AdaGraph: A Graph-Native Clustering Algorithm That Overcomes the Curse of Dimensionality and Enables Scientific Discovery
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Computer Science > Machine Learning
arXiv:2605.16320 (cs)
[Submitted on 5 May 2026]
Title:AdaGraph: A Graph-Native Clustering Algorithm That Overcomes the Curse of Dimensionality and Enables Scientific Discovery
Authors:Ahmed Elmahdi
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Abstract: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.
| Comments: | 12 pages, 4 figures, 1 table. Full paper in preparation for KDD 2027 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| MSC classes: | 62H30, 05C85 |
| ACM classes: | I.5.3; I.2.6 |
| Cite as: | arXiv:2605.16320 [cs.LG] |
| (or arXiv:2605.16320v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.16320
arXiv-issued DOI via DataCite
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