Disentangling homogeneous and heterogeneous representation of human functional connectome via graph learning

Objective. Functional connectivity analysis of fMRI data provides critical insight into large-scale brain organization; however, conventional approaches often ignore the specific information mixed with population-level structure and individual- or condition-specific variability. We aimed to develop an interpretable framework that separates these shared and heterogeneous components of the human functional connectome. Approach. We developed Joint Individual Graph Learning (JIGL), a multi-view graph learning framework that jointly estimates a low-rank common graph and sparse view-specific graphs across subjects or experimental conditions. We evaluated JIGL using resting-state and task-based fMRI data from 422 individuals across eight conditions and compared it with Pearson correlation, SIMLR (CIMLR), and Simplex. Performance was assessed using alignment with established resting-state network organization, associations with age and cognitive phenotypes, task identifiability, and low-dimensional representations of task-specific connectivity. Main results. The common graph learned by JIGL captured a biologically meaningful functional backbone and showed stronger alignment with established resting-state network organization than the comparison methods. JIGL-derived individual graphs preserved biologically relevant inter-individual variability, yielding stronger associations with age and cognitive phenotypes. The task-specific graphs also showed improved identifiability, as quantified by the intraclass correlation coefficient. Furthermore, low-dimensional embeddings of the connectivity matrices revealed structured, network-dependent task signatures that were consistently distinct from both the common graph and the resting-state condition. Significance. JIGL provides a principled framework for disentangling shared functional architecture from individual- and condition-specific connectivity patterns. This decomposition improves sensitivity to biologically meaningful variability and supports more interpretable analyses of functional brain organization across individuals and cognitive states.