arXiv subjects

John Stewart Fabila Carrasco

Publications and source records attributed to John Stewart Fabila Carrasco.

3 recordsLinked to original sources

arXiv2026

Sample entropy for graph signals: An approach to nonlinear dynamic analysis of data on networks

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 (SampEnG), 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, including weather station, wireless sensor monitoring, and traffic systems, verify that SampEnG recovers known nonlinear dynamical features on paths and grids. In the traffic-flow analysis, SampEnG on a directed topology (encoding causal flow constraint) shows promise to detect phase transitions between free-flow and congestion, offering information that is complementary to existing Shannon-entropy based approaches. We expect SampEnG to open up new ways to analyse graph signals, generalising sample entropy and the concept of conditional entropy to extending nonlinear analysis to a wide variety of network data.

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arXiv2026

Sample entropy for graph signals: An approach to nonlinear analysis of graph signals

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.

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arXiv2024

Graph Permutation Entropy: Extensions to the Continuous Case, A step towards Ordinal Deep Learning, and More

Nonlinear dynamics play an important role in the analysis of signals. A popular, readily interpretable nonlinear measure is Permutation Entropy. It has recently been extended for the analysis of graph signals, thus providing a framework for non-linear analysis of data sampled on irregular domains. Here, we introduce a continuous version of Permutation Entropy, extend it to the graph domain, and develop a ordinal activation function akin to the one of neural networks. This is a step towards Ordinal Deep Learning, a potentially effective and very recently posited concept. We also formally extend ordinal contrasts to the graph domain. Continuous versions of ordinal contrasts of length 3 are also introduced and their advantage is shown in experiments. We also integrate specific contrasts for the analysis of images and show that it generalizes well to the graph domain allowing a representation of images, represented as graph signals, in a plane similar to the entropy-complexity one. Applications to synthetic data, including fractal patterns and popular non-linear maps, and real-life MRI data show the validity of these novel extensions and potential benefits over the state of the art. By extending very recent concepts related to permutation entropy to the graph domain, we expect to accelerate the development of more graph-based entropy methods to enable nonlinear analysis of a broader kind of data and establishing relationships with emerging ideas in data science.

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