Joint estimation of low-rank components and connectivity graph in high-dimensional graph signals: Application to brain imaging

•We formulate the problem of joint estimation of low-rank components and connectivity graph for distorted high-dimensional graph signal.•We propose two approaches to this joint estimation problem. One approach applies alternating optimization to solve the related subproblems. Another approach solves the joint estimation directly.•We provide analysis to understand the impact of inexact graph on the low- rank components estimation accuracy, and we apply the analysis result to inform the choice of regularization parameter when the graph is inexact.•We perform extensive experiments on synthetic and real data, especially brain imaging (MEG) data, to illustrate and validate our proposed algo- rithms. Given high-dimensional, graph-smooth and grossly-corrupted signals, this paper presents the algorithm to simultaneously estimate the intrinsic low-rank components and the underlying graph from high-dimensional noisy graph signal. We assume that the perturbation on low-rank components is sparse and signals are smooth on unknown underlying graph. The proposed algorithm learns the low-rank components by exploiting estimate of the graph, and refines the graph estimation with learned low-rank components. We propose two solutions to this problem: One applies alternating optimization to solve the subproblems. The other solves the problem directly. Furthermore, we analyze the impact of inexact graph on low-rank components estimation to justify our approach. We conduct extensive experiments on the proposed algorithm with synthetic data and real brain imaging data, Magnetoencephalography (MEG) and compare it with state-of-the-art methods. In particular, our algorithm is applied to estimate the low-rank components for classifying MEG signals evoked when a subject views a face or non-face image. We observe that our proposed algorithm is competitive in estimating low-rank components, adequately capturing intrinsic task-related information in lower-dimensional representation. This leads to improved classification performance. Furthermore, we notice that our estimated graph indicates brain active regions for the visual activity that are consistent with neuroscientific findings.