Title: Mixture of Spectral Wavelets on Simplicial Complex: Analysis of Brain Connectome with Neurodegeneration
Primary area: applications to neuroscience & cognitive science
Keywords: neurodegenerative disease, spectral graph analysis, simplicial complex

Abstract: Accurate analysis of brain networks is essential for understanding progression of neurodegenerative diseases and their early diagnosis. While various Graph Neural Networks (GNNs) have shown promise in identifying disease-related biomarkers, most existing approaches focus primarily on node-level features, overlooking crucial edge-level interactions. Furthermore, many spectral GNNs rely on fixed-bandwidth filtering, limiting their ability to capture diverse frequency components in graph-structured data. To address these limitations, we propose a novel framework that integrates two key components: 1) a Spectral Simplicial Wavelet Transform (SSWT) for jointly analyzing node and edge features, and 2) a Spectral Mixture of Experts (SpMoE) for adaptive multi-scale filtering. Our approach utilizes richer spectral decomposition and dynamically selects the most relevant wavelet scales for each graph. Extensive experiments on benchmark brain network datasets demonstrate its effectiveness in improving classification and interpretability, highlighting its potential for facilitating analysis of neurodegenerative disease. The implementation of this work will be released upon publication.