by 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 |xMax – xMin|. The threshold can then be, e.g., 10% of it, ε = 0.1|xMax – xMin|.