Increment entropy as a measure of complexity for time series

TL;DR

Increment entropy (IncrEn) is a new complexity measure for time series that uses symbolic encoding of increments and Shannon entropy, effectively detecting abrupt changes in diverse data including EEG signals.

Contribution

The paper introduces increment entropy, a novel complexity measure based on symbolic encoding of increments, applicable to any time series without assumptions.

Findings

Successfully detects abrupt changes in synthetic and real data

Effective in analyzing epileptic EEG signals

Does not require assumptions on data properties

Abstract

Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters, one letter corresponding to direction and the other corresponding to magnitude. The Shannon entropy of the words is termed as increment entropy (IncrEn). Simulations on synthetic data and tests on epileptic EEG signals have demonstrated its ability of detecting the abrupt change, regardless of energetic (e.g. spikes or bursts) or structural changes. The computation of IncrEn does not make any assumption on time series and it can be applicable to arbitrary real-world data.