Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology
Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimize the selection of parameters such as emb...
| Main Authors: | , , , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Online Access: | http://purl.org/au-research/grants/arc/IC180100030 http://hdl.handle.net/20.500.11937/96144 |
| _version_ | 1848766101144469504 |
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| author | Tan, E. Algar, S. Corrêa, D. Small, Michael Stemler, T. Walker, D. |
| author_facet | Tan, E. Algar, S. Corrêa, D. Small, Michael Stemler, T. Walker, D. |
| author_sort | Tan, E. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimize the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, Significant Times on Persistent Strands (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic, and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, n-step predictors trained on embeddings constructed with SToPS were found to outperform other embedding methods when predicting fast-slow time series. |
| first_indexed | 2025-11-14T11:45:47Z |
| format | Journal Article |
| id | curtin-20.500.11937-96144 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | eng |
| last_indexed | 2025-11-14T11:45:47Z |
| publishDate | 2023 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-961442024-11-07T01:10:07Z Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology Tan, E. Algar, S. Corrêa, D. Small, Michael Stemler, T. Walker, D. Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimize the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, Significant Times on Persistent Strands (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic, and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, n-step predictors trained on embeddings constructed with SToPS were found to outperform other embedding methods when predicting fast-slow time series. 2023 Journal Article http://hdl.handle.net/20.500.11937/96144 10.1063/5.0137223 eng http://purl.org/au-research/grants/arc/IC180100030 https://creativecommons.org/licenses/by/4.0/ fulltext |
| spellingShingle | Tan, E. Algar, S. Corrêa, D. Small, Michael Stemler, T. Walker, D. Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology |
| title | Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology |
| title_full | Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology |
| title_fullStr | Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology |
| title_full_unstemmed | Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology |
| title_short | Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology |
| title_sort | selecting embedding delays: an overview of embedding techniques and a new method using persistent homology |
| url | http://purl.org/au-research/grants/arc/IC180100030 http://hdl.handle.net/20.500.11937/96144 |