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• W4322732972 abstract "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 optimise 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, {em 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 was found to outperform other embedding methods when predicting fast-slow time series." @default.
• W4322732972 created "2023-03-03" @default.
• W4322732972 creator A5015055144 @default.
• W4322732972 creator A5031723819 @default.
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• W4322732972 creator A5081724915 @default.
• W4322732972 date "2023-03-01" @default.
• W4322732972 modified "2023-10-18" @default.
• W4322732972 title "Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology" @default.
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• W4322732972 doi "https://doi.org/10.1063/5.0137223" @default.
• W4322732972 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/37003815" @default.
• W4322732972 hasPublicationYear "2023" @default.
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