Round-Trip KNN Clustering: multiscale hierarchical cluster detection on directed nearest-neighbour graphs

Existing graph-clustering methods typically improve clustering performance by optimizing model parameters and node representations. Effective means of further improving the clustering results of an already trained and frozen model, however, remain limited. We study post-processing for frozen graph clustering. After checkpoint fixation, the procedure uses no labels and updates neither model parameters, node representations, nor the original graph structure. Instead, it exploits an attribute hypergraph to supplement higher-order relations that ordinary graphs cannot readily express, thereby refining existing cluster assignments. Because global hypergraph refinement can yield both performance gains and erroneous updates, we propose Selective Hypergraph Refinement (SHR). The method generates candidate residual directions from the hypergraph and evaluates their reliability using graph structure, node attributes, and matched-null evidence. It updates only nodes with sufficient support and otherwise retains their original assignments. Further analysis shows that whether a node changes cluster is jointly governed by its native assignment gap and the directional strength of the refinement. In a controlled common-suite evaluation, 13 of 15 backbone-dataset cells had a positive mean macro gain, one produced exact no-action, and one was negative. The cell-equal macro gain was 0.066 pp (95% bootstrap CI, [0.030, 0.107] pp), while only 0.209% of hard assignments changed on average. A broader 15-combination native-interface evaluation yielded a macro gain of 0.137 pp at a mean change ratio of 0.375%. These results indicate that frozen clustering outputs retain a limited but measurable refinement space after training. The effect is heterogeneous across backbone-dataset pairs, and broader coverage also increases exposure to negative transfer.

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.

We introduce Graph Neural Automata Clustering (G-NAC), an unsupervised clustering method in which observations interact as cells on a fixed neighborhood graph. A shared recurrent graph-neural cellular rule evolves latent domain states through local interactions, which are converted into a rank-based spectral affinity for partitioning. Across 73 clustering tasks from 57 benchmark datasets, G-NAC achieved a mean adjusted Rand index (ARI) of 0.7951, comparable to Genie at 0.7941 and higher than the other evaluated baselines. Empirical training time and GPU memory scaled approximately linearly from 5,000 to 100,000 nodes. Learned transition rules also transferred from smaller source graphs to independent 100,000-node samples generated under matched conditions. These results demonstrate a recurrent graph-clustering formulation while identifying dependencies on graph quality, readout design, and source-target similarity.