Riemannian Regression and Classification Models of Brain Networks Applied to Autism.

Area of Science:

• Neuroimaging
• Machine Learning
• Computational Neuroscience

Background:

• Resting-state functional MRI (rsfMRI) data is often represented as symmetric positive definite (SPD) matrices.
• Traditional Euclidean methods do not fully respect the geometric properties of SPD matrices.
• Existing advanced Riemannian methods for rsfMRI analysis are accurate but computationally demanding and lack interpretability.

Purpose of the Study:

• To develop computationally efficient and interpretable models for rsfMRI analysis using Riemannian geometry.
• To evaluate the performance of log-Euclidean and affine-invariant Riemannian metrics for brain connectivity analysis.
• To compare Riemannian methods against baseline approaches for classifying autism and predicting symptom severity.

Main Methods:

• Representing functional connectivity as SPD matrices.
• Applying log-Euclidean and affine-invariant Riemannian metrics for connectivity analysis.
• Utilizing machine learning models for classification and regression tasks on the ABIDE dataset.

Main Results:

• Achieved 71.1% accuracy in classifying autism versus control subjects on the ABIDE Preprocessed dataset.
• Demonstrated comparable results to more complex methods using simpler, interpretable Riemannian models.
• Showed that Riemannian methods outperform baseline approaches in regressing connectome features to autism severity scores.

Conclusions:

• Log-Euclidean and affine-invariant Riemannian metrics offer a computationally feasible and interpretable alternative for rsfMRI analysis.
• These methods are effective for identifying neuroimaging biomarkers of autism spectrum disorder.
• Riemannian approaches provide a robust framework for understanding brain connectivity in neurological conditions.