提出定向图信号的置信度检验新方法，解决传统方法无法处理方向性关系的问题。
Statistical Testing on Directed Graphs by Surrogate Data Generation
- 基于图移位算子特征分解，定义定向图广义平稳信号
- 生成保持协方差结构的代理信号，构建零假设分布
- 在真实数据上验证优于无向图方法和简单置换法
近年来，图信号处理作为信号处理与图论的交叉领域，为节点上信号的分析提供了强大工具，同时考虑了边所代表的关系。这些工具已成功应用于多种场景，包括统计假设检验。特别是基于代理数据生成的非参数方法已被用于无向图信号。然而，这类方法尚未扩展到有向图。本文首先重新审视有向图上的平稳图信号概念，通过图移位算子的特征分解，定义了有向图广义平稳信号。随后，提出一种新框架，生成在平稳假设下保持协方差结构的代理图信号。由此构建的零假设分布可作为实测数据的参考。最后，通过引导示例和真实数据应用，将本方法与现有无向图方法或基于简单置换的方法进行比较，证明了该方法的可行性与优越性。
原文摘要 · Abstract (English)
In recent years, graph signal processing has emerged as a powerful framework at the intersection of signal processing and graph theory, providing tools for the analysis of signals defined on nodes while accounting for their relationships represented by edges. These tools have been successfully applied to various settings, including statistical hypothesis testing. In particular, non-parametric approaches based on surrogate generation have been proposed for signals on undirected graphs. However, they are yet to be extended to directed graphs. In this work, we first revisit the notion of stationary graph signals on directed graphs. Specifically, and through the eigendecomposition of the graph shift operator, we define directed graph wide-sense stationary signals. Then, we propose a new framework to generate surrogate graph signals that preserve covariance structure under stationarity assumptions. Null distributions of the test metric can then be constructed from these surrogates and serve as a reference for the empirical data. Finally, we provide guiding examples and an application on real data, in which we compare the performance of our framework with existing techniques for undirected graphs or based on naive permutation, demonstrating feasibility and superiority of the proposed approach.
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