Simplicial complex entropy for time series analysis
Abstract The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-12-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-49958-6 |
| _version_ | 1797376959225790464 |
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| author | Lev Guzmán-Vargas Alvaro Zabaleta-Ortega Aldo Guzmán-Sáenz |
| author_facet | Lev Guzmán-Vargas Alvaro Zabaleta-Ortega Aldo Guzmán-Sáenz |
| author_sort | Lev Guzmán-Vargas |
| collection | DOAJ |
| description | Abstract The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irregularity. However, for some types of dynamics such as stochastic and chaotic, new approaches are required that can provide a better characterization of them. In this paper we present the simplicial complex approximate entropy, which is based on the conditional probability of the occurrence of elements of a simplicial complex. Our results show that this entropy measure provides a wide range of values with details not easily identifiable with standard methods. In particular, we show that our method is able to quantify the irregularity in simulated random sequences and those from low-dimensional chaotic dynamics. Furthermore, it is possible to consistently differentiate cardiac interbeat sequences from healthy subjects and from patients with heart failure, as well as to identify changes between dynamical states of coupled chaotic maps. Our results highlight the importance of the structures revealed by the simplicial complexes, which holds promise for applications of this approach in various contexts. |
| first_indexed | 2024-03-08T19:46:54Z |
| format | Article |
| id | doaj.art-1d2c79b938a24b9a9d62563ea155b92b |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-08T19:46:54Z |
| publishDate | 2023-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-1d2c79b938a24b9a9d62563ea155b92b2023-12-24T12:18:26ZengNature PortfolioScientific Reports2045-23222023-12-0113111010.1038/s41598-023-49958-6Simplicial complex entropy for time series analysisLev Guzmán-Vargas0Alvaro Zabaleta-Ortega1Aldo Guzmán-Sáenz2Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico NacionalUnidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico NacionalTopological Data Analysis in Genomics, Thomas J. Watson Research CenterAbstract The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irregularity. However, for some types of dynamics such as stochastic and chaotic, new approaches are required that can provide a better characterization of them. In this paper we present the simplicial complex approximate entropy, which is based on the conditional probability of the occurrence of elements of a simplicial complex. Our results show that this entropy measure provides a wide range of values with details not easily identifiable with standard methods. In particular, we show that our method is able to quantify the irregularity in simulated random sequences and those from low-dimensional chaotic dynamics. Furthermore, it is possible to consistently differentiate cardiac interbeat sequences from healthy subjects and from patients with heart failure, as well as to identify changes between dynamical states of coupled chaotic maps. Our results highlight the importance of the structures revealed by the simplicial complexes, which holds promise for applications of this approach in various contexts.https://doi.org/10.1038/s41598-023-49958-6 |
| spellingShingle | Lev Guzmán-Vargas Alvaro Zabaleta-Ortega Aldo Guzmán-Sáenz Simplicial complex entropy for time series analysis Scientific Reports |
| title | Simplicial complex entropy for time series analysis |
| title_full | Simplicial complex entropy for time series analysis |
| title_fullStr | Simplicial complex entropy for time series analysis |
| title_full_unstemmed | Simplicial complex entropy for time series analysis |
| title_short | Simplicial complex entropy for time series analysis |
| title_sort | simplicial complex entropy for time series analysis |
| url | https://doi.org/10.1038/s41598-023-49958-6 |
| work_keys_str_mv | AT levguzmanvargas simplicialcomplexentropyfortimeseriesanalysis AT alvarozabaletaortega simplicialcomplexentropyfortimeseriesanalysis AT aldoguzmansaenz simplicialcomplexentropyfortimeseriesanalysis |