AI 中文总结
研究旨在刻画图信号高阶相互作用，基于图傅里叶系数三阶矩定义图双谱张量及图双相干度量，建立相关性质，通过合成信号与脑电图实验验证其能检测非线性依赖，为图信号高阶分析提供可解释且高效的工具。
AI 中文摘要
我们引入一种图双谱公式来表征图信号中的高阶相互作用。传统图谱方法仅捕捉二阶结构，而许多图信号存在协方差或图功率谱未反映的非线性相互作用。受经典高阶谱分析启发，我们基于图傅里叶系数的三阶矩定义图双谱张量，并导出紧凑的图双相干度量，以低维且尺度不变形式总结非线性模式相互作用。我们建立了所提量的关键性质，包括高斯图信号的三阶矩消失及非线性模式耦合的动力学解释。合成随机图信号实验表明，该方法能检测互补的非线性依赖性。我们还将此方法应用于CHB - MIT头皮脑电图数据库的脑电图记录，发现发作期活动的非线性图谱耦合比发作间期显著增加。所提方法为图信号的高阶相互作用分析提供了一个可解释且计算高效的工具。
英文摘要
We introduce a graph bispectrum formulation for characterizing higher-order interactions in graph signals. While conventional graph spectral methods capture only second-order structure, many graph signals exhibit nonlinear interactions that are not reflected in covariance or graph power spectra. Motivated by classical higher-order spectral analysis, we define a graph bispectrum tensor based on third-order moments of graph Fourier coefficients and derive a compact graph bicoherence measure that summarizes nonlinear mode interactions in a low-dimensional and scale-invariant form. We establish key properties of the proposed quantities, including vanishing third-order moments for Gaussian graph signals and a dynamical interpretation in terms of nonlinear mode coupling. Experiments on synthetic random graph signals demonstrate that the proposed measures detect complementary nonlinear dependencies even when second-order statistics are similar. We further apply the method to EEG recordings from the CHB-MIT Scalp EEG Database and show that ictal activity exhibits substantially increased nonlinear graph spectral coupling compared to interictal periods. The proposed approach provides an interpretable and computationally efficient tool for higher-order interaction analysis for graph signals.
