Smooth graph learning for functional connectivity estimation

Functional connectivity (FC) estimated from functional magnetic resonance imaging (fMRI) signals is important in understanding neural representation and information processing in cortical networks. However, due to a lack of "ground truth" FC pattern, the reliability and robustness of FC estimates are usually examined in downstream FC analysis tasks, such as performing participant's identification (also known as "fingerprinting"). In this paper, we propose to learn FC via a smooth graph learning framework. In particular, we treat each time frame of the fMRI time series as a graph signal on an underlying functional brain graph, and estimate the smooth graph functional connectivity (SGFC) by learning the weighted graph adjacency matrix based on graph signal smoothness assumption. We demonstrate that our approach gives rise to a natural and sparse graph representation of FC from which reliable graph measures can be extracted. Reliability of SGFC is evaluated in the context of fingerprinting and compared to correlation FC (CFC). SGFC achieves higher fingerprinting accuracy across several different experiment settings; the improvement is even more significant when a shorter fMRI scanning length is used for FC estimation. In addition to being reliable, we also validate the cognitive relevance of SGFC by using it to predict fluid intelligence. Finally, in evaluating topological measures of the sparse graph, SGFC reveals a more small-world and modular structure compared to CFC. Together, our results suggest that the smooth graph learning framework produces a naturally sparse, reliable, and cognitive-relevant representation of functional connectivity.