AdaGraph: A Graph-Native Clustering Algorithm That Overcomes the Curse of Dimensionality and Enables Scientific Discovery
Authors: Ahmed Elmahdi
Summary
arXiv:2605. 16320v1 Announce Type: new 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.
Relevance
Read next because AdaGraph: A Graph-Native Clustering Algorithm That Overcomes the Curse of Dimensionality and Enables Scientific Discovery overlaps with clean result "LoRA persona trained on alone emits at 23.5% when a co-trained partner learns ..., vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)", clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)". Matching terms: text, rect, correct, rate, language. Source: arxiv cs.LG (Machine Learning).
Threat model
Potential threat/caveat for clean result "LoRA persona trained on alone emits at 23.5% when a co-trained partner learns ..., vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)": this item discusses benchmark.
Abstract
arXiv:2605.16320v1 Announce Type: new 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.