Abstract
Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce an increment entropy to measure the complexity of time series in which each increment is mapped onto a word of two letters, one corresponding to the sign and the other corresponding to the magnitude. Increment entropy (IncrEn) is defined as the Shannon entropy of the words. Simulations on synthetic data and tests on epileptic electroencephalogram (EEG) signals demonstrate its ability of detecting abrupt changes, regardless of the 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.
Highlights
Nowadays, the notion of complexity has been ubiquitously used to examine a variety of time series, ranging from diverse physiological signals [1,2,3,4,5,6,7,8,9] to financial time series [10,11] and ecological time series [12]
We focus on the increments of signals because they indicate the characteristics of dynamic changes hidden in a signal
We demonstrate that Increment entropy (IncrEn) can effectively and accurately indicate the complexity of dynamic system using the well-known logistic map xn = rxn−1 (1 − xn−1 ) already shown in previous studies [25,33]
Summary
The notion of complexity has been ubiquitously used to examine a variety of time series, ranging from diverse physiological signals [1,2,3,4,5,6,7,8,9] to financial time series [10,11] and ecological time series [12]. Various measures of complexity have been developed to characterize the behaviors of time series, e.g., regular, chaotic, and stochastic behaviors [8,14,15,16,17,18]. Among these methods, approximate entropy (ApEn) proposed by Pincus [16] is one of the most commonly used methods. For very short data length (less than 100), SampEn deviates from predictions due to correlation of templates [8]
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