2021/07/06 by B. R. R. Boaretto, Boaretto, B. R. R., Roberto C. Budzinski +13 · 2 citations
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Artificial neural network #Chaos control and synchronization #Chaotic #Complex Systems and Time Series Analysis #Computer science #Data Analysis #Entropy (arrow of time) #FOS: Physical sciences #Fractal and DNA sequence analysis #Machine learning #Mathematics #Noise (video) #Nonlinear system #Pattern recognition (psychology) #Robustness (evolution) #Series (stratigraphy) #Statistics #Statistics and Probability (physics.data-an) #Stochastic process #Time series #physics.data-an
paper · pdf · doi:10.48550/arxiv.2107.02860
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/07/06 · openalex publication_date 2021/07/06 · arxiv updated 2021/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, α, that determines the strength of the correlation of the noise. To predict α the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the α value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same α parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community.