Work

Exploring singularities in data with the graph Laplacian: An explicit approach

Year: 2025

Type: article

Abstract: We develop theory and methods that use the graph Laplacian to analyze the geometry of the underlying manifolds of datasets. Our theory provides theoretical guarantees and explicit bounds on the functional forms of the graph Laplacian when it acts on functions defined close to singularities of the underlying manifold. We use these explicit bounds to develop tests for singularities and propose methods that can be used to estimate geometric properties of singularities in the datasets.

Source: Journal of Computational Mathematics and Data Science

DOI: 10.1016/j.jcmds.2025.100113

Authors: Martin Andersson, Benny Avelin

Institution: Uppsala University

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,070

Funders: Royal Swedish Academy of Sciences, Knut och Alice Wallenbergs Stiftelse, Vetenskapsrådet