Chaos-Embedding.I : An innovative approach to exploring chaos through Higuchi’s dimension with application to brain signals

An effective approach to characterize chaotic time series is the largest Lyapunov exponent λ. It can be used to detect non-chaotic (λ<0), weakly chaotic (λ≈0), and strongly chaotic (λ≫0) regimes, which is important for identifying state transitions and detecting key changes in the system’s behavior. The problem with λ is that its estimation is strongly distorted by noise, and even more so when the series is short. By addressing those challenges, in this paper, we propose an innovative approach for noisy chaotic time series analysis, referred to as Chaos-Embedding. It is based on adding a chaotic signal of modifiable amplitude to the processed signal and then calculating the fractal dimension by Higuchi’s algorithm, this allows the detection of different regimes of studied time series. In the first part of this paper, we will conduct a rigorous evaluation of the effectiveness of this technique through nonlinear time series recorded from the three benchmark maps (Gauss’s, Hénon’s, and the Logistic), the separation of different regimes is achieved even by adding noise to the processed time series. According to a literature review, EEGs are chaotic data and its attractor depends on patient state’s. In addition, noise in electroencephalographic signals is undeniable, mainly caused by physiological artifacts and instrumentation. In the second part of this paper, we will explore Chaos-Embedding and HFD to extract features from EEG for epilepsy monitoring. We have achieved both seizure and epilepsy detection using the BONN database and detected the pre-ictal phase using the CHB-MIT database.