High-Dimensional BWDM: A Robust Nonparametric Clustering Validation Index for Large-Scale Data
This provides a robust alternative to traditional clustering validation indices for data scientists working with large-scale, high-dimensional datasets, though it is incremental as it extends an existing method.
The paper tackles the problem of determining the number of clusters in high-dimensional or contaminated data by proposing the HD-BWDM validation index, which demonstrates stability and interpretability in simulations under such conditions.
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.