## Calculation of embedding dimension

General discussions and questions about recurrence plot related methods.

### Calculation of embedding dimension

Hi,

I am trying to plot a phase portrait of a pressure signal (5000 data points obtained at a sampling frequency of 20 kHz) using the CRP toolbox. I have a few doubts regarding the input parameters to find the false nearest neighborhood.

1. What is the meaning of falseness and neighborhood that appear in the GUI? The manual talks about neighborhood criteria and size of the neighborhood. Do these refer to falseness and neighborhood respectively?

2. The embedding dimension is very sensitive to falseness. It reduces from 23 to 9 for an increase in the value of falseness from 1 to 10 keeping other parameters constant (delay (4), size of the neighborhood (infinity), no. of random samples (5000) and Euclidean norm). But, the embedding dimension is not at all sensitive to size of the neighborhood. Its value remains as 6 even when the size of the neighborhood is changed from 10 to 10,000,000. How to choose the value of falseness and size of neighborhood?

3. After reading the paper “Determining embedding dimension for phase space reconstruction using a geometrical construction” by Matthew Kennel et al., I understand that there are 5 input parameters- (1) r = rth nearest neighbor, (2) Rtol = threshold (for criteria I), (3) T = time delay, (4) RA = size of the attractor and (5) Atol = tolerance (criteria II ). Are falseness and neighborhood related to any of these parameters? Are the values of Rtol and Atol already fixed in the toolbox?

Any help in this regard would be highly appreciable. I know you are busy there with your research. Hope you can take some time for this.
Abin Krishnan
Junior

Posts: 3
Joined: Tue Oct 4, 2016 03:06

### Re: Calculation of embedding dimension

Hi,
Now I understand that the falseness in the GUI corresponds to the threshold 'R_tol', as mentioned in the first criteria in the paper “Determining embedding dimension for phase space reconstruction using a geometrical construction” by Matthew Kennel et al.

Thank You.
Abin Krishnan
Junior

Posts: 3
Joined: Tue Oct 4, 2016 03:06