Bracketing Uncertainty in Clustering Under the Manifold Hypothesis
The manifold hypothesis suggests a natural criterion for clustering: partition data according to the manifold component from which each point is drawn. Whether two components are separable depends on a geometric tradeoff: the ambient separation between components versus the largest gap in sampling. In practice, this tradeoff is rarely assessed explicitly, leading standard methods to over-commit to a single clustering assignment even when the data do not support a unique answer. We formalize this tradeoff by combining intrinsic manifold geometry (volume growth and reach) with sample-level quantities (fill distance and density), yielding a threshold phenomenon for mutual-$k$-nearest-neighbo...
| Authors | Savik Kinger, Luciano Dyballa, Steven W. Zucker |
|---|---|
| Primary category | stat.ML |
| Published | 15 September 2026 |
| Last updated at source | 15 September 2026 |
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