Regularized Shared Response Models for fMRI

Abstract

We mathematically model the joint brain activity of multiple human subjects viewing a movie in an fMRI scanner. The model is used to learn mappings from the subjects’ idiosyncratic voxel spaces, in which different dimensions do not necessarily serve the same neural function from subject to subject, into a lowerdimensional common space. In this common space, fMRI data may be pooled across subjects to boost discriminative power in neural decoding experiments. Variants of the model assume different properties about the brain systems, including orthogonality, spatial smoothness, and sparsity. In order to combine the orthogonality constraint with any arbitrary number of convex constraints, we propose to relax the non-convex orthogonality constraint into a convex spectral norm constraint. We present an alternating direction method of multipliers algorithm to solve the resulting optimization problem.