Graph Variogram: A novel tool to measure spatial stationarity

TL;DR

This paper introduces the graph variogram, a new tool for measuring spatial intrinsic stationarity in irregularly sampled signals on graphs, extending classical variograms to graph domains.

Contribution

It defines graph stationarity based on intrinsic stationarity and develops the graph variogram as a novel measurement tool for local and global spatial stationarity.

Findings

Graph variograms accurately estimate theoretical models with small bias.

They are robust to sampling variation in irregularly sampled data.

The method extends classical variogram concepts to graph-structured data.

Abstract

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.