  We developed a convolution neural network (CNN) on semi-regular triangulated
meshes whose vertices have 6 neighbours. The key blocks of the proposed CNN,
including convolution and down-sampling, are directly defined in a vertex
domain. By exploiting the ordering property of semi-regular meshes, the
convolution is defined on a vertex domain with strong motivation from the
spatial definition of classic convolution. Moreover, the down-sampling of a
semi-regular mesh embedded in a 3D Euclidean space can achieve a down-sampling
rate of 4, 16, 64, etc. We demonstrated the use of this vertex-based graph CNN
for the classification of mild cognitive impairment (MCI) and Alzheimer's
disease (AD) based on 3169 MRI scans of the Alzheimer's Disease Neuroimaging
Initiative (ADNI). We compared the performance of the vertex-based graph CNN
with that of the spectral graph CNN.
