IEEE J Biomed Health Inform. 2023 May;27(5):2411-2422. doi: 10.1109/JBHI.2023.3250711. Epub 2023 May 4.
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.
由于脑网络组织本质上是由潜在拉普拉斯矩阵的特征系统产生的谐波所控制，因此发现基于谐波的改变为在统一的参考空间中理解阿尔茨海默病（AD）的发病机制提供了一个新的窗口。然而，目前对个体谐波的基于参考（常见谐波）的估计研究往往容易受到离群值的影响，这些离群值是通过对异质的个体脑网络进行平均得到的。为了解决这一挑战，我们提出了一种新的流形学习方法来识别一组具有抗离群值能力的常见谐波。我们框架的核心是在 Stiefel 流形上计算所有个体谐波的几何中位数，而不是 Fréchet 均值，从而提高了学习到的常见谐波对离群值的鲁棒性。我们还量身定制了一种具有理论保证收敛性的流形优化方案来解决我们的方法。在合成数据和真实数据上的实验结果表明，我们的方法学习到的常见谐波不仅比最先进的方法更能抵抗离群值，而且还提供了一种潜在的成像生物标志物来预测 AD 的早期阶段。
