radius threshold

General discussions and questions about recurrence plot and recurrence network related methods.
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miquel
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Affiliation (Univ., Inst., Dept.): University of Girona
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radius threshold

Post by miquel »

Hi everyone

There is something that I do not have so clear. The value of radius threshold introduced in the RCP toolbox is the percentage of the maximal phase space diameter? The maximum value of the radius threshold is 100 (100 %)?
saravana
Junior
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Re: radius threshold

Post by saravana »

Hey. I'm also looking for the same answer. Did you find out what it is?
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Norbert
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Location: Potsdam Institute for Climate Impact Research, Germany

Re: radius threshold

Post by Norbert »

Maybe let's start with the definition of the RP:
Θ(ε–||x(i) – x(j)||
The threshold ε is just a scalar value. Its choice is somehow related to the value range of the time series or the diameter of the phase space. One way to relate ε to this value range or diameter is to have it as a certain fraction of this value range/diameter. Another way is to select it in terms of the standard deviation of the time series.

But back to the phase space diameter:
The phase space is spanned by the components of the vector x(i). We just need to find the minimal xMin and the maximal component xMax of all x(i) and can then calculate the maximal phase space diameter as |xMaxxMin|. The threshold can then be, e.g., 10% of it, ε = 0.1|xMaxxMin|.
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