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Alzheimer's disease (AD) is the most common form of dementia, which causesproblems with memory, thinking and behavior. Growing evidence has shown thatthe brain connectivity network experiences alterations for such a complexdisease. Network comparison, also known as differential network analysis, isthus particularly powerful to reveal the disease pathologies and identifyclinical biomarkers for medical diagnoses (classification). Data fromneurophysiological measurements are multi-dimensional and in matrix-form, whichposes major challenges in brain connectivity analysis and medical diagnoses.Naive vectorization method is not sufficient as it ignores the structuralinformation within the matrix. In the article, we adopt the Kronecker productcovariance matrix framework to capture both spatial and temporal correlationsof the matrix-variate data while the temporal covariance matrix is treated as anuisance parameter. By recognizing that the strengths of network connectionsmay vary across subjects, we develop an ensemble-learning procedure, whichidentifies the differential interaction patterns of brain regions between theAD group and the control group and conducts medical diagnosis (classification)of AD simultaneously. We applied the proposed procedure to functionalconnectivity analysis of fMRI dataset related with Alzheimer's disease. The hubnodes and differential interaction patterns identified are consistent withexisting experimental studies, and satisfactory out-of-sample classificationperformance is achieved for medical diagnosis of Alzheimer's disease. An Rpackage \SDNCMV" for implementation is available athttps://github.com/heyongstat/SDNCMV.

Simultaneous Differential Network Analysis and Classification for  High-dimensional Matrix-variate Data, with application to Brain Connectivity  Alteration Detection and fMRI-guided Medical Diagnoses of Alzheimer's Disease