# Graph Variogram: A novel tool to measure spatial stationarity

arXiv: https://arxiv.org/abs/1809.09342 · HTML: https://mlsanity.com/paper/1809.09342/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2018.

## Built on by (most cited first, 1 of 1)

- [Locally Stationary Graph Processes](https://mlsanity.com/paper/2309.01657/) (2023)

## Abstract (arXiv)

Irregularly sampling a spatially stationary random field does not yield a graph stationary signal in general. Based on this observation, we build a definition of graph stationarity based on intrinsic stationarity, a less restrictive definition of classical stationarity. We introduce the concept of graph variogram, a novel tool for measuring spatial intrinsic stationarity at local and global scales for irregularly sampled signals by selecting subgraphs of local neighborhoods. Graph variograms are extensions of variograms used for signals defined on continuous Euclidean space. Our experiments with intrinsically stationary signals sampled on a graph, demonstrate that graph variograms yield estimates with small bias of true theoretical models, while being robust to sampling variation of the space.