Adaptive Constrained ICA with Mixing Matrix Column Constraints: Application to fMRI Data

Independent Component Analysis (ICA) is a powerful data-driven method that has been widely applied in functional magnetic resonance imaging (fMRI) data analysis to uncover underlying sources. An attractive way to boost ICA performance is via constraints to guide ICA factors to be similar to user-supplied "references", allowing incorporation of prior-knowledge into the factorization. However, most of existing constrained ICA methods typically only impose source constraints and are unable to impose constraints on the mixing matrix. With multi-subject medical imaging datasets, constraining the mixing matrix with subjects’ symptom-related measurements, such as clinical scores or cognitive variables, enhances the algorithm’s ability to identify brain activities associated with these symptoms. This offers a novel perspective for understanding the pathologies underlying various psychiatric disorders. Therefore, to overcome the limitations of existing constrained ICA algorithms, we introduce a new constrained ICA algorithm: adaptive-reverse constrained matrix entropy bound minimization (arc-M-EBM), which imposes constraints on the mixing matrix and uses adaptive-reverse thresholding to avoid overfitting or underfitting. This approach ensures flexibility and leads to more accurate and interpretable source separation. Simulations demonstrate that arc-M-EBM outperforms traditional ICA methods. Application to resting-state fMRI data from 176 subjects from healthy controls and patients reveals significant relationships between constrained components and clinical measures, enhancing our understanding of brain-behavior relationships.