AdaGraph用拓扑结构代替距离计算，解决高维聚类难题，助力科学发现。
AdaGraph: A Graph-Native Clustering Algorithm That Overcomes the Curse of Dimensionality and Enables Scientific Discovery
- 基于kNN图拓扑，不依赖距离度量，天然克服维度诅咒。
- 在10个高维合成数据集上平均ARI达0.900，正确识别聚类数占比90%。
- 适用于基因、文本、材料科学等真实场景，显著优于传统方法。
我们提出AdaGraph，一种源于结构中心机器学习（SC-ML）范式的图原生聚类算法——该范式以拓扑计算替代传统的几何距离计算，从根本上消除维度诅咒。AdaGraph完全在kNN图拓扑中运行，该表示在任意高维空间中仍能保留有意义的关联结构，而欧氏距离在此类场景下已失去信息量。该算法无需预设聚类数k，原生处理噪声，并通过SLCD（采样-学习-校准-部署）框架实现可扩展性。其无监督调优目标与另一项独立提出的SC-ML贡献——图-SCOPE（拓扑型聚类有效性指标）配合使用。在10个维度从10到5000的合成基准测试中，图-SCOPE平均ARI达到0.900，在9/10数据集上正确选择聚类数，优于轮廓系数、戴维斯-布尔丁和卡林斯基-哈拉巴兹指数；且在所有维度下与真实聚类质量保持肯德尔tau ≥ 0.92（轮廓系数约0.46）。我们在三个科学领域验证了AdaGraph：(1) 肝细胞癌基因共表达发现（GSE14520，10,000基因，488例患者，无降维），成功识别出WGCNA、ICA、NMF和谱双聚类无法解析的条件特异性基因模块；(2) 自然语言文本聚类，20NG-6cat数据集上达ARI=0.751，相比HDBSCAN提升62%；(3) 材料科学中对超导体（145维Magpie特征）、钙钛矿及JARVIS-DFT材料的聚类，均取得最高图-SCOPE得分。
原文摘要 · Abstract (English)
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.
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