arXiv Machine Learning By Diede P. M. van der Hoorn, Alessio Arleo, Fernando V. Paulovich

Why Can't I See My Clusters? A Precision-Recall Approach to Dimensionality Reduction Validation

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arXiv:2509. 04222v2 Announce Type: replace Abstract: Dimensionality Reduction (DR) is widely used for visualizing high-dimensional data, often with the goal of revealing expected cluster structure.

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arXiv Machine Learning
Sep 17

Bracketing Uncertainty in Clustering Under the Manifold Hypothesis

The paper formalizes a geometric tradeoff between ambient separation and sampling gaps to determine when distinct manifold components can be reliably separated in clustering. It introduces a threshold phenomenon for mutual‑k‑nearest‑neighbor graphs, defining an uncertainty zone where the number of clusters cannot be identified. The authors propose Manifold‑Based Clustering (MBC), which outputs a bracket interval quantifying this uncertainty rather than forcing a single cluster count.

By Savik Kinger, Luciano Dyballa, Steven W. Zucker