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Graph convolutional networks (GCN) leverage topology-driven graphconvolutional operations to combine information across the graph for inferencetasks. In our recent work, we have studied GCNs with covariance matrices asgraphs in the form of coVariance neural networks (VNNs) that draw similaritieswith traditional PCA-driven data analysis approaches while offering significantadvantages over them. In this paper, we first focus on theoreticallycharacterizing the transferability of VNNs. The notion of transferability ismotivated from the intuitive expectation that learning models could generalizeto "compatible" datasets (possibly of different dimensionalities) with minimaleffort. VNNs inherit the scale-free data processing architecture from GCNs andhere, we show that VNNs exhibit transferability of performance over datasetswhose covariance matrices converge to a limit object. Multi-scale neuroimagingdatasets enable the study of the brain at multiple scales and hence, canvalidate the theoretical results on the transferability of VNNs. To gauge theadvantages offered by VNNs in neuroimaging data analysis, we focus on the taskof "brain age" prediction using cortical thickness features. In clinicalneuroscience, there has been an increased interest in machine learningalgorithms which provide estimates of "brain age" that deviate fromchronological age. We leverage the architecture of VNNs to extend beyond thecoarse metric of brain age gap in Alzheimer's disease (AD) and make twoimportant observations: (i) VNNs can assign anatomical interpretability toelevated brain age gap in AD, and (ii) the interpretability offered by VNNs iscontingent on their ability to exploit specific principal components of theanatomical covariance matrix. We further leverage the transferability of VNNsto cross validate the above observations across different datasets.

Transferability of coVariance Neural Networks and Application to Interpretable Brain Age Prediction using Anatomical Features