Hyperalignment uses Procrustean transformation to align individual subjects’ voxel spaces to each other, time point by time point. This was done separately for each hemisphere. A fixed number of top-ranking voxels (500 for main analyses) were selected from each hemisphere of all subjects. A subject was chosen arbitrarily to serve as the reference. The reference subject’s time-point vectors during the movie study were taken as the initial group reference. In the first pass, the nonreference subjects were iteratively chosen and their time-point vectors were aligned to the time-point vectors of the current reference using the Procrustean transformation (procrustes as Sunitinib implemented in MATLAB).

After each iteration, a new vector was calculated at each time point by averaging Dasatinib the vectors of the current reference and the current subject in the transformed space. The final reference time-point vectors after iterating through all subjects in the first pass were the reference for the second pass. In the second pass, we computed Procrustean transformations to align each subject’s time-point vectors to the corresponding time-point vectors in this reference. At the end of the second pass, a new vector was calculated at each time point by averaging all subjects’ vectors in the transformed space, which served as reference for the next

pass. In the final pass, we calculated Procrustean transformations for each subject that aligned that subject’s voxel space to the reference space.

This pair of transformations, one for each hemisphere of a subject, served as the hyperalignment parameters for that subject. Procrustean transformation finds the optimal rotation matrix for two sets of vectors that minimizes the sum of squared Euclidean distances between corresponding vectors in Cytidine deaminase those sets. The Procrustean transformation also derives a translation vector, but we did not use this vector because the data for each voxel were standardized. Movie data from each subject’s left and right hemispheres were projected into the hyperaligned common spaces, and a group mean time-point vector was computed for each time point of the movie. Mean movie data from both hemispheres’ hyperaligned common spaces were concatenated, and PCA was performed (princomp in MATLAB) on these data. This gave us 1,000 components, in descending order of their eigenvalues, corresponding to the 1,000 dimensions of the hyperaligned common space. Patterns of response from any experiment in the same VT voxels of an individual can be mapped into the common model using that individual’s hyperalignment parameters by multiplying the rows of voxel responses for those time points or stimuli with the hyperalignment parameter matrix of that subject (Figure S1B). The resulting vectors were the mappings in the common model space.