Deep Linear Matrix Approximate Reconstruction Reveals Reproducible Large-Scale Functional Connectivity Networks in the Human Brain

Deep Neural Networks (DNNs) have successfully uncovered hierarchical functional connectivity networks (FCNs) in the human brain. In particular, the FCNs identified in the deep layers of DNNs usually represent the combinations of traditional FCNs, which are closely relevant to neurological disorders. We define these deep-layer FCNs as large-scale FCNs (LS-FCNs). A few existing studies reported LS-FCNs, but reproducibility remains a challenge. To address this, we propose an innovative deep matrix factorization technique, named Deep Linear Matrix Approximate Reconstruction (DELMAR), designed to identify reproducible LS-FCNs. DELMAR introduces several methodological advancements in functional Magnetic Resonance Imaging (fMRI) analytics. Firstly, it incorporates an efficient, non-fully connected layer to reduce the computational complexity associated with traditional fully connected layers. Additionally, we have developed a hyperparameter tuning technique that enables automatic hyperparameter estimation, and we introduce matrix backpropagation to minimize potential accumulative errors. Validation experiments were conducted using Multi-band Multiecho (MBME) resting-state fMRI data alongside two peer methods to assess the reproducibility of LS-FCNs. The results demonstrate that DELMAR effectively extracts various reproducible, and even previously unreported LS-FCNs.