Estimating Outlier-Immunized Common Harmonic Waves for Brain Network Analyses on the Stiefel Manifold

Area of Science:

• Neuroscience
• Computational Biology
• Medical Imaging

Background:

• Brain network organization is governed by harmonic waves from the Laplacian matrix's Eigen-system.
• Understanding harmonic-based alterations offers insights into Alzheimer's disease (AD) pathogenesis.
• Current methods for estimating common harmonic waves are sensitive to outliers in individual brain networks.

Purpose of the Study:

• To develop a novel manifold learning approach for identifying outlier-immunized common harmonic waves.
• To improve the robustness of common harmonic wave estimation in brain network analysis.
• To establish a potential imaging biomarker for early-stage Alzheimer's disease detection.

Main Methods:

• Utilized a manifold learning framework on the Stiefel manifold.
• Calculated the geometric median of individual harmonic waves, enhancing outlier robustness over the Fréchet mean.
• Employed a tailored manifold optimization scheme with guaranteed convergence.

Main Results:

• The proposed method successfully identified outlier-immunized common harmonic waves.
• Learned common harmonic waves demonstrated superior robustness to outliers compared to state-of-the-art techniques.
• The approach yielded a potential imaging biomarker for predicting early-stage Alzheimer's disease.

Conclusions:

• The novel manifold learning approach provides a robust method for analyzing brain network harmonic properties.
• This technique overcomes limitations of existing methods sensitive to outliers.
• The identified common harmonic waves show promise as a reliable biomarker for early Alzheimer's disease diagnosis.