Graph Hyperalignment for Multi-subject fMRI Functional Alignment

Abstract

In fMRI analysis, the scientist seeks to aggregate multi-subject fMRI data so that inferences shared across subjects can be achieved. The challenge is to eliminate the variability of anatomical structure and functional topography of the human brain, which calls for aligning fMRI data across subjects. However, the existing methods do not exploit the geometry of the stimuli, which can be inferred by using certain domain knowledge and then serve as a priori. In this paper, such geometry is encoded in a graph matrix, and we propose an algorithm named Graph Hyperalignment for leveraging it. Specifically, a kernel-based optimization is developed to allow for non-linear feature extraction. To tackle overfitting caused by the high-spatial-and-low-temporal resolution of fMRI, the data in the new feature space are assumed to lie in a low-dimensional affine subspace, which can be implicitly integrated into the proposed optimization. Unlike other iterative existing methods, GHA reaches an optimal solution directly. Examining over four real datasets, Graph Hyperaligment achieves superior results to other methods.