Multi-Domain Clustering via Measure Quantization

Abstract

Clustering is a fundamental task in data analysis, typically addressed through centroid-based methods such as K-means. In this work, we present a general framework for multi-domain clustering via measure quantization: given samples from multiple domains, we learn a shared set of cluster prototypes by minimizing a probability metric, such as the Sinkhorn divergence or the Maximum Mean Discrepancy, between each domain's probability measure and the measure of prototypes. Data points are then assigned to clusters either via nearest centroid, or via optimal transport, a collaborative strategy that couples all samples within a domain. A mini-batch optimization strategy makes both fitting and assignment scalable, reducing memory and computational cost while preserving clustering performance. Experimental results on 5 multi-domain benchmarks spanning image, audio and sensor data show that our Sinkhorn-based method consistently outperforms classical and multi-domain clustering baselines, and that this advantage persists when scaling to hundreds of thousands of samples.

Robust K-means Clustering using the Density Power Divergence Measure
Anirban Mondal, Paromita Banerjee, Abhijit Mandal
arXiv30 Aug 2026PreprintCC BY-NC-SA 4.0Full textStatisticsarXiv
On the measure of the boundary of a Hajłasz-Sobolev (M^1,p,M^1,q)-extension domain
Ryan Alvarado, Riddhi Mishra
arXiv28 Aug 2026PreprintarXiv licenceFull textAnalysis & PDEsarXiv
Multi-Bitwidth Quantization for LLMs Using Additive Codebooks
Liza Babaoglu, Shuangyi Chen, Ashish Khisti
arXiv26 Sep 2026PreprintCC BY 4.0Full textGeneral mathematicsarXiv
Sparsity-Corrected Tensor Clustering for Multi-Layer Networks
Xuefei Wang, Gaorong Li, Wenyang Zhang
arXiv16 Oct 2026PreprintarXiv licenceFull textStatisticsarXiv
Minimax Rates and Improved Spectral Convergence for Multi-Manifold Clustering
Haoyu Chen, Chenghui Li
arXiv11 Oct 2026PreprintCC BY 4.0Full textStatisticsarXiv

Cite

BibTeX RIS

BibTeX

@misc{eufrazio2026multidomain,
  title = {{Multi-Domain Clustering via Measure Quantization}},
  author = {Rafael Pereira Eufrazio and Eduardo Fernandes Montesuma and Charles Casimiro Cavalcante},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21664},
  eprint = {2609.21664},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21664},
}

RIS

TY  - UNPB
TI  - Multi-Domain Clustering via Measure Quantization
AU  - Rafael Pereira Eufrazio
AU  - Eduardo Fernandes Montesuma
AU  - Charles Casimiro Cavalcante
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21664
UR  - https://arxiv.org/abs/2609.21664
AB  - Clustering is a fundamental task in data analysis, typically addressed through centroid-based methods such as K-means. In this work, we present a general framework for multi-domain clustering via measure quantization: given samples from multiple domains, we learn a shared set of cluster prototypes by minimizing a probability metric, such as the Sinkhorn divergence or the Maximum Mean Discrepancy, between each domain's probability measure and the measure of prototypes. Data points are then assigned to clusters either via nearest centroid, or via optimal transport, a collaborative strategy that couples all samples within a domain. A mini-batch optimization strategy makes both fitting and assignment scalable, reducing memory and computational cost while preserving clustering performance. Experimental results on 5 multi-domain benchmarks spanning image, audio and sensor data show that our Sinkhorn-based method consistently outperforms classical and multi-domain clustering baselines, and that this advantage persists when scaling to hundreds of thousands of samples.
ER  -

Abstract

Related

Cite