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arXiv Statistics ML

BalLOT: Balanced $k$-means clustering with optimal transport

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arXiv Statistics ML
2d ago

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.

By Yikun Zhang, Yen-Chi Chen
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arXiv Machine Learning
2d ago

T-ARC: Topology-Aware Randomized Clustering via Distributionally Robust Stochastic Block Models

The paper introduces T-ARC, a clustering algorithm that integrates topological information into the K‑means objective by coupling a data‑fidelity term with a graph‑cut penalty. The latent graph is modeled as a random realization from a Stochastic Block Model, whose parameter is optimized via Distributionally Robust Optimization, using a persistence‑based similarity matrix derived from zero‑dimensional persistent homology. Experiments on synthetic non‑convex data and Fashion‑MNIST subsets demonstrate that T‑ARC recovers latent topological structures and outperforms K‑means on curved and interleaved clusters while remaining competitive and more stable on real data.

By Serena Grazia De Benedictis, Andersen Ang, Nicoletta Del Buono, Flavia Esposito, Laura Selicato
ragsafety
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arXiv Machine Learning
Jul 30

Randomizing the Number of Centers in k-means++

arXiv:2607. 26202v1 Announce Type: cross Abstract: The $k$-means++ algorithm is a standard and widely used seeding method for $k$-means clustering, but for a fixed number $k$ of centers its worst-case expected approximation ratio is $\Theta(\log k)$.

By Vaclav Rozhon
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arXiv Machine Learning
Jul 20

Cluster-Aware Matching via Laplacian Optimal Transport

arXiv:2607. 16178v1 Announce Type: cross Abstract: In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure.

By Gabriel Samberg, YoonHaeng Hur, Yuehaw Khoo, Nir Sharon
safety
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arXiv Statistics ML
Sep 11

A Mean Field Games Perspective on Evolutionary Clustering

The paper introduces a control‑theoretic framework for evolutionary clustering using quasi‑stationary Mean Field Games. Each cluster is modeled as a probability density whose dynamics follow a Fokker–Planck equation, while a stationary Hamilton–Jacobi equation determines the velocity field. In a Gaussian specialization, affine dynamics replicate the mean and covariance trajectories of the classical Expectation–Maximization algorithm, and the authors propose causal and non‑causal time‑averaged log‑likelihood objectives to enhance temporal coherence, along with a fully density‑based numerical implementation for non‑Gaussian components. The method is evaluated on synthetic and real time‑dependent datasets, compared to snapshot Expectation–Maximization, temporally smoothed observations, and an evolutionary k‑means baseline.

By Alessio Basti, Fabio Camilli, Adriano Festa
benchmarks
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arXiv Machine Learning
Sep 10

A Sub-4 Approximation for Fair $k$-Means

arXiv:2609.07974v1 Announce Type: cross Abstract: Fairness in clustering has attracted sustained research interest, motivated by the need to ensure equitable representation of protected groups in mac...

By Kangke Cheng, Guanlin Mo, Shihong Song, Hu Ding
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