False nearest neighborhood calculation

General discussions and questions about recurrence plot and recurrence network related methods.
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Abin Krishnan
Posts: 3
Joined: Tue Oct 4, 2016 03:06
Affiliation (Univ., Inst., Dept.): Indian Institute of Technology Madras, India
Location: Chennai, Tamil Nadu, India
Research field: Aerospace Engineering

False nearest neighborhood calculation

Post by Abin Krishnan »

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 (for 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.

Thank You.
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