Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.14145 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912651470176256 |
|---|---|
| author | Baragilly, Mohammed Gabr, Hend |
| author_facet | Baragilly, Mohammed Gabr, Hend |
| contents | Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based distances and therefore degrade in high-dimensional or contaminated data. This paper proposes a new robust, nonparametric clustering validation framework, the High-Dimensional Between-Within Distance Median (HD-BWDM), which extends the recently introduced BWDM criterion to high-dimensional spaces. HD-BWDM integrates random projection and principal component analysis to mitigate the curse of dimensionality and applies trimmed clustering and medoid-based distances to ensure robustness against outliers. We derive theoretical results showing consistency and convergence under Johnson-Lindenstrauss embeddings. Extensive simulations demonstrate that HD-BWDM remains stable and interpretable under high-dimensional projections and contamination, providing a robust alternative to traditional centroid-based validation criteria. The proposed method provides a theoretically grounded, computationally efficient stopping rule for nonparametric clustering in modern high-dimensional applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Dimensional BWDM: A Robust Nonparametric Clustering Validation Index for Large-Scale Data Baragilly, Mohammed Gabr, Hend Machine Learning Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based distances and therefore degrade in high-dimensional or contaminated data. This paper proposes a new robust, nonparametric clustering validation framework, the High-Dimensional Between-Within Distance Median (HD-BWDM), which extends the recently introduced BWDM criterion to high-dimensional spaces. HD-BWDM integrates random projection and principal component analysis to mitigate the curse of dimensionality and applies trimmed clustering and medoid-based distances to ensure robustness against outliers. We derive theoretical results showing consistency and convergence under Johnson-Lindenstrauss embeddings. Extensive simulations demonstrate that HD-BWDM remains stable and interpretable under high-dimensional projections and contamination, providing a robust alternative to traditional centroid-based validation criteria. The proposed method provides a theoretically grounded, computationally efficient stopping rule for nonparametric clustering in modern high-dimensional applications. |
| title | High-Dimensional BWDM: A Robust Nonparametric Clustering Validation Index for Large-Scale Data |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.14145 |