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Sample entropy for graph signals: an approach to nonlinear dynamic analysis of data on networks
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DOI：10.1007/s11071-026-12885-y.png)
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Abstract
En 中文
The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in Shannon entropy and symbol dynamics. In this paper, we explore, for the first time, whether and how a popular conditional-entropy based measure—Sample Entropy (SampEn)—can be effectively defined for graph signals and used to characterise the nonlinear dynamics of data on complex networks. We introduce sample entropy for graph signals (SampEn $$_{G}$$ ), a unified framework that generalises classical sample entropy from uni- and bi-dimensional signals, including time series and images, by building on topology-aware embeddings using multi-hop neighbourhoods and computing finite scale of correlation sums in the continuous embedding state space. Experiments on synthetic and real-world datasets verify that SampEn $$_G$$ recovers known nonlinear dynamical features on paths and grids. In a traffic-flow analysis, SampEn $$_{G}$$ on a directed topology (encoding causal flow constraint) shows promise to detect phase transition between free-flow and congestion, offering information that is complementary to existing Shannon-entropy based approaches. We expect SampEn $$_{G}$$ to open up new ways to analyse graph signals, generalising sample entropy and nonlinear analysis based on conditional entropy to a wide variety of network data.
Keywords:
Complex network
Nonlinear dynamic analysis
Graph signals
Sample entropy
Conditional entropy
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