用双曲几何更精准建模脑功能网络层次结构
Brain-HGCN: A Hyperbolic Graph Convolutional Network for Brain Functional Network Analysis
- 采用双曲空间和符号聚合机制，区分兴奋与抑制连接
- 在两个大规模fMRI数据集上分类准确率显著优于传统方法
- 适合脑科学、计算精神病学方向研究者参考
功能磁共振成像（fMRI）揭示了具有层级拓扑结构的复杂脑功能网络，这些结构对认知处理至关重要。标准欧几里得图神经网络（GNN）因固有空间限制，在表示此类层次结构时常产生高失真。本文提出Brain-HGCN，一种基于双曲几何的几何深度学习框架，利用负曲率空间以高保真度建模脑网络层级结构。基于洛伦兹模型，框架引入新型双曲图注意力层，通过符号聚合机制分别处理兴奋性与抑制性连接；同时，采用几何上合理的弗雷歇均值进行图读出，学习鲁棒的图级别表示。在两个大规模fMRI数据集上的精神疾病分类实验表明，Brain-HGCN显著优于当前最先进的欧几里得基线方法。本工作展示了双曲GNN在计算精神病学中的潜力，开创了fMRI分析的新几何范式。
原文摘要 · Abstract (English)
Functional magnetic resonance imaging (fMRI) reveals complex brain functional networks with hierarchical topologies crucial for cognitive processing. Standard Euclidean Graph Neural Networks (GNNs) often struggle to represent these hierarchical structures without high distortion due to inherent spatial constraints. We propose Brain-HGCN, a geometric deep learning framework based on hyperbolic geometry, which leverages negatively curved space to model brain network hierarchy with high fidelity. Grounded in the Lorentz model, our framework employs a novel hyperbolic graph attention layer with a signed aggregation mechanism to distinctly process excitatory and inhibitory connections. Furthermore, we learn robust graph-level representations via a geometrically principled Fréchet mean for graph readout. Experiments on two large-scale fMRI datasets for psychiatric disorder classification demonstrate that Brain-HGCN significantly outperforms state-of-the-art Euclidean baselines. This work highlights the potential of hyperbolic GNNs in computational psychiatry by pioneering a new geometric paradigm for fMRI analysis.
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