# High-Dimensional BWDM: A Robust Nonparametric Clustering Validation Index for Large-Scale Data

arXiv: https://arxiv.org/abs/2510.14145 · HTML: https://mlsanity.com/paper/2510.14145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
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- First posted on arXiv 15 Oct 2025.

## Abstract (arXiv)

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.