  Discovering components that are shared in multiple datasets, next to
dataset-specific features, has great potential for studying the relationships
between different subjects or tasks in functional Magnetic Resonance Imaging
(fMRI) data. Coupled matrix and tensor factorization approaches have been
useful for flexible data fusion, or decomposition to extract features that can
be used in multiple ways. However, existing methods do not directly recover
shared and dataset-specific components, which requires post-processing steps
involving additional hyperparameter selection. In this paper, we propose a
tensor-based framework for multi-task fMRI data fusion, using a partially
constrained canonical polyadic (CP) decomposition model. Differently from
previous approaches, the proposed method directly recovers shared and
dataset-specific components, leading to results that are directly
interpretable. A strategy to select a highly reproducible solution to the
decomposition is also proposed. We evaluate the proposed methodology on real
fMRI data of three tasks, and show that the proposed method finds meaningful
components that clearly identify group differences between patients with
schizophrenia and healthy controls.
