Distance Correlation-Based Brain Functional Connectivity Estimation and Non-Convex Multi-Task Learning for Developmental fMRI Studies

Objective: Resting-state functional magnetic resonance imaging (rs-fMRI)-derived functional connectivity (FC) patterns have been extensively used to delineate global functional organization of the human brain in healthy development and neuropsychiatric disorders. In this paper, we investigate how FC in males and females differs in an age prediction framework. Methods: We first estimate FC between regions-of-interest (ROIs) using distance correlation instead of Pearson's correlation. Distance correlation, as a multivariate statistical method, explores spatial relations of voxel-wise time courses within individual ROIs and measures both linear and nonlinear dependence, capturing more complex between-ROI interactions. Then, we propose a novel non-convex multi-task learning (NC-MTL) model to study age-related gender differences in FC, where age prediction for each gender group is viewed as one task, and a composite regularizer with a combination of the non-convex l(2,1-2) and l(1-2) terms is introduced for selecting both common and task-specific features. Results and Conclusion:We validate the effectiveness of our NC-MTL model with distance correlation-based FC derived from rs-fMRI for predicting ages of both genders. The experimental results on the Philadelphia Neurodevelopmental Cohort demonstrate that our NC-MTL model outperforms several other competing MTL models in age prediction. We also compare the age prediction performance of our NC-MTL model using FC estimated by Pearson's correlation and distance correlation, which shows that distance correlation-based FC is more discriminative for age prediction than Pearson's correlation-based FC. Significance: This paper presents a novel framework for functional connectome developmental studies, characterizing developmental gender differences in FC patterns.