Advances in Distributed Graph Filtering

Abstract

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this work generalizes state-of-the-art distributed graph filters to filters where every node weights the signal of its neighbors with different values while keeping the aggregation operation linear. This new implementation, labeled as edge-variant graph filter, yields a significant reduction in terms of communication rounds while preserving the approximation accuracy. In addition, we characterize the subset of shift-invariant graph filters that can be described with edge-variant recursions. By using a low-dimensional parametrization the proposed graph filters provide insights in approximating linear operators through the succession and composition of local operators, i.e., fixed support matrices, which span applications beyond the field of graph signal processing. A set of numerical results shows the benefits of the edge-variant filters over current methods and illustrates their potential to a wider range of applications than graph filtering.

References in corpus (13)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Discrete Signal Processing on Graphs
• Convolutional Neural Network Architectures for Signals Supported on Graphs
• GSPBOX: A toolbox for signal processing on graphs
• Autoregressive Moving Average Graph Filtering
• Stationary signal processing on graphs
• Stationary Graph Processes and Spectral Estimation
• Estimating time-varying networks
• Distributed Autoregressive Moving Average Graph Filters
• Filtering Random Graph Processes Over Random Time-Varying Graphs
• Compressive Spectral Clustering
• Flexible Multi-layer Sparse Approximations of Matrices and Applications
• Filter Design for Autoregressive Moving Average Graph Filters

Cited by in corpus (18)

• Gated Graph Recurrent Neural Networks
• Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks
• A Hilbert Space Theory of Generalized Graph Signal Processing
• Graphon Filters: Graph Signal Processing in the Limit
• Distributed Training of Graph Convolutional Networks
• DCT and DST Filtering with Sparse Graph Operators
• Preconditioned Gradient Descent Algorithm for Inverse Filtering on Spatially Distributed Networks
• Designing Asymmetric Shift Operators for Decentralized Subspace Projection
• A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks
• Learning Stochastic Graph Neural Networks with Constrained Variance
• Polynomial graph filter of multiple shifts and distributed implementation of inverse filtering
• Node-Adaptive Regularization for Graph Signal Reconstruction
• Graph Convolutional Neural Networks Sensitivity under Probabilistic Error Model
• Signal Processing on Directed Graphs
• Stability of Graph Convolutional Neural Networks to Stochastic Perturbations
• Online Distributed Learning over Graphs with Multitask Graph-Filter Models
• Blind Demixing of Diffused Graph Signals
• Fast Decentralized Linear Functions Over Edge Fluctuating Graphs