Kernel-Based Multilayer Graph Signal Recovery via Median Truncation of Gradient Descent

Complex structured data-driven applications frequently encompass a higher-order connectivity or interaction among data samples and can be represented by a multilayer graph. In this paper, we consider the problem of signal recovery on multilayer graphs that are corrupted by both noise and outliers within a general recovery framework. A robust and layer-aware multilayer graph signal recovery based on median truncation of the gradient descent, MT-GSR (Median Truncated-Graph Signal Recovery) is proposed. It adaptively truncates node values on each layer that diverge considerably from the sample median of its neighborhood measurements. A local joint-intra-inter-layer regularization operator that relies on graph kernels is formulated to capture the prior information of the layered network topology. The graph kernels exhibit the linear and nonlinear dependencies of the regularization operators. In addition, the layer-aware MT-GSR is extended to a layer-aware-distributed approach, the MT-LDGSR (MT-Layer-aware Distributed Graph Signal Recovery). The MT-LDGSR employs the local properties of each node on each layer and provides a robust signal recovery framework on multilayer networks. Numerical tests provide an analysis of performance guarantees and evaluate the proposed recovery methods on synthetic and real-world data to validate the proposed multilayer kernel-based signal recovery methods.