mlsanityData to 7 Oct 2026

Stationary signal processing on graphs

arXiv 1601.02522 ↗First posted 11 Jan 2016cs.DS stat.AP stat.MLcited by 28

Not on the map. Why?

Abstract (arXiv)

Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs. We show that stationarity is expressed through the graph localization operator reminiscent of translation. We prove that stationary graph signals are characterized by a well-defined Power Spectral Density that can be efficiently estimated even for large graphs. We leverage this new concept to derive Wiener-type estimation procedures of noisy and partially observed signals and illustrate the performance of this new model for denoising and regression.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jan 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2020: 1; 2021: 4; 2022: 3; 2023: 4; 2024: 5; 2025: 5; 2026: 6.

28 papers.

Sort:

By area:

  1. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  2. 2022Wiener Graph Deconvolutional Network Improves Graph Self-Supervised Learningcited by 13
  3. 2020Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learningcited by 12
  4. 2024Gegenbauer Graph Neural Networks for Time-varying Signal Reconstructioncited by 12
  5. 2024Polynomial Graphical Lasso: Learning Edges from Gaussian Graph-Stationary Signalscited by 8
  6. 2024Spatiotemporal Covariance Neural Networkscited by 8
  7. 2021Node-Variant Graph Filters in Graph Neural Networkscited by 7
  8. 2024Network Topology Inference from Smooth Signals Under Partial Observabilitycited by 2
  9. 2025Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approachescited by 2
  10. 2021Propagation on Multi-relational Graphs for Node Regressioncited by 1
  11. 2023Learning Graph ARMA Processes from Time-Vertex Spectracited by 1
  12. 2023LogSpecT: Feasible Graph Learning Model from Stationary Signals with Recovery Guaranteescited by 1
16 more
  1. 2023Barron Space for Graph Convolution Neural Networkscited by 1
  2. 2026Stationarity and Spectral Characterization of Random Signals on Simplicial Complexescited by 1
  3. 2026Statistical Testing on Directed Graphs by Surrogate Data Generationcited by 1
  4. 2026Generative Diffusion Models of Stochastic Graph Signalscited by 1
  5. 2021Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimizationcited by 0
  6. 2021Online non-parametric change-point detection for heterogeneous data streams observed over graph nodescited by 0
  7. 2022Graph Filter Transfer via Probability Density Ratio Weightingcited by 0
  8. 2023Locally Stationary Graph Processescited by 0
  9. 2024Sampling Transferable Graph Neural Networks with Limited Graph Informationcited by 0
  10. 2025CoVariance Filters and Neural Networks over Hilbert Spacescited by 0
  11. 2025Sampling Method for Generalized Graph Signals with Pre-selected Vertices via DC Optimizationcited by 0
  12. 2025A Generative Model for Controllable Feature Heterophily in Graphscited by 0
  13. 2025Estimating Fair Graphs from Graph-Stationary Datacited by 0
  14. 2026Decorrelating the Future: Joint Frequency Domain Learning for Spatio-temporal Forecastingcited by 0
  15. 2026Filter Learning for Subgraphs: Algebras and Performance Risk Boundscited by 0
  16. 2026Role-Specific Predictive Geometries for Nonstationary Multivariate Graph-Signal Forecastingcited by 0