# Locally Stationary Graph Processes

arXiv: https://arxiv.org/abs/2309.01657 · HTML: https://mlsanity.com/paper/2309.01657/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 57 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Learning heat diffusion graphs](https://mlsanity.com/paper/1611.01456/) (2016)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Scalable Semidefinite Programming](https://mlsanity.com/paper/1912.02949/) (2019)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [Signal Processing on Graphs: Causal Modeling of Unstructured Data](https://mlsanity.com/paper/1503.00173/) (2015)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [Vertex-Frequency Analysis on Graphs](https://mlsanity.com/paper/1307.5708/) (2013)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Semi-supervised Learning in Network-Structured Data via Total Variation Minimization](https://mlsanity.com/paper/1901.09838/) (2019)
- [Stationary time-vertex signal processing](https://mlsanity.com/paper/1611.00255/) (2016)
- [Filter Design for Autoregressive Moving Average Graph Filters](https://mlsanity.com/paper/1711.09086/) (2017)
- [Node-Variant Graph Filters in Graph Neural Networks](https://mlsanity.com/paper/2106.00089/) (2021)
- [A Class of Doubly Stochastic Shift Operators for Random Graph Signals and their Boundedness](https://mlsanity.com/paper/1908.01596/) (2019)
- [QSDPNAL: A two-phase augmented Lagrangian method for convex quadratic semidefinite programming](https://mlsanity.com/paper/1512.08872/) (2015)
- [Convolutional Neural Networks Via Node-Varying Graph Filters](https://mlsanity.com/paper/1710.10355/) (2017)
- [Graph Variogram: A novel tool to measure spatial stationarity](https://mlsanity.com/paper/1809.09342/) (2018)
- [Learning Graph ARMA Processes from Time-Vertex Spectra](https://mlsanity.com/paper/2302.06887/) (2023)

## Abstract (arXiv)

Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that is globally valid on the entire graph, in many practical problems, the characteristics of the process may be subject to local variations in different regions of the graph. In this work, we propose a locally stationary graph process (LSGP) model that aims to extend the classical concept of local stationarity to irregular graph domains. We characterize local stationarity by expressing the overall process as the combination of a set of component processes such that the extent to which the process adheres to each component varies smoothly over the graph. We propose an algorithm for computing LSGP models from realizations of the process, and also study the approximation of LSGPs locally with WSS processes. Experiments on signal interpolation problems show that the proposed process model provides accurate signal representations competitive with the state of the art.