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arXiv Statistics ML

Gradient-Guided Density Peak Clustering

Gradient-Guided Density Peak Clustering (GGDPC) enhances traditional density peak clustering by performing a gradient ascent step before each nearest‑neighbor uphill search, aiming to stabilize uphill paths in low‑density regions. The authors develop a stability theory linking the GGDPC graph to the gradient ascent flow of the population density, and establish consistency across five criteria: recovery of local modes, adjusted Rand index, dendrogram (cluster tree), path length, and waterfall measure. These results offer new statistical, geometric, and topological insights into DPC‑type clustering algorithms.

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arXiv Machine Learning
Aug 27

Towards Robust and Scalable Density-based Clustering via Graph Propagation

The paper introduces CluProp, a framework that treats varied‑density clustering in high‑dimensional spaces as a label propagation process over neighborhood graphs. By combining density‑based ideas with graph connectivity, it offers a deterministic propagation strategy that reduces parameter sensitivity and scales efficiently to millions of points. CluProp is agnostic to distance metrics and consistently outperforms existing baselines in accuracy while processing large datasets in minutes.

By Yingtao Zheng, Hugo Phibbs, Ninh Pham
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arXiv Machine Learning
Jul 13

Scalable Varied-Density Clustering via Graph Propagation

arXiv:2508. 02989v2 Announce Type: replace Abstract: We propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations.

By Ninh Pham, Yingtao Zheng, Hugo Phibbs
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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
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