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Relative Wasserstein Spatial Depth for Cluster Number Selection in Distributional Data — arXiv:2610.09153

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.09153
License (as archived): CC0-1.0
Archived: 2026-10-08T12:39:58.710Z
SHA-256 of the archived text: c3cfffdecc68992645bec355c7093c46a8478972498303185427a184159bdaf8
Stable URL of this page: https://metraipolis.com/documento/dc_4eaec07e35ab

How to cite

Relative Wasserstein Spatial Depth for Cluster Number Selection in Distributional Data — arXiv:2610.09153 — arXiv (en), https://arxiv.org/abs/2610.09153 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4eaec07e35ab (Metraipolis archive dc_4eaec07e35ab, sha256 c3cfffdecc68992645bec355c7093c46a8478972498303185427a184159bdaf8)

BibTeX

@misc{dc4eaec07e35ab,
  title = {Relative Wasserstein Spatial Depth for Cluster Number Selection in Distributional Data — arXiv:2610.09153},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.09153},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4eaec07e35ab; sha256 c3cfffdecc68992645bec355c7093c46a8478972498303185427a184159bdaf8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.09153. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Contemporary data in many scientific domains, such as images, media streams, biomedical omics, are naturally modeled as probability distributions in Wasserstein space instead of points in Euclidean space. Consequently, clustering methods for distributions are in high demand, as they provide exploratory frameworks to group objects with similarity. Clustering distribution-valued data in Wasserstein space often requires choosing the number of clusters in advance. We propose Relative Wasserstein Spatial Depth (RWSD) as a selection criterion for optimal number of clusters. It compares the depth of each distribution in its assigned cluster with its depth in competing clusters. We pair this criterion with Wasserstein K-means or a proposed K-medians algorithm. Under suitable assumptions, we establish consistency of the cluster centers and of the selected optimal number of clusters. We also give an error rate under two-stage sampling and characterize the robustness of RWSD under any fixed partition. In extensive simulations, RWSD selects the intended number of clusters under unequal separations, heterogeneous dispersion, heavy tails, and outliers, where silhouette score or the Davies-Bouldin Index often fails. Applications to MNIST images and flow cytometry data illustrate the practical value of RWSD. In some cases where a cluster is not geodesically convex and lacks a meaningful depth center, the RWSD can fail.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ML, nuovi lavori del giorno).
Categorie arXiv: Methodology (stat.ME) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.09153 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T12:15:00.337Z dalla pagina https://arxiv.org/list/stat.ML/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).