Abstract
The development of new measures and algorithms to quantify the entropy or related concepts of a data series is a continuous effort that has brought many innovations in this regard in recent years. The ultimate goal is usually to find new methods with a higher discriminating power, more efficient, more robust to noise and artifacts, less dependent on parameters or configurations, or any other possibly desirable feature. Among all these methods, Permutation Entropy (PE) is a complexity estimator for a time series that stands out due to its many strengths, with very few weaknesses. One of these weaknesses is the PE’s disregarding of time series amplitude information. Some PE algorithm modifications have been proposed in order to introduce such information into the calculations. We propose in this paper a new method, Slope Entropy (SlopEn), that also addresses this flaw but in a different way, keeping the symbolic representation of subsequences using a novel encoding method based on the slope generated by two consecutive data samples. By means of a thorough and extensive set of comparative experiments with PE and Sample Entropy (SampEn), we demonstrate that SlopEn is a very promising method with clearly a better time series classification performance than those previous methods.
Highlights
The capability of entropy or complexity measures to distinguish among time series classes and to understand the underlying dynamics is very well known [1,2,3]
Based on the scaffolding provided by the standard Permutation Entropy (PE) algorithm, we propose in this paper a new entropy statistic termed Slope Entropy (SlopEn) that satisfies the requirements stated above
Sample Entropy (SampEn) and SlopEn classification accuracy was significant in all cases, with SampEn performing best for m = 3, as usually recommended for SampEn and ApEn [4,36]
Summary
The capability of entropy or complexity measures to distinguish among time series classes and to understand the underlying dynamics is very well known [1,2,3]. Many different formulas, statistics, algorithms, or methods have been proposed since the introduction of the first method that arguably became widespread and generally used across a varied and diverse set of scientific and technological frameworks, Approximate Entropy, ApEn [4]. Most of these methods are based on counting events found or derived from the input time series under entropy analysis, in order to estimate probabilities from relative frequencies of such events. These mapping frequently takes place using entropy definitions, such as Shannon [5], Renyi [6], Tsallis [7], or Kolmogorov–Sinai [8] entropies, among others not so often used.
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