Procrustes Analysis for High-Dimensional Data.

Area of Science:

• Statistics
• Machine Learning
• Neuroimaging

Background:

• The Procrustes-based perturbation model minimizes matrix Frobenius distance via similarity transformation.
• Existing models face challenges with non-identifiability, interpretability, and high-dimensional data applicability.

Purpose of the Study:

• To extend the Procrustes perturbation model for high-dimensional data analysis.
• To address non-identifiability and interpretability issues in matrix alignment.
• To improve neuroimaging connectivity analysis using a novel statistical framework.

Main Methods:

• Introduced the Procrustes von Mises-Fisher (ProMises) model, incorporating a von Mises-Fisher prior for orthogonal matrices.
• Developed an Efficient ProMises model tailored for high-dimensional data, such as in neuroimaging.
• Utilized a conjugate prior for a fast and stable estimation process.

Main Results:

• The ProMises model resolves ill-posed problems and enhances interpretability of transformed matrices.
• Demonstrated significant improvements in functional magnetic resonance imaging (fMRI) connectivity analysis.
• Enabled the incorporation of topological brain information into the alignment estimation process.

Conclusions:

• The ProMises model offers a robust solution for high-dimensional matrix alignment problems.
• The Efficient ProMises model is particularly valuable for complex neuroimaging data.
• This approach advances the analysis of brain connectivity by integrating structural information.