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

Jakub Frac, Alexander Schmatz, Qiang Li, Guido Van Wingen, Shujian Yu

TL;DR

This work presents a graph-structured adaptation of Hierarchical Functional Maximal Correlation Algorithm (HFMCA) for self-supervised learning on fMRI connectivity graphs. By modeling statistical dependence across hierarchical graph features, the approach leverages a density-ratio decomposition in an RKHS and a graph-transformer backbone to produce robust, transferable embeddings. Evaluations across five neuroimaging datasets show competitive downstream performance and effective transfer to unseen data, with nuanced findings on data scaling and potential negative transfer. The results highlight the potential of graph-based HFMCA as a principled component for neuroimaging representation learning and foundations for brain-function models.

Abstract

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

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

TL;DR

This work presents a graph-structured adaptation of Hierarchical Functional Maximal Correlation Algorithm (HFMCA) for self-supervised learning on fMRI connectivity graphs. By modeling statistical dependence across hierarchical graph features, the approach leverages a density-ratio decomposition in an RKHS and a graph-transformer backbone to produce robust, transferable embeddings. Evaluations across five neuroimaging datasets show competitive downstream performance and effective transfer to unseen data, with nuanced findings on data scaling and potential negative transfer. The results highlight the potential of graph-based HFMCA as a principled component for neuroimaging representation learning and foundations for brain-function models.

Abstract

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

Paper Structure

This paper contains 15 sections, 8 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Functional Maximal Correlation Algorithm
  4. Methods
  5. Problem formulation
  6. Graph Construction from fMRI Data
  7. Hierarchical FMCA with Graphs
  8. Graph Transformer Architecture
  9. Experiments
  10. Datasets and Tasks
  11. Training Protocol and Evaluation
  12. Quality of Learned Representations
  13. Transfer Learning Evaluation
  14. Scaling Laws
  15. Conclusion

Figures (2)

  • Figure 1: HFMCA learns representations by maximising the statistical dependence between low- and high-level features of the graph. Each subsampling augmentation (e.g., random walk sampling) is processed through a shared backbone $f^1_\theta$, producing low-level features. These features are either projected individually through a local head $Z^L = [f^2_\omega \circ f^1_\theta(Y_1) \dots f^2_\omega \circ f^1_\theta(Y_T)]$ or jointly aggregated through a high-level head $Z^H = \sum_i^Tf^3_{\omega'_i} \circ f^1_\theta(Y_i)$. In pretraining, both projection heads are used to enforce multi-view consistency, while only the backbone is retained for downstream tasks.
  • Figure 2: Encoders were trained with HFMCA using varying amounts of pretraining data and fine-tuned with linear heads. No clear linear relationship was observed between the amount of pretraining data and downstream performance, which aligns with findings from recent studies.