Semiparametric Elliptical Mixture Clustering for High-Dimensional Data
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913107038699520 |
|---|---|
| author | Feng, Long Zhuang, Dan |
| author_facet | Feng, Long Zhuang, Dan |
| contents | Clustering high-dimensional data is especially challenging when cluster distributions are heavy tailed and only approximately elliptical. Existing high-dimensional methods are largely built for Gaussian or other light-tailed models, whereas classical robust elliptical procedures are mostly low dimensional or rely on fully parametric radial families. We propose a semiparametric elliptical mixture clustering framework with cluster-specific centers, an unknown common radial generator, and a common sparse precision-shape matrix, together with a data-driven rule for selecting the number of clusters. A generalized expectation-maximization (GEM) algorithm is developed by combining transformed-radius estimation of the radial generator, radial-score center updates, and a Tyler-POET-GLASSO update for the common precision-shape matrix. The method avoids specifying a parametric radial family and remains computationally feasible in high dimensions. We establish high-dimensional consistency for the estimated model components and the excess misclustering error. Simulation studies and a handwritten-digit application demonstrate the competitive performance and robustness of the proposed method, particularly in heavy-tailed elliptical settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08995 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semiparametric Elliptical Mixture Clustering for High-Dimensional Data Feng, Long Zhuang, Dan Methodology Clustering high-dimensional data is especially challenging when cluster distributions are heavy tailed and only approximately elliptical. Existing high-dimensional methods are largely built for Gaussian or other light-tailed models, whereas classical robust elliptical procedures are mostly low dimensional or rely on fully parametric radial families. We propose a semiparametric elliptical mixture clustering framework with cluster-specific centers, an unknown common radial generator, and a common sparse precision-shape matrix, together with a data-driven rule for selecting the number of clusters. A generalized expectation-maximization (GEM) algorithm is developed by combining transformed-radius estimation of the radial generator, radial-score center updates, and a Tyler-POET-GLASSO update for the common precision-shape matrix. The method avoids specifying a parametric radial family and remains computationally feasible in high dimensions. We establish high-dimensional consistency for the estimated model components and the excess misclustering error. Simulation studies and a handwritten-digit application demonstrate the competitive performance and robustness of the proposed method, particularly in heavy-tailed elliptical settings. |
| title | Semiparametric Elliptical Mixture Clustering for High-Dimensional Data |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.08995 |