Simultaneous Cluster Structure Learning and Estimation of Heterogeneous Graphs for Matrix-variate fMRI Data
2021
Graphical models play an important role in neuroscience studies, particularly
in brain connectivity analysis. Typically, observations/samples are from
several heterogenous groups and the group membership of each observation/sample
is unavailable, which poses a great challenge for graph structure learning. In
this article, we propose a method which can achieve Simultaneous Clustering and
Estimation of Heterogeneous Graphs (briefly denoted as SCEHG) for
matrix-variate function Magnetic Resonance Imaging (fMRI) data. Unlike the
conventional clustering methods which rely on the mean differences of various
groups, the proposed SCEHG method fully exploits the group differences of
conditional dependence relationships among brain regions for learning cluster
structure. In essence, by constructing individual-level between-region network
measures, we formulate clustering as penalized regression with grouping and
sparsity pursuit, which transforms the unsupervised learning into supervised
learning. An ADMM algorithm is proposed to solve the corresponding optimization
problem. We also propose a generalized criterion to specify the number of
clusters. Extensive simulation studies illustrate the superiority of the SCEHG
method over some state-of-the-art methods in terms of both clustering and graph
recovery accuracy. We also apply the SCEHG procedure to analyze fMRI data
associated with ADHD (abbreviated for Attention Deficit Hyperactivity
Disorder), which illustrate its empirical usefulness. An R package ``SCEHG" to
implement the method is available at https://github.com/heyongstat/SCEHG.
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