Adaptive Weight and Wasserstein Distance Constrained Low-Rank Sparse Representation Method for Functional Connectivity Network Estimation

Functional connectivity (FC) network derived from resting-state functional magnetic resonance imaging (rs-fMRI) has been extensively employed in the automated identification of brain disorders. Conventional FC network modeling methods typically assign equal importance to different sampling points of rs-fMRI and brain regions of interest (ROIs). Nevertheless, considering temporal and regional heterogeneity, this assumption may not always be applicable. Moreover, sparse regression algorithms with regularization terms are commonly adopted to eliminate spurious FC. However, these conventional regularization terms impose a uniform sparse penalty on all FC without considering the prior knowledge that the brain tends to transmit information in an energetically efficient manner. To address the above problems, we propose an adaptive weight and Wasserstein distance constrained low-rank sparse representation (AW-WD-LSR) method to construct FC networks. Specifically, we employ adaptive weights to the reconstruction errors of rs-fMRI time series across various ROIs and sampling points, thereby amplifying the significance of crucial features in the joint representation, leading to a more robust FC network. Meanwhile, we incorporate a local constraint by introducing the optimal transport distance (i.e., Wasserstein distance) between ROIs to adjust the sparse penalty on the corresponding FC. The larger Wasserstein distance, the higher information transmission cost between two ROIs, resulting in a greater penalty imposed on the corresponding FC. The efficacy of the innovation modules is demonstrated in classification tasks involving major depressive disorder (MDD) with mixed features (MMF), MDD without mixed features (MDD_noMF), and healthy controls (HCs).