Efficient Mean Curvature Computation on High-Dimensional Data Manifolds
Estimating local mean curvature at each point of a high-dimensional dataset is a key ingredient of geometry-aware machine learning algorithms, such as the Mean Curvature Boundary Points (MCBP) method. The naive implementation of this computation, based on a local shape operator approximated from k-nearest neighbor patches, involves an explicit construction of a matrix $H$ whose trace form yields an $O(m^4)$ cost per point, rendering the approach intractable for datasets with more than a few dozen features. This paper introduces two complementary contributions that together reduce this cost by several orders of magnitude. The first contribution is an exact algebraic identity. This identity...
| Authors | Alexandre L. M. Levada |
|---|---|
| Primary category | cs.LG |
| Published | 4 June 2026 |
| Last updated at source | 4 June 2026 |
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