Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information

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.

Development of Automated Sleep Stage Classification System Using Multivariate Projection-Based Fixed Boundary Empirical Wavelet Transform and Entropy Features Extracted from Multichannel EEG Signals

“…The limitation of this work is that we used multi-channel EEG recordings obtained from only 25 subjects. In future, we intend to consider other entropy-based measures such as slope entropy [ 50 ], distribution entropy [ 51 ], state space domain correlation entropy [ 52 , 53 ], and other entropy measures [ 31 ] to improve the classification performance of sleep stages using more subjects.…”

Fever Time Series Analysis Using Slope Entropy. Application to Early Unobtrusive Differential Diagnosis

“…Specifically, the present study is mainly based on [ 17 ]. However, as [ 17 ] employed SampEn as the discriminating feature, when SlopEn was not available yet, and since SlopEn seemed very promising as it outperformed SampEn in many comparative analyzes [ 22 ], it was necessary to assess the capability of this new method in the framework of temperature time series. The present study used a more diverse experimental dataset, implemented a novel windowing approach, analyzed the influence of record duration, and did not use any feature extraction method such as Trace Segmentation [ 17 ].…”

“…SlopEn was first described in [ 22 ]. It is based on computing relative frequencies of subsequences, as many other entropy methods, but instead of using amplitude or ordinal information, it uses as symbols the representation of the slope between two consecutive samples.…”

“…The final values were normalized by the maximum SlopEn obtained in order to keep their range between 0 and 1. A more detailed SlopEn algorithm is described in [ 22 ]. The SlopEn result of each record was the single classification feature to be used in the performance analysis carried out in Section 3 .…”

“…This way it would not be necessary to monitor for 24 h before the differences became detectable, and diagnosis could be anticipated several hours, triggering earlier patient isolation and/or treatment, if necessary. The entropy measure employed was Slope Entropy (SlopEn), a recently proposed method [ 22 ] based on gradient patterns between consecutive samples. The results achieved demonstrated a high disease classification potential that could be re–assessed using also other pathologies in order to achieve an additional inexpensive and unobtrusive diagnosis tool.…”