Coupled canonical polyadic decomposition of multi-group fMRI data with spatial reference and orthonormality constraints

•A novel constrained CCPD by incorporating spatial reference and orthonormality is proposed for multi-group fMRI data.•The shared SMs and group-specific TCs and subject differences can be decomposed by the proposed method.•Based on accelerated ALS, shared SMs are further twice updated by orthnormalization and minimizing square error of shared SMs and spatial references.•By using AdaBoost, resting-state group-specific TCs estimated by the proposed method exhibit significant difference between HC and SZ groups. Multi-group fMRI data may possess different types of subjects, tasks, scans, etc. Fortunately, coupled canonical polyadic decomposition (CCPD) requires multiple tensor datasets to share one or more factor matrices. Considering that spatial variability is generally smaller than temporal variability, we attempt CCPD to decompose multi-group fMRI data into shared spatial maps (SMs), group-specific time courses (TCs) and subject intensities. As spatial references of interested components are generally available and the spatial orthonormality can reduce crosstalk among components, we propose a novel CCPD by adding spatial reference and orthonormality constraints. Specifically, based on accelerated alternating least squares, we further update shared SMs twice: 1) we orthonormalize shared SM components by orthogonal Procrustes solution; 2) after identifying the interested components by maximizing Pearson correlation coefficients between shared SMs and spatial references, we update interested shared SMs by minimizing the square error between magnitude part of normalized shared SMs and corresponding normalized spatial references. The results of two-group simulated and experimental task-related fMRI data as well as resting-state fMRI data with 24 healthy controls (HCs) and 24 schizophrenia patients (SZs) all show outperformed performance for the proposed method compared with unconstrained CCPD, CCPD with a spatial orthonormality constraint, widely-used tensor independent component analysis (ICA) and semi-blind group information guide ICA in both magnitude-only analysis and complex-valued analysis. Moreover, by using AdaBoost, resting-state group-specific TCs estimated by the proposed method significantly exhibit larger group differences, especially for the sensorimotor network, and thus provide a potential biomarker for schizophrenia.