Abstract
Permutation Entropy (PE) is a very popular complexity analysis tool for time series. De-spite its simplicity, it is very robust and yields goods results in applications related to assessing the randomness of a sequence, or as a quantitative feature for signal classification. It is based on com-puting the Shannon entropy of the relative frequency of all the ordinal patterns found in a time series. However, there is a basic consensus on the fact that only analysing sample order and not amplitude might have a detrimental effect on the performance of PE. As a consequence, a number of methods based on PE have been proposed in the last years to include the possible influence of sample ampli-tude. These methods claim to outperform PE but there is no general comparative analysis that confirms such claims independently. Furthermore, other statistics such as Sample Entropy (SampEn) are based solely on amplitude, and it could be argued that other tools like this one are better suited to exploit the amplitude differences than PE. The present study quantifies the performance of the standard PE method and other amplitude-included PE methods using a disparity of time series to find out if there are really significant performance differences. In addition, the study compares statistics based uniquely on ordinal or amplitude patterns. The objective was to ascertain whether the whole was more than the sum of its parts. The results confirmed that highest classification accuracy was achieved using both types of patterns simultaneously, instead of using standard PE (ordinal patterns), or SampEn (ampli-tude patterns) isolatedly.
Highlights
Permutation Entropy (PE) [6] is probably becoming one of the most successful complexity estimators in the recent years
The present study quantifies the performance of the standard PE method and other amplitude–included PE methods using a disparity of time series to find out if there are really significant performance differences
The first experiment was devised to assess the classification performance in terms of accuracy of all the individual methods tested. This accuracy corresponds to the proportion of correctly classified time series over the total number of records in the dataset
Summary
Permutation Entropy (PE) [6] is probably becoming one of the most successful complexity estimators in the recent years. The number of works based on this measure is sky-rocketing [38], arguably due its simplicity, robustness, and ability to capture the underlying dynamics of the time series under analysis. In cardiology, it has been applied to heart rate variability data series for sleep breathing pause detection [29], to classify emotional changes [33], to assess a possible cardiac autonomic neuropathy [9], or to find out if atrial fibrillation is stochastic or deterministic [3]. In physical medicine and rehabilitation, there are many studies based on PE analysis of gait data, as in [37], where authors successfully classified normal and pathological gait using PE. PE has had its place in time series analysis related to climate data [19]
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