2022/12/31 by Martin Andersson, Andersson, Martin, Benny Avelin +1 · 1 citation
Computer Science · Engineering · #3D Shape Modeling and Analysis #58K99 (Primary) #60B99 #62G10 (Secondary) #68R99 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2301.00201
openalex publication_date 2022/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We develop theory and methods that use the graph Laplacian to analyze the geometry of the underlying manifold 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.