The elbow statistic: Multiscale clustering statistical significance
Selecting the number of clusters remains a fundamental challenge in unsupervised learning. Existing approaches typically focus on identifying a single "optimal" partition, often overlooking statistically meaningful structure present across multiple resolutions. We introduce ElbowSig, a general inferential framework for assessing clustering structure over a range of resolutions. The method formalizes the elbow heuristic by defining a normalized discrete curvature statistic based on the sequence of within-cluster heterogeneity values, and evaluates its significance relative to a null distribution of unstructured data. This yields hypothesis tests across resolutions, enabling simultaneous in...
| Authors | Francisco J. Perez-Reche |
|---|---|
| Primary category | stat.ML |
| Published | 3 March 2026 |
| Last updated at source | 3 May 2026 |
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