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Diffusion Curvature for Estimating Local Curvature in High Dimensional Data.
In: (Advances in Neural Information Processing Systems). 2022. (Advances in Neural Information Processing Systems ; 35)
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes.
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Publication type
Article: Conference contribution
Language
english
Publication Year
2022
HGF-reported in Year
2022
ISSN (print) / ISBN
1049-5258
Conference Title
Advances in Neural Information Processing Systems
Quellenangaben
Volume: 35
Institute(s)
Institute of AI for Health (AIH)
POF-Topic(s)
30205 - Bioengineering and Digital Health
Research field(s)
Enabling and Novel Technologies
PSP Element(s)
G-540003-001
Scopus ID
85163150051
Erfassungsdatum
2023-10-18