Brain connectivity alteration detection via matrix-variate differential network model

Brain functional connectivity reveals the synchronization of brain systems through correlations in neurophysiological measures of brain activities. Growing evidence now suggests that the brain connectivity network experiences alterations with the presence of numerous neurological disorders, thus differential brain network analysis may provide new insights into disease pathologies. The data from neurophysiological measurement are often multidimensional and in a matrix form, posing a challenge in brain connectivity analysis. Existing graphical model estimation methods either assume a vector normal distribution that in essence requires the columns of the matrix data to be independent or fail to address the estimation of differential networks across different populations. To tackle these issues, we propose an innovative matrix-variate differential network (MVDN) model. We exploit the D-trace loss function and a Lasso-type penalty to directly estimate the spatial differential partial correlation matrix and use an alternating direction method of multipliers algorithm for the optimization problem. Theoretical and simulation studies demonstrate that MVDN significantly outperforms other state-of-the-art methods in dynamic differential network analysis. We illustrate with a functional connectivity analysis of an attention deficit hyperactivity disorder dataset. The hub nodes and differential interaction patterns identified are consistent with existing experimental studies.