估计Stiefel流形上用于脑网络分析的异常免疫共谐波matlab代码.zip

# Outlier-Immunized_Common_Harmonic_Waves_JBHI https://pubmed.ncbi.nlm.nih.gov/37028067/ Hongmin Cai, Huan Liu, Defu Yang, Guorong Wu, Bin Hu, and Jiazhou Chen*. *“Estimating Outlier-Immunized Common Harmonic Waves for Brain Network Analyses on the Stiefel Manifold”*, IEEE Journal of Biomedical and Health Informatics, vol. 27, issue 5, pp. 2411-2422, May 2023. *Abstract* — Since brain network organization is essentially governed by the harmonic waves derived from the Eigen-system of the underlying Laplacian matrix, discovering the harmonic-based alterations provides a new window to understand the pathogenic mechanism of Alzheimer’s disease (AD) in a unified reference space. However, current reference (common harmonic waves) estimation studies over the individual harmonic waves are often sensitive to outliers, which are obtained by averaging the heterogenous individual brain networks. To address this challenge, we propose a novel manifold learning approach to identify a set of outlier-immunized common harmonic waves. The backbone of our framework is calculating the geometric median of all individual harmonic waves on the Stiefel manifold, instead of Fréchet mean, thus improving the robustness of learned common harmonic waves to the outliers. A manifold optimization scheme with theoretically guaranteed convergence is tailored to solve our method. The experimental results on synthetic data and real data demonstrate that the common harmonic waves learned by our approach are not only more robust to the outliers than the state-of-the-art methods, but also provide a putative imaging biomarker to predict the early stage of AD. *Index Terms* — Alzheimer’s disease, brain network, harmonic waves, manifold optimization