Group ICA 2.0: Closing the Gap Between Subjects and Group Latent Decomposition with Copula-Linked Group ICA (CoLiG-ICA)

Group Independent Component Analysis (gICA) is widely used to decompose high-dimensional functional MRI data into interpretable brain networks. However, conventional gICA primarily identifies components shared across subjects. This group-level assumption can limit the recovery of networks present only in individuals or subject subsets, reducing sensitivity to intersubject heterogeneity in clinical neuroimaging datasets. We introduce Copula-Linked Group ICA (CoLiG-ICA), an algorithm in the Group ICA 2.0 framework that jointly estimates template-linked, cohort-only, and subject-only brain networks within a unified model. CoLiG-ICA combines ICA-based spatial decomposition, copula-based dependence modeling, and deep learning optimization to preserve the consistency and interpretability of template-constrained ICA while enabling free components beyond the reference networks. By linking subject decompositions to shared templates and jointly estimating cohort-only and subject-only sources, CoLiG-ICA represents individual variability not captured by conventional group priors. We evaluate CoLiG-ICA using resting-state fMRI data from the UCLA-CNP dataset and compare it with conventional constrained ICA in estimating template-linked components, discovering additional free components, improving component independence, and capturing subject-level variability beyond the shared group prior. Compared with MOO-ICAR, CoLiG-ICA showed significantly lower intercomponent spatial dependence, indicating improved subject-level component independence, and significantly reduced motion-related variance in the template-linked components. Additionally, in a schizophrenia-only group analysis, CoLiG-ICA identified three additional resting-state networks beyond the 53 template-linked NeuroMark components: one sensorimotor and two visual networks.