End-to-end Graph-structured Brain Representation Learning

The construction of the brain functional network often follows the hand-crafted Correlation Coefficients of blood-oxygen-level-dependent (BOLD) time series without any learnable components. Meanwhile, most efforts are made to the models, such as graph neural networks, that make predictions with the constructed brain network as input. Unfortunately, the fixed brain network may lose critical information during construction and lead to difficulty in performance improvement, even with deliberately designed graph models. From this perspective, the current situation is similar to the machine learning community, i.e., hand-crafted features and learnable predictors, before the advent of representation learning. In fact, the brain network can be regarded as a graph-structured learnable representation of the brain. By drawing on representation learning, this paper presents the Brain Representation (BRep) learning problem. To this end, the widely used linear and nonlinear correlations are enhanced to be high-order, parametric, and learnable. The flexible brain representation makes the following predictor simple and leads the framework to possess an end-to-end characteristic. The framework is implemented by combining the parametric correlation and a TopK sparsification. Theoretical analysis guarantees the model's universal approximation to any U/V-statistics. Extensive evaluations demonstrate that the proposed BRep possesses superior performance, high efficiency, and interpretability. The source code is publicly available at https://anonymous.4open.science/r/BRep-demo-1A3E/