# Stationary time-vertex signal processing

arXiv: https://arxiv.org/abs/1611.00255 · HTML: https://mlsanity.com/paper/1611.00255/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2016.

## Built on by (most cited first, 8 of 8)

- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [Learning Cartesian Product Graphs with Laplacian Constraints](https://mlsanity.com/paper/2402.08105/) (2024)
- [Learning Graph ARMA Processes from Time-Vertex Spectra](https://mlsanity.com/paper/2302.06887/) (2023)
- [Locally Stationary Graph Processes](https://mlsanity.com/paper/2309.01657/) (2023)
- [Diffusion Maps for Signal Filtering in Graph Learning](https://mlsanity.com/paper/2312.14758/) (2023)
- [Decorrelating the Future: Joint Frequency Domain Learning for Spatio-temporal Forecasting](https://mlsanity.com/paper/2603.04418/) (2026)
- [Role-Specific Predictive Geometries for Nonstationary Multivariate Graph-Signal Forecasting](https://mlsanity.com/paper/2609.06519/) (2026)

## Abstract (arXiv)

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some {known} graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that goes beyond product graphs. Joint stationarity helps by reducing the estimation variance and recovery complexity. In particular, for any jointly stationary process (a) one reliably learns the covariance structure from as little as a single realization of the process, and (b) solves MMSE recovery problems, such as interpolation and denoising, in computational time nearly linear on the number of edges and timesteps. Experiments with three datasets suggest that joint stationarity can yield accuracy improvements in the recovery of high-dimensional processes evolving over a graph, even when the latter is only approximately known, or the process is not strictly stationary.