SENDER: SEmi-Nonlinear Deep Efficient Reconstructor for Extraction Canonical, Meta, and Sub Functional Connectivity in the Human Brain

Deep Linear and Nonlinear learning methods have already been vital machine learning methods for investigating the hierarchical features such as functional connectivity in the human brain via functional Magnetic Resonance signals; however, there are three major shortcomings: 1). For deep linear learning methods, although the identified hierarchy of functional connectivity is easily explainable, it is challenging to reveal more hierarchical functional connectivity; 2). For deep nonlinear learning methods, although non-fully connected architecture reduces the complexity of neural network structures that are easy to optimize and not vulnerable to overfitting, the functional connectivity hierarchy is difficult to explain; 3). Importantly, it is challenging for Deep Linear/Nonlinear methods to detect meta and sub-functional connectivity even in the shallow layers; 4). Like most conventional Deep Nonlinear Methods, such as Deep Neural Networks, the hyperparameters must be tuned manually, which is time-consuming. Thus, in this work, we propose a novel deep hybrid learning method named SEmi-Nonlinear Deep Efficient Reconstruction (SENDER), to overcome the aforementioned shortcomings: 1). SENDER utilizes a multiple-layer stacked structure for the linear learning methods to detect the canonical functional connectivity; 2). SENDER implements a non-fully connected architecture conducted for the nonlinear learning methods to reveal the meta-functional connectivity through shallow and deeper layers; 3). SENDER incorporates the proposed background components to extract the sub-functional connectivity; 4). SENDER adopts a novel rank reduction operator to implement the hyperparameters tuning automatically. To further validate the effectiveness, we compared SENDER with four peer methodologies using real functional Magnetic Resonance Imaging data for the human brain.