Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs
Theoretical tutorial establishes equivalence between covariance neural networks and PCA, with stability and transferability bounds and brain-age applications.
The paper reviews the theory of coVariance neural networks (VNNs), graph neural networks that operate on covariance matrices as graphs. It derives a conceptual equivalence between VNNs and PCA-based information processing, refined stability bounds under finite-sample covariance perturbations, and transferability characterizations across multiscale datasets. Demonstrated applications include brain age gap estimation for neurodegenerative conditions from neuroimaging data.
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