Mixture of Wavelets on Simplicial Complex for Analysis of Brain Connectome with Neurodegeneration

Comprehensive analysis of brain networks is essential for understanding neurodegenerative disease progression 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 Scale-aware eXpert on simplicial complex (ScaleX) 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 the analysis of neurodegenerative diseases. The code will be released upon publication.