Transferability of Covariance Neural Networks

Graph convolutional networks (GCN) leverage topology-driven graph convolutional operations to combine information across the graph for inference tasks. In our recent work, we have studied GCNs with covariance matrices as graphs in the form of coVariance neural networks (VNNs) that draw similarities with traditional principal component analysis (PCA) while overcoming its limitations regarding instability. In this paper, we focus on characterizing the transferability of VNNs. The notion of transferability is motivated from the intuitive expectation that learning models could generalize to "compatible" datasets i.e., datasets of different dimensionalities describing the same domain) with minimal effort. VNNs inherit the scale-free data processing architecture from GCNs and here, we show that VNNs exhibit transferability of performance (without re-training) over datasets whose covariance matrices converge to a limit object. Multi-scale neuroimaging datasets enable the study of the brain at multiple scales and hence, provide an ideal scenario to validate the transferability of VNNs. We demonstrate the quantitative transferability of VNNs over a regression task based on a multi-scale dataset of cortical thickness features. Further, to elucidate the advantages offered by VNNs in neuroimaging data analysis, we also deploy VNNs as regression models in a pipeline for "brain age" prediction from cortical thickness features. The discordance between brain age and chronological age ("brain age gap") can reflect increased vulnerability or resilience toward neurological disease or cognitive impairments. The architecture of VNNs allows us to extend beyond the coarse metric of brain age gap and associate anatomical interpretability to elevated brain age gap in Alzheimer's disease (AD). We leverage the transferability of VNNs to cross validate the anatomical interpretability offered by VNNs to brain age gap across datasets of different dimensionalities.