radius threshold

General discussions and questions about recurrence plot related methods.

radius threshold

Postby miquel » Thu Sep 11, 2014 08:22

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 %)?
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Re: radius threshold

Postby saravana » Sat Jun 18, 2016 16:58

Hey. I'm also looking for the same answer. Did you find out what it is?
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Re: radius threshold

Postby Norbert » Wed Jul 13, 2016 07:25

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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