Multi-subject fMRI analysis via combined independent component analysis and shift-invariant canonical polyadic decomposition

BACKGROUND Canonical polyadic decomposition (CPD) may face a local optimal problem when analyzing multi-subject fMRI data with inter-subject variability. Beckmann and Smith proposed a tensor PICA approach that incorporated an independence constraint to the spatial modality by combining CPD with ICA, and alleviated the problem of inter-subject spatial map (SM) variability. NEW METHOD This study extends tensor PICA to incorporate additional inter-subject time course (TC) variability and to connect CPD and ICA in a new way. Assuming multiple subjects share common TCs but with different time delays, we accommodate subject-dependent TC delays into the CP model based on the idea of shift-invariant CP (SCP). We use ICA as an initialization step to provide the aggregating mixing matrix for shift-invariant CPD to estimate shared TCs with subject-dependent delays and intensities. We then estimate shared SMs using a least-squares fit post shift-invariant CPD. RESULTS Using simulated fMRI data as well as actual fMRI data we demonstrate that the proposed approach improves the estimates of the shared SMs and TCs, and the subject-dependent TC delays and intensities. The default mode component illustrates larger TC delays than the task-related component. COMPARISON WITH EXISTING METHOD(S) The proposed approach shows improvements over tensor PICA in particular when TC delays are large, and also outperforms SCP with SM orthogonality constraint and SCP with ICA-based SM initialization. CONCLUSIONS TCs with subject-dependent delays conform to the true situation of multi-subject fMRI data. The proposed approach is suitable for decomposing multi-subject fMRI data with large inter-subject temporal and spatial variability.