Otherwise, they cannot be plainly symbolized by a permutation without using additional rules, which actually treat equal values as not being such.

In the standard permutation entropy methodology, it is preferable that embedding vectors have all their components different. Interesting modification of the permutation entropy method has been proposed in for 3-tuple EEG data. Examples of such a modification can be found in for taking into account absolute values or in for treating equal values. In the latter case, the bare idea in about how to treat equal values can/should be modified in order to meet a purpose of concrete situation. In this connection, it should be taken into account that any redundancy reduction method leaves out some types of information, which may be useless for one process/task and may carry useful information for another one. Nevertheless, this method is subjected to a critique for not taking into account absolute values of the raw data and for not treating properly a possibility of having equal values in the embedding vector (ties). , have been obtained with straightforward application of the permutation entropy methodology in its initial form, as it is described in. This method is simple and transparent, is robust with respect to monotonic distortions of the raw data, and is suitable for estimating the dynamical complexity of the underlying dynamical process. Examples of those reduced data for time series can be mean value, variance, Lyapunov exponents, correlation dimension, and attractor dimension.Ī remarkable method suitable for reducing the excess of redundancy in time series has been proposed by Bandt and Pompe in, known as permutation entropy. As a result, new data are obtained, small in size and digestible by a human being. The data processing and classification, aimed at extracting meaningful for nonspecialist characteristics, is based on reducing the excess of redundancy. Introductionīecause of technical progress in the areas of sensors and storage devices, a huge amount of raw data about time course of different processes, such as ECG, EEG, climate data recordings, and stock market data, have become available. If embedding vectors have equal components, this method could be more precise in discriminating between similar data sets. In the latter case, this method can be used instead of the permutation one. The characteristic features of this method are as follows: it preserves information about equal values, if any, in the embedding vectors it is exempt from combinatorics and it delivers the same entropy value as does the permutation method, provided the embedding vectors do not have equal components. A method for analyzing sequential data sets, similar to the permutation entropy one, is discussed.

Entropy magazine