Asymmetry of FAN CRPs

General discussions and questions about recurrence plot and recurrence network related methods.
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Asymmetry of FAN CRPs

Post by Mircea_Stoica »


I just noticed that cross-recurrence plots created with FAN are asymmetric. As in crpxy = crp(x,y,m,t,e,'fan') is different than crpyx = crp(y,x,m,t,e,'fan'). For other methods crpxy is the same as crpyx transposed.

I thought of calculating both crpxy and crpyx with half the desired amount of neighbours (e = 0.05 instead of e = 0.1), adding them together and capping the maximum value at 1. Otherwise we're clearly not getting all the information, right?

And more generally, since for other methods crpxy = crpyx', what would happen if crpxy has horizontal lines but no vertical ones? Many RQA measures would be NaN. But applied to crpyx they wouldn't be because the horizontal lines are now vertical.

Any thoughts?

Mircea Stoica
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Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
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Location: Potsdam Institute for Climate Impact Research, Germany

Re: Asymmetry of FAN CRPs

Post by Norbert »

Hi Mircea,

you are right, when using the fixed number of neighbours (which is the original definition of an RP by Eckmann 1987) the RP is not symmetric. This should be clear because for recurrence pair i and j the k nearest neighbours of the state at time point i are not necessarily the k nearest neighbours of the state at time point j. This you can find in most of the basic literature on RPs.

Summing up the RPxy and RPyx would not make much sense, in my opinion. Why should we do this? If we strictly need a symmetric version then we can use the other options. We should also ask when should we use which option. The FAN approach is nice because it can be used to fix a desired recurrence rate. But this can also be achieved by the RR option (which produces a symmetric RP). The latter one is the standard RP with applying the threshold, but the threshold is preselected in a way that it fixes the recurence rate.

The other question on the effect of the assymetry on vertical lines goes into the same direction. I would strongly suggest to use a recurrence criterion that results in a symmetric RP.

I hope I could clarify your points. Best wishes and good luck for working with this methods.
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