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Bracketing Uncertainty in Clustering Under the Manifold Hypothesis

arXiv · AI, language, vision and robotics · article · Sep 15, 2026 · UTC

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 quant

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