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Open AccessArticle

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

1
Technological Institute of Informatics, Universitat Politècnica de València, 03801 Alcoi Campus, Spain
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Innovatec Sensorización y Comunicación S.L., Avda. Elx, 3, 03801 Alcoi, Spain
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Department of Internal Medicine, Móstoles Teaching Hospital, Móstoles, 28935 Madrid, Spain
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(10), 1013; https://doi.org/10.3390/e21101013
Received: 21 September 2019 / Revised: 15 October 2019 / Accepted: 16 October 2019 / Published: 18 October 2019
Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear I R n mapping into I R , where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures. View Full-Text
Keywords: permutation entropy; hidden Markov models; k-means clustering; signal classification; relative frequency estimation; feature selection; body temperature permutation entropy; hidden Markov models; k-means clustering; signal classification; relative frequency estimation; feature selection; body temperature
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Cuesta-Frau, D.; Molina-Picó, A.; Vargas, B.; González, P. Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy. Entropy 2019, 21, 1013.

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