Simultaneous Low-rank Component and Graph Estimation for High-dimensional Graph Signals: Application to Brain Imaging

We propose an algorithm to uncover the intrinsic low-rank component of a high-dimensional, graph-smooth and grossly-corrupted dataset, under the situations that the underlying graph is unknown. Based on a model with a low-rank component plus a sparse perturbation, and an initial graph estimation, our proposed algorithm simultaneously learns the low-rank component and refines the graph. The refined graph improves the effectiveness of the graph smoothness constraint and increases the accuracy of the low-rank estimation. We derive the learning steps using ADMM. Our evaluations using synthetic and real brain imaging data in a supervised classification task demonstrate encouraging performance.