Permutation entropy has become a standard tool for time series analysis that exploits the temporal and ordinal relationships within data. Motivated by a Kullback–Leibler divergence interpretation of permutation entropy as divergence from white noise, we extend pattern-based methods to the setting of random walk data. We analyze random walk null models for correlated time series and describe a m...

Permutation entropy and order patterns in an EEG signal have been applied by several authors to study sleep, anesthesia, and epileptic absences. Here, we discuss a new version of permutation entropy, which is interpreted as distance to white noise. It has a scale similar to the well-known χ2 distributions and can be supported by a statistical model. Critical values for significance are provided...

In this paper, we propose to use permutation entropy to explore whether the changes in electroencephalogram (EEG) data can effectively distinguish different phases in human absence epilepsy, i.e., the seizure-free, the pre-seizure and seizure phases. Permutation entropy is applied to analyze the EEG data from these three phases, each containing 100 19-channel EEG epochs of 2 s duration. The exp...

In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. We generally discuss this phenomenon by considering the distribution of ordinal patterns, which describe the up and down in the orbits of a Borel measurable map on a subset of the real numbers. In particular, we give a natural ordinal description of...

Ordinal patterns are a time-series data analysis tool used as preliminary step to construct the permutation entropy, which itself allows same characterization of dynamics chaotic or regular more theoretical constructs such Lyapunov exponent. However, ordinal store strictly information than entropy exponents. We present results working with Duffing oscillator showing that reflect changes in dyna...