Ahmed Elmahdi

Ahmed Elmahdi

Density-based clustering algorithms like DBSCAN and HDBSCAN are foundational tools for discovering arbitrarily shaped clusters, yet their practical utility is undermined by acute hyperparameter sensitivity -- parameters tuned on one dataset frequently fail to transfer to others, requiring expensive re-optimization for each deployment. We introduce AdaBox (Adaptive Density-Based Box Clustering), a grid-based density clustering algorithm designed for robustness across diverse data geometries. AdaBox features a six-parameter design where parameters capture cluster structure rather than pairwise point relationships. Four parameters are inherently scale-invariant, one self-corrects for sampling bias, and one is adjusted via a density scaling stage, enabling reliable parameter transfer across 30-200x scale factors. AdaBox processes data through five stages: adaptive grid construction, liberal seed initialization, iterative growth with graduation, statistical cluster merging, and Gaussian boundary refinement. Comprehensive evaluation across 111 datasets demonstrates three key findings: (1) AdaBox significantly outperforms DBSCAN and HDBSCAN across five evaluation metrics, achieving the best score on 78\% of datasets with p < 0.05; (2) AdaBox uniquely exhibits parameter generalization. Protocol A (direct transfer to 30-100x larger datasets) shows AdaBox maintains performance while baselines collapse. (3) Ablation studies confirm the necessity of all five architectural stages for maintaining robustness.

Ahmed Elmahdi

We present AdaGraph, a graph-native clustering algorithm born from the Structure-Centric Machine Learning (SC-ML) paradigm -- a new field of unsupervised learning that replaces geometry-centric (distance-based) computation with structure-centric (topology-based) computation, fundamentally dissolving the curse of dimensionality. AdaGraph operates entirely within the kNN graph topology, a representation that retains meaningful relational structure in arbitrarily high dimensions where Euclidean distance metrics become uninformative. AdaGraph requires no a priori specification of the number of clusters k, handles noise natively, and scales via the SLCD (Sample-Learn-Calibrate-Deploy) prototype-deployment framework. As its unsupervised tuning objective, AdaGraph pairs with Graph-SCOPE, the topology-based cluster validity index introduced as a separate SC-ML contribution. On 10 synthetic benchmarks spanning d=10 to d=5000, Graph-SCOPE achieves mean ARI=0.900 and correctly selects k on 9/10 datasets -- outperforming Silhouette, Davies-Bouldin, and Calinski-Harabasz -- while maintaining Kendall tau >= 0.92 with ground-truth cluster quality across all dimensionalities (Silhouette: tau ~= 0.46). We validate AdaGraph across three scientific domains: (1) gene co-expression discovery in hepatocellular carcinoma (GSE14520, 10,000 genes, 488 patients, no dimensionality reduction), where AdaGraph identifies condition-specific gene modules that WGCNA, ICA, NMF, and Spectral Biclustering fail to resolve; (2) natural language text clustering, where AdaGraph achieves ARI=0.751 on 20NG-6cat versus HDBSCAN's 0.464 (62% relative improvement); (3) materials science clustering of superconductors (145-dimensional Magpie features), perovskites, and JARVIS-DFT materials, where AdaGraph achieves the highest Graph-SCOPE on all three datasets.