arXiv subjects

Qinji Shu

Publications and source records attributed to Qinji Shu.

3 recordsLinked to original sources

arXiv2025

Subset Random Sampling and Reconstruction of Finite Time-Vertex Graph Signals

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.

eess.SP↗

arXiv2024

Subset Random Sampling of Finite Time-vertex Graph Signals

Time-varying data with irregular structures can be described by finite time-vertex graph signals (FTVGS), which represent potential temporal and spatial relationships among multiple sources. While sampling and corresponding reconstruction of FTVGS with known spectral support are well investigated, methods for the case of unknown spectral support remain underdeveloped. Existing random sampling schemes may acquire samples from any vertex at any time, which is uncommon in practical applications where sampling typically involves only a subset of vertices and time instants. In sight of this requirement, this paper proposes a subset random sampling scheme for FTVGS. We first randomly select some rows and columns of the FTVGS to form a submatrix, and then randomly sample within the submatrix. Theoretically, we prove sufficient conditions to ensure that the original FTVGS is reconstructed with high probability. Also, we validate the feasibility of reconstructing the original FTVGS by experiments.

eess.SP↗

arXiv2024

The Transferability of Downsamped Sparse Graph Convolutional Networks

To accelerate the training of graph convolutional networks (GCNs) on real-world large-scale sparse graphs, downsampling methods are commonly employed as a preprocessing step. However, the effects of graph sparsity and topological structure on the transferability of downsampling methods have not been rigorously analyzed or theoretically guaranteed, particularly when the topological structure is affected by graph sparsity. In this paper, we introduce a novel downsampling method based on a sparse random graph model and derive an expected upper bound for the transfer error. Our findings show that smaller original graph sizes, higher expected average degrees, and increased sampling rates contribute to reducing this upper bound. Experimental results validate the theoretical predictions. By incorporating both sparsity and topological similarity into the model, this study establishes an upper bound on the transfer error for downsampling in the training of large-scale sparse graphs and provides insight into the influence of topological structure on transfer performance.

cs.LG↗