  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.
