Independent component analysis on Lie groups for multi-object analysis of first episode depression

We propose a method for the analysis of brain structural data to simultaneously identify differences in position, orientation and size (i.e. pose), and in shape of multiple brain regions between young people with, and without, a depressive disorder. Different structures in both hemispheres of the brain of depressed and control participants were segmented and corresponding points on the surface of each structure were extracted. Coordinates of these surface points were used to obtain shape variations, and parameters of similarity transformations between brain structures across subjects were used to generate pose variations. Since these surface points and similarity transformations form Lie groups, a logarithmic mapping of members of the Lie groups was performed to transform them to a linear tangent space. Then, Independent Component Analysis (ICA) was used to obtain the independent sources of pose and shape variations on Lie group members, and their corresponding modulation profiles. A method for ordering the independent sources is proposed. The top ordered sources were used to detect pose and shape differences between the two groups, and confirm that even in their first depressive episode, the brains of depressed adolescents differ structurally from the brains of their nondepressed age- and sex-matched peers.