Learning Optimal Spectral Clustering for Functional Brain Network Generation and Classification

Functional brain network (FBN) analysis aims to enhance the understanding of brain organization and support the diagnosis of neurological and psychiatric disorders. Prior studies have shown that FBNs exhibit small-world topology, where brain regions form functional clusters, and abnormalities in these clusters are strongly associated with disease. However, current learning-based methods either ignore this special topological structure or impose it as a post-hoc step outside the learning process, limiting both performance and interpretability. In this paper, we propose Learning Optimal Spectral Clustering (LOSC), a new framework that integrates the FBN generation, clustering, and classification with a novel graph theory grounded loss to fully exploit the small-world topology. Firstly, LOSC learns brain connectivity in a nonlinear spatio-spectral embedding space, guided by our proposed Rayleigh Quotient Loss (RQL), to preserve the small-world properties in generated FBNs. Then, the FBNs are partitioned into clusters of functionally synchronized regions, and both intra- and inter-cluster relations are utilized for brain network classification. Our contributions are threefold: (1) Improved brain network classification accuracy: by leveraging small-world functional clusters, LOSC achieves consistent gains of 2.0%, 3.6%, and 2.6% on the ABIDE, ADHD-200, and HCP datasets compared with state-of-the-art models, respectively; (2) Theoretical grounding: with our proposed RQL, LOSC bridges the gap between the graph theory and learning-based FBN analysis; and (3) Interpretability: the discovered functional clusters align with known neuropathology and contribute to the discovery of new functional community biomarkers.