Adaptive Graph Convolution Pooling for Brain Surface Analysis

Learning surface data is fundamental to neuroscience. Recent advances has enabled the use of graph convolution filters directly within neural network frameworks. These filters are, however, constrained to a single fixed-graph structure. A pooling strategy remains yet to be defined for learning graph-node data in non-predefined graph structures. This lack of flexibility in graph convolutional architectures currently limits applications on brain surfaces. Graph structures and number of mesh nodes, indeed, highly vary across brain geometries. This paper proposes a new general graph-based pooling method for processing full-sized surface-valued data, as input layers of graph neural networks, towards predicting subject-based variables, as output information. This novel method learns an intrinsic aggregation of input graph nodes based on the geometry of the input graph. This is leveraged using recent advances in spectral graph alignment where the surface parameterization becomes common across multiple brain geometries. These novel adaptive intrinsic pooling layers enable the exploration of entirely new architectures of graph neural networks, which were previously constrained to one single fixed structure in a dataset. We demonstrate the flexibility of the new pooling strategy in two proof-of-concept applications, namely, the classification of disease stages and regression of subject's ages using directly the surface data from varying mesh geometries.

学习表面数据对神经科学至关重要。近期的进展使得能够在神经网络框架内直接使用图卷积滤波器。然而，这些滤波器局限于单一的固定图结构。对于在非预定义图结构中学习图节点数据，池化策略仍有待确定。图卷积架构缺乏这种灵活性，目前限制了其在脑表面的应用。实际上，图结构和网格节点数量在不同的大脑几何形状中差异很大。本文提出了一种新的基于通用图的池化方法，用于处理全尺寸的表面值数据，作为图神经网络的输入层，以预测基于个体的变量作为输出信息。这种新方法根据输入图的几何形状学习输入图节点的内在聚合。这是利用光谱图对齐的最新进展实现的，其中表面参数化在多个大脑几何形状中变得通用。这些新颖的自适应内在池化层使得能够探索图神经网络全新的架构，而之前在数据集中图神经网络局限于一种单一的固定结构。我们在两个概念验证应用中展示了新池化策略的灵活性，即直接使用来自不同网格几何形状的表面数据对疾病阶段进行分类以及对个体年龄进行回归。