DEMAND: Deep Matrix Approximately Nonlinear Decomposition to Identify Meta, Canonical, and Sub-Spatial Pattern of functional Magnetic Resonance Imaging in the Human Brain

Deep Neural Networks (DNNs) have already become a crucial computational approach to revealing the spatial patterns in the human brain; however, there are three major shortcomings in utilizing DNNs to detect the spatial patterns in functional Magnetic Resonance Signals: 1). It is a fully connected architecture that increases the complexity of network structures that is difficult to optimize and vulnerable to overfitting; 2). The requirement of large training samples results in erasing the individual/minor patterns in feature extraction; 3). The hyperparameters are required to be tuned manually, which is time-consuming. Therefore, we propose a novel deep nonlinear matrix factorization named Deep Matrix Approximately Nonlinear Decomposition (DEMAND) in this work to take advantage of the shallow linear model, e.g., Sparse Dictionary Learning (SDL) and DNNs. At first, the proposed DEMAND employs a non-fully connected and multilayer-stacked architecture that is easier to be optimized compared with canonical DNNs; furthermore, due to the efficient architecture, training DEMAND can avoid overfitting and enables the recognition of individual/minor features based on a small dataset such as an individual data; finally, a novel rank estimator technique is introduced to tune all hyperparameters of DEMAND automatically. Moreover, the proposed DEMAND is validated by four other peer methodologies via real functional Magnetic Resonance Imaging data in the human brain. In short, the validation results demonstrate that DEMAND can reveal the reproducible meta, canonical, and sub-spatial features of the human brain more efficiently than other peer methodologies.