Entropies from Markov Models as Complexity Measures of Embedded Attractors
This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the att...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-06-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/17/6/3595 |
| _version_ | 1798002433913257984 |
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| author | Julián D. Arias-Londoño Juan I. Godino-Llorente |
| author_facet | Julián D. Arias-Londoño Juan I. Godino-Llorente |
| author_sort | Julián D. Arias-Londoño |
| collection | DOAJ |
| description | This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes. |
| first_indexed | 2024-04-11T11:52:11Z |
| format | Article |
| id | doaj.art-95c8cbb1ec4a4e2391d5a8650d357e3e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T11:52:11Z |
| publishDate | 2015-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-95c8cbb1ec4a4e2391d5a8650d357e3e2022-12-22T04:25:18ZengMDPI AGEntropy1099-43002015-06-011763595362010.3390/e17063595e17063595Entropies from Markov Models as Complexity Measures of Embedded AttractorsJulián D. Arias-Londoño0Juan I. Godino-Llorente1Department of Systems Engineering, Universidad de Antioquia, Cll 70 No. 52-21, Medellín, ColombiaCenter for Biomedical Technologies, Universidad Politécnica de Madrid, Crta. M40, km. 38, Pozuelode Alarcón, 28223, Madrid, SpainThis paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes.http://www.mdpi.com/1099-4300/17/6/3595complexity analysishidden Markov modelsprincipal curveentropy measures |
| spellingShingle | Julián D. Arias-Londoño Juan I. Godino-Llorente Entropies from Markov Models as Complexity Measures of Embedded Attractors Entropy complexity analysis hidden Markov models principal curve entropy measures |
| title | Entropies from Markov Models as Complexity Measures of Embedded Attractors |
| title_full | Entropies from Markov Models as Complexity Measures of Embedded Attractors |
| title_fullStr | Entropies from Markov Models as Complexity Measures of Embedded Attractors |
| title_full_unstemmed | Entropies from Markov Models as Complexity Measures of Embedded Attractors |
| title_short | Entropies from Markov Models as Complexity Measures of Embedded Attractors |
| title_sort | entropies from markov models as complexity measures of embedded attractors |
| topic | complexity analysis hidden Markov models principal curve entropy measures |
| url | http://www.mdpi.com/1099-4300/17/6/3595 |
| work_keys_str_mv | AT juliandariaslondono entropiesfrommarkovmodelsascomplexitymeasuresofembeddedattractors AT juanigodinollorente entropiesfrommarkovmodelsascomplexitymeasuresofembeddedattractors |