Inter-subject correspondence is an important aspect of multi-subject fMRI studies. Recently, a new approach, called hyperalignment, has shown very promising results in fMRI functional alignment. Hyperalignment is based on Procrustean rotations and is connected, mathematically, to canonical correlation analysis. We review the core details of each approach, relate them through an SVD analysis, and indicate why they can yield different levels of performance. We then examine the effectiveness of regularization in mediating between the extremes of these methods. An inter-subject classification experiment based on functional aligned fMRI datasets illustrates the resulting improved performance.