IEEE Trans Med Imaging. 2022 Oct;41(10):2752-2763. doi: 10.1109/TMI.2022.3169640. Epub 2022 Sep 30.
Functional connectivities (FC) of brain network manifest remarkable geometric patterns, which is the gateway to understanding brain dynamics. In this work, we present a novel geometric-attention neural network to characterize the time-evolving brain state change from the functional neuroimages by tracking the trajectory of functional dynamics on high-dimension Riemannian manifold of symmetric positive definite (SPD) matrices. Specifically, we put the spotlight on learning the common state-specific manifold signatures that represent the underlying cognition. In this context, the driving force of our neural network is tied up with the learning of the evolution functionals on the Riemannian manifold of SPD matrix that underlies the known evolving brain states. To do so, we train a convolution neural network (CNN) on the Riemannian manifold of SPD matrices to seek for the putative low-dimension feature representations, followed by an end-to-end recurrent neural network (RNN) to yield the time-varying mapping function of SPD matrices which fits the evolutionary trajectories of the underlying states. Furthermore, we devise a geometric attention mechanism in CNN, allowing us to discover the latent geometric patterns in SPD matrices that are associated with the underlying states. Notably, our work has the potential to understand how brain function emerges behavior by investigating the geometrical patterns from functional brain networks, which is essentially a correlation matrix of neuronal activity signals. Our proposed manifold-based neural network achieves promising results in predicting brain state changes on both simulated data and task functional neuroimaging data from Human Connectome Project, which implies great applicability in neuroscience studies.
功能连接（FC）的脑网络表现出显著的几何模式，这是理解大脑动力学的关键。在这项工作中，我们提出了一种新颖的几何注意神经网络，通过跟踪功能动力学在对称正定（SPD）矩阵的高维黎曼流形上的轨迹，从功能神经影像中描述时间演化的大脑状态变化。具体来说，我们专注于学习代表潜在认知的常见状态特定流形特征。在这种情况下，我们的神经网络的驱动力与学习 SPD 矩阵黎曼流形上的演化函数有关，该函数是已知演化大脑状态的基础。为此，我们在 SPD 矩阵的黎曼流形上训练卷积神经网络（CNN），以寻找假定的低维特征表示，然后是端到端的循环神经网络（RNN），以产生适合潜在状态的 SPD 矩阵的时变映射函数。此外，我们在 CNN 中设计了一种几何注意力机制，使我们能够发现与潜在状态相关的 SPD 矩阵中的潜在几何模式。值得注意的是，我们的工作通过研究功能脑网络中的几何模式，有潜力通过调查神经元活动信号的相关矩阵来理解大脑功能如何产生行为。我们提出的基于流形的神经网络在模拟数据和人类连接组计划的任务功能神经影像学数据上的大脑状态变化预测中取得了有希望的结果，这意味着在神经科学研究中有很大的适用性。
