Sample entropy for graph signals: An approach to nonlinear analysis of graph signals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Lei, Mei-San Maggie Carrasco, John Stewart Fabila Escudero, Javier |
| author_facet | Lei, Mei-San Maggie Carrasco, John Stewart Fabila Escudero, Javier |
| contents | We introduce a graph-signal generalisation of Sample Entropy, denoted SampEn$_{G}$, to quantify irregularity of graph signals on a continuous state space, complementing existing methods on symbolic dynamics. Our approach replaces the temporal delay embedding of classical SampEn with a multi-hop graph-based embedding: for each node, we aggregate patterns from local walk-weighted neighbourhood averages computed via powers of the graph shift operator. We show empirically that SampEn$_{G}$ reduces to classical 1D SampEn on directed path graphs, and validate its nonlinear sensitivity using the logistic map. Experiments on directed Erdős--Rényi graph signals further characterise its behaviour with connectivity and pattern length $m$, with practical runtimes on the order of thousands of nodes. We expect SampEn$_{G}$ to open up new ways to analyse graph signals, generalising SampEn and the concept of conditional entropy to extending nonlinear analysis to a wide variety of network data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20655 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sample entropy for graph signals: An approach to nonlinear analysis of graph signals Lei, Mei-San Maggie Carrasco, John Stewart Fabila Escudero, Javier Signal Processing We introduce a graph-signal generalisation of Sample Entropy, denoted SampEn$_{G}$, to quantify irregularity of graph signals on a continuous state space, complementing existing methods on symbolic dynamics. Our approach replaces the temporal delay embedding of classical SampEn with a multi-hop graph-based embedding: for each node, we aggregate patterns from local walk-weighted neighbourhood averages computed via powers of the graph shift operator. We show empirically that SampEn$_{G}$ reduces to classical 1D SampEn on directed path graphs, and validate its nonlinear sensitivity using the logistic map. Experiments on directed Erdős--Rényi graph signals further characterise its behaviour with connectivity and pattern length $m$, with practical runtimes on the order of thousands of nodes. We expect SampEn$_{G}$ to open up new ways to analyse graph signals, generalising SampEn and the concept of conditional entropy to extending nonlinear analysis to a wide variety of network data. |
| title | Sample entropy for graph signals: An approach to nonlinear analysis of graph signals |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2604.20655 |