Structure-seeking multilinear methods for the analysis of fMRI data.

Area of Science:

• Neuroimaging
• Functional Magnetic Resonance Imaging (fMRI)
• Multivariate Data Analysis

Background:

• fMRI data analysis often involves complex, higher-order structures beyond space and time.
• Traditional bilinear methods (e.g., PCA) require data unfolding, leading to non-unique decompositions and loss of multiway interactions.
• Retaining higher-order dimensions is crucial for preserving data integrity and enabling meaningful interpretations.

Purpose of the Study:

• To apply multilinear models, specifically the parallel factor (PARAFAC) model, to analyze higher-order fMRI data.
• To demonstrate the advantages of multilinear analysis over traditional bilinear methods for fMRI data.
• To extract unique and neurophysiologically interpretable spatial and temporal response components from fMRI data.

Main Methods:

• Functional MRI data from a bilateral finger-tapping paradigm were analyzed.
• A trilinear model (voxels × time × run) and a quadrilinear model (voxels × time × trial × run) were fitted using the PARAFAC model.
• Results were validated against traditional Singular Value Decomposition (SVD)/Principal Component Analysis (PCA) methods.

Main Results:

• Multilinear models successfully retained higher-order data structures (trial, task condition, subject, group).
• PARAFAC analysis yielded unique spatial and temporal response components.
• The multilinear approach preserved multiway linkages and interactions within the fMRI data.

Conclusions:

• Multilinear models, such as PARAFAC, provide a more robust and interpretable framework for analyzing complex fMRI data.
• This method overcomes the limitations of traditional bilinear approaches by preserving higher-order data structures.
• The extracted components offer neurophysiologically meaningful insights into brain function during tasks.