Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities
Despite its widely tested and proven usefulness, there is still room for improvement in the basic permutation entropy (PE) algorithm, as several subsequent studies have demonstrated in recent years. Some of these new methods try to address the well-known PE weaknesses, such as its focus only on ordi...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2020-04-01
|
Series: | Entropy |
Subjects: | |
Online Access: | https://www.mdpi.com/1099-4300/22/5/494 |
id |
doaj-24647b733c39497b99e80a0c179d98d0 |
---|---|
record_format |
Article |
spelling |
doaj-24647b733c39497b99e80a0c179d98d02020-11-25T03:23:15ZengMDPI AGEntropy1099-43002020-04-012249449410.3390/e22050494Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination CapabilitiesDavid Cuesta-Frau0Technological Institute of Informatics, Universitat Politècnica de València, 03801 Alcoi Campus, SpainDespite its widely tested and proven usefulness, there is still room for improvement in the basic permutation entropy (PE) algorithm, as several subsequent studies have demonstrated in recent years. Some of these new methods try to address the well-known PE weaknesses, such as its focus only on ordinal and not on amplitude information, and the possible detrimental impact of equal values found in subsequences. Other new methods address less specific weaknesses, such as the PE results’ dependence on input parameter values, a common problem found in many entropy calculation methods. The lack of discriminating power among classes in some cases is also a generic problem when entropy measures are used for data series classification. This last problem is the one specifically addressed in the present study. Toward that purpose, the classification performance of the standard PE method was first assessed by conducting several time series classification tests over a varied and diverse set of data. Then, this performance was reassessed using a new Shannon Entropy normalisation scheme proposed in this paper: divide the relative frequencies in PE by the number of different ordinal patterns actually found in the time series, instead of by the theoretically expected number. According to the classification accuracy obtained, this last approach exhibited a higher class discriminating power. It was capable of finding significant differences in six out of seven experimental datasets—whereas the standard PE method only did in four—and it also had better classification accuracy. It can be concluded that using the additional information provided by the number of forbidden/found patterns, it is possible to achieve a higher discriminating power than using the classical PE normalisation method. The resulting algorithm is also very similar to that of PE and very easy to implement.https://www.mdpi.com/1099-4300/22/5/494permutation entropyordinal patternsforbidden patternssignal classification |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
David Cuesta-Frau |
spellingShingle |
David Cuesta-Frau Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities Entropy permutation entropy ordinal patterns forbidden patterns signal classification |
author_facet |
David Cuesta-Frau |
author_sort |
David Cuesta-Frau |
title |
Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities |
title_short |
Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities |
title_full |
Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities |
title_fullStr |
Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities |
title_full_unstemmed |
Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities |
title_sort |
using the information provided by forbidden ordinal patterns in permutation entropy to reinforce time series discrimination capabilities |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2020-04-01 |
description |
Despite its widely tested and proven usefulness, there is still room for improvement in the basic permutation entropy (PE) algorithm, as several subsequent studies have demonstrated in recent years. Some of these new methods try to address the well-known PE weaknesses, such as its focus only on ordinal and not on amplitude information, and the possible detrimental impact of equal values found in subsequences. Other new methods address less specific weaknesses, such as the PE results’ dependence on input parameter values, a common problem found in many entropy calculation methods. The lack of discriminating power among classes in some cases is also a generic problem when entropy measures are used for data series classification. This last problem is the one specifically addressed in the present study. Toward that purpose, the classification performance of the standard PE method was first assessed by conducting several time series classification tests over a varied and diverse set of data. Then, this performance was reassessed using a new Shannon Entropy normalisation scheme proposed in this paper: divide the relative frequencies in PE by the number of different ordinal patterns actually found in the time series, instead of by the theoretically expected number. According to the classification accuracy obtained, this last approach exhibited a higher class discriminating power. It was capable of finding significant differences in six out of seven experimental datasets—whereas the standard PE method only did in four—and it also had better classification accuracy. It can be concluded that using the additional information provided by the number of forbidden/found patterns, it is possible to achieve a higher discriminating power than using the classical PE normalisation method. The resulting algorithm is also very similar to that of PE and very easy to implement. |
topic |
permutation entropy ordinal patterns forbidden patterns signal classification |
url |
https://www.mdpi.com/1099-4300/22/5/494 |
work_keys_str_mv |
AT davidcuestafrau usingtheinformationprovidedbyforbiddenordinalpatternsinpermutationentropytoreinforcetimeseriesdiscriminationcapabilities |
_version_ |
1724606601243918336 |