Adaptive Graph Convolution Pooling for Brain Surface Analysis

Karthik Gopinath, Christian Desrosiers, Herve Lombaert

Abstract: 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.