A Mean Curvature Approach to Boundary Detection: Geometric Insights for Unsupervised Learning
Accurate boundary detection in high-dimensional data remains a central challenge in unsupervised learning, particularly in the presence of non-linear structures and heterogeneous densities. In this work, we introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning that departs from traditional density-based approaches by explicitly modeling the intrinsic curvature of the data manifold. The method relies on a discrete approximation of the shape operator, estimated from local k-nearest neighbor patches, to compute pointwise mean curvature without requiring explicit manifold parametrization. The key insight of MCBP is to use mean curv...
| Authors | Alexandre L. M. Levada |
|---|---|
| Primary category | cs.LG |
| Published | 5 May 2026 |
| Last updated at source | 9 May 2026 |
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