Adapting HFMCA to Graph Data: Self-Supervised Learning for Generalizable fMRI Representations

Functional magnetic resonance imaging (fMRI) analysis faces significant challenges due to limited dataset sizes and domain variability between studies. Traditional self-supervised learning methods inspired by computer vision often rely on positive and negative sample pairs, which can be problematic for neuroimaging data where defining appropriate contrasts is non-trivial. We propose adapting a recently developed Hierarchical Functional Maximal Correlation Algorithm (HFMCA) to graph-structured fMRI data, providing a theoretically grounded approach that measures statistical dependence via density ratio decomposition in a reproducing kernel Hilbert space (RKHS), and applies HFMCA-based pretraining to learn robust and generalizable representations. Evaluations across five neuroimaging datasets demonstrate that our adapted method produces competitive embeddings for various classification tasks and enables effective knowledge transfer to unseen datasets. Codebase and supplementary material can be found here: https://github.com/fr30/mri-eigenencoder