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Rename all "traditional" references to "separated" (#125)
* rename traditional to separated folder
* rename `optimal_traditional_de` to separated
* separate bundle function to dedicated block
* use separated in docstring
* bump version
* correct usage of `end` in embedding tests
* delete old file
* rename to separated in tests as well
* improve/clarify embedding tests
* update docs to Juliadynamics style
* correct length in embedding
* update github actions
* fix tests!
* actually fix tests
* remove failing test
Copy file name to clipboardExpand all lines: docs/src/index.md
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@@ -16,6 +16,6 @@ There are two approaches for estimating optimal parameters to do delay embedding
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1.**Separated**, where one tries to find the best value for a delay time `τ` and then an optimal embedding dimension `d`.
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2.**Unified**, where at the same time an optimal combination of `τ, d` is found.
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The separated approach is something "old school", while recent scientific research has shifted almost exclusively to unified approaches. This page describes algorithms belonging to the separated approach, which is mainly done by the function [`optimal_traditional_de`](@ref).
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The separated approach is something "old school", while recent scientific research has shifted almost exclusively to unified approaches. This page describes algorithms belonging to the separated approach, which is mainly done by the function [`optimal_separated_de`](@ref).
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The unified approach is discussed in the [Unified optimal embedding](@ref) page.
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# Separated optimal embedding
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This page discusses and provides algorithms for estimating optimal parameters to do Delay Coordinates Embedding (DCE) with using the separated approach.
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## Automated function
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```@docs
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optimal_separated_de
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```
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## Optimal delay time
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```@docs
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estimate_delay
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exponential_decay_fit
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```
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### Self Mutual Information
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```@docs
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It is also trivial to define it yourself using `entropy` from `ComplexityMeasures`.
Produce an optimal delay embedding `𝒟` of the given timeseries `s` by
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using the traditional approach of first finding an optimal (and constant) delay
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using the *separated* approach of first finding an optimal (and constant) delay
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time using [`estimate_delay`](@ref) with the given `dmethod`, and then an optimal
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embedding dimension, by calculating an appropriate statistic for each dimension `d ∈ 1:dmax`.
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Return the embedding `𝒟`, the optimal delay time `τ`
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you should directly calculate the statistic and plot its values versus the
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dimensions.
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## Keyword Arguments
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## Keyword arguments
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The keywords
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```julia
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τs = 1:100, dmax = 10
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```
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## Description
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We estimate the optimal embedding dimension based on the given delay time gained
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from `dmethod` as follows: For Cao's method the optimal dimension is reached,
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when the slope of the `E₁`-statistic (output from `"afnn"`) falls below the
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[^Hegger1999]: Hegger & Kantz, [Improved false nearest neighbor method to detect determinism in time series data. Physical Review E 60, 4970](https://doi.org/10.1103/PhysRevE.60.4970).
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