  The statistical shape analysis called Procrustes analysis minimizes the
distance between matrices by similarity transformations. The method returns a
set of optimal orthogonal matrices, which project each matrix into a common
space. This manuscript presents two types of distances derived from Procrustes
analysis for exploring between-matrices similarity. The first one focuses on
the residuals from the Procrustes analysis, i.e., the residual-based distance
metric. In contrast, the second one exploits the fitted orthogonal matrices,
i.e., the rotational-based distance metric. Thanks to these distances,
similarity-based techniques such as the multidimensional scaling method can be
applied to visualize and explore patterns and similarities among observations.
The proposed distances result in being helpful in functional magnetic resonance
imaging (fMRI) data analysis. The brain activation measured over space and time
can be represented by a matrix. The proposed distances applied to a sample of
subjects -- i.e., matrices -- revealed groups of individuals sharing patterns
of neural brain activation.
