Fast vertex-based graph convolutional neural network and its application to brain images

Abstract

This paper proposes a vertex-based graph convolutional neural network (vertex-CNN) for analyzing structured data on graphs. We represent graphs using semi-regular triangulated meshes in which each vertex has 6 connected neighbors. We generalize classical CNN defined on equi-spaced grids to that defined on semi-regular triangulated meshes by introducing main building blocks of the CNN, including convolution, down-sampling, and pooling, on a vertex domain. By exploiting the regularity of semi-regular meshes in terms of vertex connections, the proposed vertex-CNN keeps the inherent properties of classical CNN in a Euclidean space, such as shift-invariance and down-sampling at a rate of 2, 4, etc. We employ brain images from Alzheimer’s Disease Neuroimaging Initiative (ADNI) (n = 6767) and extract cortical features (e.g., cortical thickness, surface area, curvature, Jacobian, sulcal depth, and volume) for the classification of healthy controls (CON), patients with mild cognitive impairment (MCI) and Alzheimer’s disease (AD). Based on cortical thickness, we show that the proposed vertex-CNN is near 3 times faster and performs significantly better in the classification performance of CON, MCI, and AD than an existing graph CNN defined on the graph spectral domain given in Defferrard (2016). Moreover, we examine the robustness of a multi-channel implementation of vertex-CNN on 6 cortical measures for the MCI and AD classification. Finally, we show a promising finding of the prediction accuracy from MCI to AD as a function of years before the onset of AD. Our experiments demonstrate the fast computation and promising classification performance of the vertex-CNN.