Consistent Estimation of Dimensionality for Data-Driven Methods in fMRI Analysis.

Area of Science:

• Neuroimaging
• Statistical analysis
• Machine learning

Background:

• Data-driven methods like Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are vital in neuroimaging.
• Selecting the correct number of components is a critical challenge in these analyses.
• Current methods often rely on log-likelihood functions for model selection.

Purpose of the Study:

• To propose a novel criterion for selecting the number of components in factor models for neuroimaging data.
• To offer an alternative to existing model selection criteria based on log-likelihood functions.

Main Methods:

• Developed a new model selection criterion using the sum of squares of the smallest eigenvalues of the sample covariance matrix.
• Derived the criterion from the asymptotic distribution of the goodness-of-fit term, establishing its consistency.
• Validated the criterion using simulated and real functional magnetic resonance imaging (fMRI) data.

Main Results:

• The proposed criterion demonstrated superior performance compared to conventional methods in fMRI data analysis.
• Achieved improved accuracy and consistency, even with data variability.
• The criterion is straightforward to implement.

Conclusions:

• The novel eigenvalue-based criterion offers a more accurate and consistent approach to component selection in neuroimaging.
• This method enhances the reliability of data-driven analyses in functional magnetic resonance imaging (fMRI).
• The proposed criterion represents a significant advancement for neuroimaging data analysis.