GMNV: Dynamic Quantile-Augmented K-Means Clustering With Variance-Based Feature Selection

The Global Minimum Nearest Value (GMNV) algorithm—where "Global" denotes consideration of all samples for quantile mapping, and "Minimum" refers to assigning each value to its nearest quantile—enhances K-Means clustering by augmenting the feature set with a quantile-based feature derived from the highest-variance feature, mapped to dynamic quantilesq1, q2, . . . , qη. Applied to the Iris, Wine, and Breast Cancer datasets using three selected features (s= 3), GMNV optimizes quantiles via grid search. Averaged over 10 runs, GMNV consistently outperforms standard K-Means on Silhouette Scores (Iris: 0.56.36 vs. 0.5405; Wine: 0.36.46 vs. 0.3539; Breast Cancer: 0.74.14 vs. 0.6857), Accuracy (e.g., Breast Cancer: 0.9033 vs. 0.8313), and Adjusted Rand Index (ARI) (e.g., Breast Cancer: 0.6461 vs. 0.4256). Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE), applied post-clustering to both baseline and GMNV-augmented data, serve dual purposes: visualization and qualitative verification of enhanced clustering accuracy through significantly improved cluster separation and cohesion before versus after GMNV augmentation—most prominently in t-SNE projections. SHapley Additive exPlanations (SHAP) analysis highlights the quantile feature’s critical contribution, whileWilcoxon signed-rank tests confirm statistical significance of improvements across all datasets. GMNV offers a robust, lightweight solution for noisy, high-dimensional data with strong performance across diverse structures.