Methods for estimating embedding dimension

[Omikron123]

TL;DR Summary

Asking for methods else from False nearest neighbor to estimate embedding dimension.

Say that I want to reconstruct the Lorenz system only using one of the original three variables using Takens theorem. What methods can I use to estimate the embedding dimension else from the False nearest Neighbor method (FNN)? The reason I wonder is because I want to compare the accuracy of FNN with some other methods.

Thanks in advance!

 

[jvicens]

Hi there,

There are a few other methods that you can use to estimate the embedding dimension for the reconstruction of the Lorenz system using Takens theorem. Some common methods include:

1. Mutual Information: This method looks at the relationship between the original variable and its delayed versions. By finding the value of the embedding dimension that maximizes the mutual information, you can estimate the optimal embedding dimension.

2. False nearest neighbors (FNN) with different thresholds: Instead of using just one threshold for FNN, you can try using multiple thresholds and see how the results vary. This can give you a better understanding of the optimal embedding dimension.

3. Correlation dimension: This method looks at the fractal dimension of the reconstructed attractor and can be used to estimate the embedding dimension. It is based on the idea that the embedding dimension should be equal to the correlation dimension.

4. Cao's method: This method uses the idea of phase space reconstruction and evaluates the embedding dimension based on the average mutual information between neighboring points in the reconstructed phase space.

I would also recommend checking out some other research papers on this topic to see if there are any other methods that have been used and compare their results with FNN.

I hope this helps and good luck with your research!