Evolutionary Weighted Hodge Laplacian Descriptors for rs-fMRI Brain Networks

Abstract Complex biological networks often exhibit multiscale organization that is not fully characterized by pairwise edge weights or fixed graph summaries, motivating compact descriptors that retain both topological and spectral information. Here, we present an evolutionary weighted Hodge Laplacian (EWHL) framework for resting-state functional magnetic resonance imaging (rs-fMRI) connectivity, in which the functional connectivity matrix of each subject is represented as a weighted Vietoris–Rips filtration and 0-dimensional and 1-dimensional weighted Hodge Laplacian spectral descriptors are extracted across 13 positive connectivity thresholds. In an autism spectrum disorder (ASD) classification task using 884 participants from the Autism Brain Imaging Data Exchange I (ABIDE I) cohort, EWHL reduced the original 6670-dimensional functional connectivity vector to 130 features and, with eXtreme Gradient Boosting (XGBoost), yielded 87.7% accuracy and an area under the receiver operating characteristic curve (AUC) of 0.946 under 20 repetitions of 10-fold cross validation. Under the same internal protocol, EWHL outperformed a rerun raw functional connectivity baseline and a single threshold ablation, suggesting that multiscale weighted Hodge spectra provide informative descriptors for functional brain networks derived from rs-fMRI, although confound control within each fold and external validation remain necessary before clinical interpretation.