Rahul Singh, Reza Abiri, Walter Besio
Most tools for analyzing signals on a network, brain regions wired together for instance, only capture pairwise, second-order relationships: how strongly two nodes move together. But real activity has richer, nonlinear interactions where three modes couple and feed each other, and plain covariance or power spectra miss those entirely. This paper builds a graph bispectrum to catch that third-order structure, plus a compact bicoherence score that boils it down to a small, scale-independent number.
They show the measure has clean mathematical properties (it vanishes for Gaussian noise, as it should) and that on synthetic data it flags nonlinear dependencies invisible to standard statistics. Applied to seizure EEG from the CHB-MIT database, seizures showed markedly stronger nonlinear coupling than the calm periods between them.
This summary is based only on the abstract, so see the paper for the math and how robust the EEG finding is.
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…
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