Test–retest reliability of spatial patterns from resting-state functional MRI using the restricted Boltzmann machine and hierarchically organized spatial patterns from the deep belief network

Background: Restricted Boltzmann machines (RBMs), including greedy layer-wise trained RBMs as part of a deep belief network (DBN), have the ability to identify spatial patterns (SPs; functional networks) in resting-state fMRI (rfMRI) data. However, there has been little research on (1) the reproducibility and test-retest reliability of SPs derived from RBMs and on (2) hierarchical SPs derived from DBNs. Methods: We applied a weight sparsity-controlled RBM and DBN to whole-brain rfMRI data from the Human Connectome Project. We evaluated the within-session reproducibility and between-session test-retest reliability of the SPs derived from the RBM approach and compared them both with those identified using independent component analysis (ICA) and with three voxel-wise statistical measures—the Hurst exponent, entropy, and kurtosis—of the rfMRI data. We also assessed the potential hierarchy of the SPs from the DBN. Results: An increase in the sparsity level of the RBM weights enhanced the reproducibility of the SPs. The SPs deriving from a stringent weight sparsity level were predominantly found in the cortical gray matter and substantially overlapped with the SPs obtained from the Hurst exponent. A hierarchical representation was shown by constructed using the default-mode network obtained from the DBN. Comparison with existing methods: The test-retest reliability of the SPs from the RBM was superior to that of the SPs from the voxel-wise statistics. Conclusions: The SPs from the RBM were reproducible within sessions and reliable across sessions. The hierarchically organized SPs from the DBN could possibly be applied to research based on rfMRI data.