Detecting and visualizing differences in brain structures with SPHARM and functional data analysis

A new procedure for classifying brain structures described by SPHARM is presented. We combine a dimension reduction technique (functional principal component analysis or functional independent component analysis) with stepwise variable selection for linear discriminant classification. This procedure is compared with many well-known methods in a novel classification problem in neuroeducation, where the reversal error (a common error in mathematical problem solving) is analyzed by using the left and right putamens of 33 participants. The comparison shows that our proposal not only provides outstanding performance in terms of predictive power, but it is also valuable in terms of interpretation, since it yields a linear discriminant function for 3D structures.