold. Since these manifolds may have different intrinsic dimensions, local topology discovers singular regions in data even when none of the points have been sampled precisely from the singularities. We showcase this method by identifying the intersection of two surfaces in the 24-dimensional space of cyclo-octane conformations and by locating all of the self-intersections of a Henneberg minimal surface immersed in 3-dimensional space. Due to the local nature of the topological computations, the algorithmic burden of performing such data stratification is readily distributable across several processors.
Symplectic ID
1064879
Favourite
Off
Publication type
Journal Article
Publication date
03 Aug 2020
Please contact us for feedback and comments about this page. Created on 26 Oct 2019 - 00:02.