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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.