arXiv Statistics ML
BalLOT: Balanced $k$-means clustering with optimal transport
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Double-Bounded Nonlinear Optimal Transport for Size Constrained Min Cut Clusterin
arXiv:2501. 18143v2 Announce Type: replace Abstract: Min cut is an important graph partitioning method.
arXiv Statistics ML
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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.
arXiv Machine Learning
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Statistical Properties of $k$-means Clustering for Data Missing Completely at Random
arXiv:2607. 01945v1 Announce Type: cross Abstract: The classical $k$-means clustering cannot be directly used to incomplete data, and existing $k$-means-based clustering for missing data primarily focus on improving the practical accuracy of clustering, whereas most of them lack theoretical guarantees in the asymptotic sense.
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.
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 $\Theta(\log k)$.
arXiv Statistics ML
Aug 25
Spectral partitioning for $k$-block averaging kernels of finite Markov chains
arXiv:2608.21466v1 Announce Type: new Abstract: We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For...