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The Matrix Decomposition techniques have been a vital computational approachto analyzing the hierarchy of functional connectivity in the human brain.However, there are still four shortcomings of these methodologies: 1). Largetraining samples; 2). Manually tuning hyperparameters; 3). Time-consuming andrequire extensive computational source; 4). It cannot guarantee convergence toa unique fixed point.  Therefore, we propose a novel deep matrix factorization technique called DeepLinear Matrix Approximate Reconstruction (DELMAR) to bridge the abovementionedgaps. The advantages of the proposed method are: at first, proposed DELMAR canestimate the important hyperparameters automatically; furthermore, DELMARemploys the matrix backpropagation to reduce the potential accumulative errors;finally, an orthogonal projection is introduced to update all variables ofDELMAR rather than directly calculating the inverse matrices.  The validation experiments of three peer methods and DELMAR using realfunctional MRI signal of the human brain demonstrates that our proposed methodcan efficiently identify the spatial feature in fMRI signal even faster andmore accurately than other peer methods. Moreover, the theoretical analysesindicate that DELMAR can converge to the unique fixed point and even enable theaccurate approximation of original input as DNNs.

DELMAR: Deep Linear Matrix Approximately Reconstruction to Extract Hierarchical Functional Connectivity in the Human Brain