Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2605.00598 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914524331769856 |
|---|---|
| author | Zhao, Ping Zhuang, Dan Feng, Long |
| author_facet | Zhao, Ping Zhuang, Dan Feng, Long |
| contents | We propose a robust clustering framework for high-dimensional data with heavy tails and a large fraction of irrelevant variables. The method replaces the mean updates of Lloyd's $K$-means with \emph{spatial medians} to enhance robustness. For the assignment step, it admits either a Euclidean rule for computational simplicity or a robust Mahalanobis-type metric constructed from the spatial sign covariance matrix to account for heterogeneous scales and feature dependence. To handle the $p \gg n$ regime, we further introduce a simple \emph{hard feature-exclusion} mechanism that removes weakly separating dimensions based on across-center dispersion, with the exclusion threshold selected automatically via a permutation-based Gap criterion. Simulation studies under correlated Gaussian and multivariate $t$ models demonstrate that the proposed approach provides competitive clustering accuracy and improved stability relative to $K$-means and sparse $K$-means baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sparse $K$-spatial-median clustering for high-dimensional data Zhao, Ping Zhuang, Dan Feng, Long Methodology We propose a robust clustering framework for high-dimensional data with heavy tails and a large fraction of irrelevant variables. The method replaces the mean updates of Lloyd's $K$-means with \emph{spatial medians} to enhance robustness. For the assignment step, it admits either a Euclidean rule for computational simplicity or a robust Mahalanobis-type metric constructed from the spatial sign covariance matrix to account for heterogeneous scales and feature dependence. To handle the $p \gg n$ regime, we further introduce a simple \emph{hard feature-exclusion} mechanism that removes weakly separating dimensions based on across-center dispersion, with the exclusion threshold selected automatically via a permutation-based Gap criterion. Simulation studies under correlated Gaussian and multivariate $t$ models demonstrate that the proposed approach provides competitive clustering accuracy and improved stability relative to $K$-means and sparse $K$-means baselines. |
| title | Sparse $K$-spatial-median clustering for high-dimensional data |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.00598 |