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.
Hou et al. (Thu,) studied this question.