Hui Feng

Signed graphs, which are characterized by both positive and negative edge weights, have recently attracted significant attention in the field of graph signal processing (GSP). Existing works on signed graph learning typically assume that all graph nodes are available. However, in some specific applications, only a subset of nodes can be observed while the remaining nodes stay hidden. To address this challenge, we propose a novel method for identifying signed graph that accounts for hidden nodes, termed \textit{signed graph learning with hidden nodes under column-sparsity regularization} (SGL-HNCS). Our method is based on the assumption that graph signals are smooth over signed graphs, i.e., signal values of two nodes connected by positive (negative) edges are similar (dissimilar). Rooted in this prior assumption, the topology inference of a signed graph is formulated as a constrained optimization problem with column-sparsity regularization, where the goal is to reconstruct the signed graph Laplacian matrix without disregarding the influence of hidden nodes. We solve the constrained optimization problem using a tailored block coordinate descent (BCD) approach. Experimental results using synthetic data and real-world data demonstrate the efficiency of the proposed SGL-HNCS method.

Time-vertex graph signal (TVGS) models describe time-varying data with irregular structures. The bandlimitedness in the joint time-vertex Fourier spectral domain reflects smoothness in both temporal and graph topology. In this paper, we study the critical sampling of three types of TVGS including continuous-time signals, infinite-length sequences, and finite-length sequences in the time domain for each vertex on the graph. For a jointly bandlimited TVGS, we prove a lower bound on sampling density or sampling ratio, which depends on the measure of the spectral support in the joint time-vertex Fourier spectral domain. We also provide a lower bound on the sampling density or sampling ratio of each vertex on sampling sets for perfect recovery. To demonstrate that critical sampling is achievable, we propose the sampling and reconstruction procedures for the different types of TVGS. Finally, we show how the proposed sampling schemes can be applied to numerical as well as real datasets.

Finite time-vertex graph signals (FTVGS) provide an efficient representation for capturing spatio-temporal correlations across multiple data sources on irregular structures. Although sampling and reconstruction of FTVGS with known spectral support have been extensively studied, the case of unknown spectral support requires further investigation. Existing random sampling methods may extract samples from any vertex at any time, but such strategies are not friendly in practice, where sampling is typically limited to a subset of vertices and moments. To address this requirement, we propose a subset random sampling scheme for FTVGS. Specifically, we first randomly select a subset of rows and columns to form a submatrix, followed by random sampling within that submatrix. In theory, we provide sufficient conditions for reconstructing the original FTVGS with high probability. Additionally, we introduce a reconstruction framework incorporating low-rank, sparsity, and smoothness priors (LSSP), and verify the feasibility of the reconstruction and the effectiveness of the framework through experiments.