Graph Signal Surrogate Generation for Statistical Testing of Covariance Structure on Directed Graphs

2026-08-03

AI Summary

Existing methods struggle to generate non-parametric surrogate data on directed graphs that preserve the signal covariance structure, thereby limiting statistical testing for nodal covariance anomalies. This work addresses this gap by introducing, for the first time, a wide-sense stationarity framework into directed graph signal processing and proposing a novel surrogate data generation method. By leveraging Dirichlet energy metrics and permutation testing, the approach explicitly accounts for graph asymmetry while rigorously preserving the original covariance properties. Experiments on the Freeman EIES social network demonstrate that the proposed method significantly outperforms conventional approaches based on symmetrized graphs, leading to markedly improved performance in detecting covariance anomalies.

Abstract

Non-parametric statistical testing is based on surrogate data generation that randomizes chosen features in the empirical data. In the graph setting, graph signal processing (GSP) brings forward versatile schemes; e.g., to preserve smoothness of graph signals as measured by the Dirichlet energy. However, how to deal with directed graphs remains an active area of research. We begin by revisiting the definition of directed graph wide-sense stationarity. The surrogate signals preserve covariance under the stationary assumption. We demonstrate the feasibility of the scheme to detect irregular node covariance and benchmark our method against conventional schemes using the symmetrized graph. We also investigate how the level of asymmetry affects the detection performance, thus assessing the advantages of the presented approach. Finally, we show results for a real-world graph extracted from the Freeman EIES social network dataset.

Problem

• directed graphs
• graph signal processing
• covariance structure
• statistical testing
• surrogate generation

Innovation

• directed graph
• graph signal processing
• surrogate data
• wide-sense stationarity
• covariance structure