Fast Whole-Brain, Geometry-Aware Functional Alignment for Cross-Subject Decoding

Functional alignment aims to map brain activity patterns across individuals to improve the performance of population-level decoders. Existing methods often struggle to balance the need for functional correspondence with the preservation of anatomical structure, frequently resulting in high computational costs that limit their use in large-scale studies. This paper introduces SpectralOT, a new approach designed to align fMRI data across subjects while maintaining both geometric integrity and computational efficiency.

SpectralOT leverages the concept of functional maps from computer graphics. It represents the cortical surface using the first three eigenmodes of the Laplace-Beltrami operator, which capture the brain's principal spatial directions (anterior-posterior, dorsal-ventral, and lateral). The method constructs a composite cost matrix by linearly interpolating between a functional dissimilarity matrix (based on fMRI signal similarity) and a geometric dissimilarity matrix (based on spectral embedding distances). This composite cost is then solved using a Sinkhorn entropic optimal transport solver, which is significantly faster than the complex, non-linear solvers required by previous methods like FUGW.

SpectralOT demonstrates superior performance across several benchmarks. In anatomical alignment tasks, it successfully transports surface atlases across different mesh templates while maintaining global spatial properties. In functional alignment experiments, it consistently achieves higher Inter-Subject Correlation (ISC) than both the FUGW and ProMises models. Furthermore, in cross-subject and group-level decoding tasks, SpectralOT effectively reduces domain shift, leading to higher classification accuracy for object categories compared to anatomical baselines. Crucially, the method is orders of magnitude faster than current state-of-the-art approaches, facilitating its use in studies requiring nested cross-validation or large datasets.