Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition With Spatial Sparsity Constraint

Tuckerdecomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI data. More precisely, we propose to impose a sparsity constraint on spatial maps by using an l(p) norm (0 < p <= 1), in addition to adding low-rank constraints on factormatrices via the Frobenius norm. We solve the constrained Tucker-2model using alternating direction method of multipliers, and propose to update both sparsity and low- rank constrained spatial maps using half quadratic splitting. Moreover, we extract new spatial and temporal features in addition to subject-specific intensities from the core tensor, and use these features to classify multiple subjects. The results from both simulated and experimental fMRI data verify the improvement of the proposed method, compared with four related algorithms including robust Kronecker component analysis, Tucker decomposition with orthogonality constraints, canonical polyadic decomposition, and block term decomposition in extracting common spatial and temporal components across subjects. The spatial and temporal features extracted from the core tensor show promise for characterizing subjects within the same group of patients or healthy controls as well.

Automated summary

Tucker decomposition is commonly used for analyzing multi-subject fMRI data, but traditional methods are insufficient for extracting common patterns across subjects. In this study, we propose a low rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI data. The results demonstrate that this method is more effective in extracting common spatial and temporal components compared to other algorithms, and the features extracted from the core tensor show promise for subject classification.