Omega-N: Interpretable Structural Node Descriptors and Their Applicability Domain
A composite structural index summarises a network in one number, and for a triangle-based index it is spectrally redundant: Tr(A^3) is the third moment of the adjacency spectrum. The non-redundant content sits one level down, in diag(A^3), which depends on eigenvectors and is not spectrally determined. A corollary in the theory paper predicted that the global scalar should tie sharpened spectral baselines rather than beat them, while the node-wise attribution should do better where the number of structural epicentres is unknown. We construct Omega-N by localizing each of the four factors. The direct localization is badly conditioned; two corrections from published practice fix it, a configuration-null excess per factor and a personalized-PageRank neighbourhood at several scales, giving ten interpretable features per node, with no attributes, training or embeddings. Against a recursive feature engine at five levels of recursion, Omega-N wins on three and ties on two of the six in-domain evaluations, the sixth a declared null where every arm returns chance, with ten features against its 28 to 252 before pruning. Two statistics from the graph and labels, not from performance, partition the eight benchmarks without error, and the two they exclude are the two on which it loses. The strongest application is drug-target prioritisation on protein interaction networks: +0.032 to +0.103 AUPRC over a six-feature centrality battery and +0.084 to +0.208 over the four-feature one, across three constructions, replicated on an independent AP-MS network and label source (degree-matched: +0.0723 on STRING, +0.0560 on BioPlex, p=0.00195). Adding Omega-N to centralities plus Node2Vec changes nothing. The claim is narrow and it is the point: ten named features, computed without training, match or beat hand-crafted centralities and a recursive engine, and do not touch learned representations.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
node2coords: Graph Representation Learning with Wasserstein Barycenters
In order to perform network analysis tasks, representations that capture the most relevant information in the graph structure are needed. However, existing methods do not learn representations that can be interpreted in …
DecoderGraph Representation LearningNode ClassificationRepresentation LearningImproving Graph Neural Networks with Learnable Propagation Operators
Graph Neural Networks (GNNs) are limited in their propagation operators. In many cases, these operators often contain non-negative elements only and are shared across channels, limiting the expressiveness of GNNs. Moreov…
Graph ClassificationDuSCN-FusionNet: An Interpretable Dual-Channel Structural Covariance Fusion Framework for ADHD Classification Using Structural MRI
Attention Deficit Hyperactivity Disorder (ADHD) is a highly prevalent neurodevelopmental condition; however, its neurobiological diagnosis remains challenging due to the lack of reliable imaging-based biomarkers, particu…
Super-resolution of positive near-colliding point sources
In this paper, we analyze the capacity of super-resolution of one-dimensional positive sources. In particular, we consider the same setting as in [arXiv:1904.09186v2 [math.NA]] and generalize the results there to the cas…
Super-ResolutionStructural Node Embeddings with Homomorphism Counts
Graph homomorphism counts, first explored by Lov\'asz in 1967, have recently garnered interest as a powerful tool in graph-based machine learning. Grohe (PODS 2020) proposed the theoretical foundations for using homomorp…
Graph LearningInterpretable Machine Learning