GABTOP: A Self-Adaptive Gabriel-Graph Topological Persistence Framework for Automatic Clinical Subgroup Identification

Clustering algorithms for precision medicine universally require manual specification of either the number of clusters k or a neighbourhood scale epsilon, a limitation that severely constrains their deployment on large-scale biomedical datasets. We present GABTOP, a fully self-adaptive clustering framework that jointly estimates both parameters without any user intervention. The methodology integrates four complementary stages: Delaunay-accelerated Gabriel graph construction, which reduces the candidate scale set from quadratic to linear complexity while preserving all topologically significant features; Topological persistence analysis for automatic estimation of the number of clusters k; Multi-criterion majority voting with a deterministic tie-breaking protocol for optimal scale selection epsilon; Perturbation stability certification under repeated Gaussian noise to quantify structural robustness stab. Evaluated on five biomedical datasets spanning from n=132 to n=253,680 observations and d=4 to $d=30$ dimensions, GABTOP achieved Adjusted Rand Index ARI_ext scores of 0.972, 0.988, and 0.996 against ground-truth clinical labels on three benchmark cohorts, outperforming five state-of-the-art baselines (K-means, DBSCAN, HDBSCAN, GMM, TOMATO) by margins up to +0.754. On large-scale cohorts (Cardiotocography and BRFSS), GABTOP reliably identified clinically interpretable subgroups with high resampling stability (0.8075) and perturbation stability (0.780 and 0.616), while reducing edge-space complexity by up to 99.2% relative to full pairwise distances.