  Alzheimer's disease (AD) is the most common form of dementia, which causes
problems with memory, thinking and behavior. Growing evidence has shown that
the brain connectivity network experiences alterations for such a complex
disease. Network comparison, also known as differential network analysis, is
thus particularly powerful to reveal the disease pathologies and identify
clinical biomarkers for medical diagnoses (classification). Data from
neurophysiological measurements are multi-dimensional and in matrix-form, which
poses major challenges in brain connectivity analysis and medical diagnoses.
Naive vectorization method is not sufficient as it ignores the structural
information within the matrix. In the article, we adopt the Kronecker product
covariance matrix framework to capture both spatial and temporal correlations
of the matrix-variate data while the temporal covariance matrix is treated as a
nuisance parameter. By recognizing that the strengths of network connections
may vary across subjects, we develop an ensemble-learning procedure, which
identifies the differential interaction patterns of brain regions between the
AD group and the control group and conducts medical diagnosis (classification)
of AD simultaneously. We applied the proposed procedure to functional
connectivity analysis of fMRI dataset related with Alzheimer's disease. The hub
nodes and differential interaction patterns identified are consistent with
existing experimental studies, and satisfactory out-of-sample classification
performance is achieved for medical diagnosis of Alzheimer's disease. An R
package \SDNCMV" for implementation is available at
https://github.com/heyongstat/SDNCMV.
