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Deep Neural Networks (DNNs) have already become a crucial computationalapproach to revealing the spatial patterns in the human brain; however, thereare three major shortcomings in utilizing DNNs to detect the spatial patternsin functional Magnetic Resonance Signals: 1). It is a fully connectedarchitecture that increases the complexity of network structures that isdifficult to optimize and vulnerable to overfitting; 2). The requirement oflarge training samples results in erasing the individual/minor patterns infeature extraction; 3). The hyperparameters are required to be tuned manually,which is time-consuming. Therefore, we propose a novel deep nonlinear matrixfactorization named Deep Matrix Approximately Nonlinear Decomposition (DEMAND)in this work to take advantage of the shallow linear model, e.g., SparseDictionary Learning (SDL) and DNNs. At first, the proposed DEMAND employs anon-fully connected and multilayer-stacked architecture that is easier to beoptimized compared with canonical DNNs; furthermore, due to the efficientarchitecture, training DEMAND can avoid overfitting and enables the recognitionof individual/minor features based on a small dataset such as an individualdata; finally, a novel rank estimator technique is introduced to tune allhyperparameters of DEMAND automatically. Moreover, the proposed DEMAND isvalidated by four other peer methodologies via real functional MagneticResonance Imaging data in the human brain. In short, the validation resultsdemonstrate that DEMAND can reveal the reproducible meta, canonical, andsub-spatial features of the human brain more efficiently than other peermethodologies.

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