Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab
Using the method or time-delayed embedding, a signal can be embedded into higher-dimensional space in order to study its dynamics. This requires knowledge of two parameters: The delay parameter τ, and the embedding dimension parameter D. Two standard methods to estimate these parameters in one-dimen...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2018-09-01
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| Series: | Frontiers in Psychology |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fpsyg.2018.01679/full |
| _version_ | 1819241421847134208 |
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| author | Sebastian Wallot Sebastian Wallot Dan Mønster Dan Mønster Dan Mønster |
| author_facet | Sebastian Wallot Sebastian Wallot Dan Mønster Dan Mønster Dan Mønster |
| author_sort | Sebastian Wallot |
| collection | DOAJ |
| description | Using the method or time-delayed embedding, a signal can be embedded into higher-dimensional space in order to study its dynamics. This requires knowledge of two parameters: The delay parameter τ, and the embedding dimension parameter D. Two standard methods to estimate these parameters in one-dimensional time series involve the inspection of the Average Mutual Information (AMI) function and the False Nearest Neighbor (FNN) function. In some contexts, however, such as phase-space reconstruction for Multidimensional Recurrence Quantification Analysis (MdRQA), the empirical time series that need to be embedded already possess a dimensionality higher than one. In the current article, we present extensions of the AMI and FNN functions for higher dimensional time series and their application to data from the Lorenz system coded in Matlab. |
| first_indexed | 2024-12-23T14:23:39Z |
| format | Article |
| id | doaj.art-f550c03846834bafa2f80563eb89c410 |
| institution | Directory Open Access Journal |
| issn | 1664-1078 |
| language | English |
| last_indexed | 2024-12-23T14:23:39Z |
| publishDate | 2018-09-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Psychology |
| spelling | doaj.art-f550c03846834bafa2f80563eb89c4102022-12-21T17:43:43ZengFrontiers Media S.A.Frontiers in Psychology1664-10782018-09-01910.3389/fpsyg.2018.01679365315Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in MatlabSebastian Wallot0Sebastian Wallot1Dan Mønster2Dan Mønster3Dan Mønster4Max Planck Institute for Empirical Aesthetics, Frankfurt, GermanyInteracting Minds Centre, School of Culture and Society, Aarhus University, Aarhus, DenmarkInteracting Minds Centre, School of Culture and Society, Aarhus University, Aarhus, DenmarkDepartment of Economics and Business Economics, Aarhus University, Aarhus, DenmarkDepartment of Management, Aarhus University, Aarhus, DenmarkUsing the method or time-delayed embedding, a signal can be embedded into higher-dimensional space in order to study its dynamics. This requires knowledge of two parameters: The delay parameter τ, and the embedding dimension parameter D. Two standard methods to estimate these parameters in one-dimensional time series involve the inspection of the Average Mutual Information (AMI) function and the False Nearest Neighbor (FNN) function. In some contexts, however, such as phase-space reconstruction for Multidimensional Recurrence Quantification Analysis (MdRQA), the empirical time series that need to be embedded already possess a dimensionality higher than one. In the current article, we present extensions of the AMI and FNN functions for higher dimensional time series and their application to data from the Lorenz system coded in Matlab.https://www.frontiersin.org/article/10.3389/fpsyg.2018.01679/fullaverage mutual informationfalse-nearest neighborstime-delayed embeddingMultidimensional Time seriesMultidimensional Recurrence Quantification Analysiscode:Matlab |
| spellingShingle | Sebastian Wallot Sebastian Wallot Dan Mønster Dan Mønster Dan Mønster Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab Frontiers in Psychology average mutual information false-nearest neighbors time-delayed embedding Multidimensional Time series Multidimensional Recurrence Quantification Analysis code:Matlab |
| title | Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab |
| title_full | Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab |
| title_fullStr | Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab |
| title_full_unstemmed | Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab |
| title_short | Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab |
| title_sort | calculation of average mutual information ami and false nearest neighbors fnn for the estimation of embedding parameters of multidimensional time series in matlab |
| topic | average mutual information false-nearest neighbors time-delayed embedding Multidimensional Time series Multidimensional Recurrence Quantification Analysis code:Matlab |
| url | https://www.frontiersin.org/article/10.3389/fpsyg.2018.01679/full |
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