Simultaneous differential network analysis and classification for matrix-variate data with application to brain connectivity

Abstract

Summary Growing evidence has shown that the brain connectivity network experiences alterations for complex diseases such as Alzheimer’s disease (AD). 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 multidimensional and in matrix-form. Naive vectorization method is not sufficient as it ignores the structural information within the matrix. In the article, we adopt the Kronecker product covariance matrices 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 case group and the control group and conducts medical diagnosis (classification) of the disease simultaneously. Simulation studies are conducted to assess the performance of the proposed method. We apply the proposed procedure to the functional connectivity analysis of an functional magnetic resonance imaging study on AD. 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 AD.

Simultaneous Cluster Structure Learning and Estimation of Heterogeneous Graphs for Matrix-variate fMRI Data

“…Optimization problem (3.3) is in essence the same with optimization problem (2.1) and can be solved by the MDC-ADMM algorithm. The SCEHG method takes advantage of the the SPRclust in the following two aspects: (I) the features of SPRclust in the fMRI setting are the individual-specific between-region connectivity measures, i.e., the functional connectivity network predictors (Chen et al, 2021;Weaver et al, 2021), and we cluster the samples by their second moment covariance information rather than the mean; (II)…”

“…The SCEHG takes the serial autocorrelation of fMRI data into account when constructing the individual region-by-region connectivity strength and thus relaxes the i.i.d. assumptions in Chen et al (2021); Dilernia et al (2021).…”

“…We first review the definition of matrix-normal distribution for characterizing the distribution of matrix-variate fMRI data. The framework is scientifically plausible in neuroimaging studies, see for example Xia and Li (2017); Zhu and Li (2018); Chen et al (2021) Definition 3.1. A matrix-variate Z p×q follows the matrix-normal distribution, denoted as…”

“…We resort to R package "huge" to generate Hub structure with 3 non-overlapping graph and use R package "rags2ridges" to generate 3 Small-World graph. For further details of these two graph structures, one may refer to Zhao et al (2012) and Chen et al (2021). We design the precision matrices of K = 3 groups such that all share the same graph structure (either Hub or Small-World) but with different partition blocks, illustrated by the heat map of the precision matrices in Figure 3.…”

“…The typical characteristic of fMRI data is that it's in matrix-form and objects from different groups share the same zero mean matrix but different covariance structures due to the the centralization preprocess step (Chen et al, 2021). Thus the clustering methods which rely on the mean difference of groups do not work for fMRI data.…”