## pss function and other methods to find proper radius for CRQA

Specific discussion regarding applications.
gionaz
Junior
Posts: 2
Joined: Tue Sep 28, 2021 08:16
Affiliation (Univ., Inst., Dept.): University of Ferrara
Location: Città di Ferrara
Research field: Neuroscience

### pss function and other methods to find proper radius for CRQA

Dear all community members,

I'm a clinical psychologist and a beginner in the usage of these measures so I kindly ask for your support. Going through the literature I found different methods to find the proper radius for computing cross recurrence measures. So I tried to compute some of them.

- Firstly, after having found the appropriate time (mi function) and dimension (fnn function), I tried to compute cross recurrence
measures on the whole series, fixing the recurrence rate at 0.02 and 0.05, in the following way:

crqa(timeseries1, timeseries2,m,t,0.02,[],'rr','normalize')
crqa(timeseries1, timeseries2,m,t,0.05,[],'rr','normalize')

- Secondly, I was trying to input as radius the 5% of the maximal phase space diameter computed with pss function. But i'm not sure to have
properly used the function. Following the line of code I used:

mpsd = 0.05*pss(timeseries1,timeseries2,m,t,'euclidean').

- Lastly I tried to find the radius computing iteratively the recurrence rate percentages for different radii searching for a linear scaling
region in the loglog plot (attached an example) of radii (on x-axis) and recurrence rates % (y-axis), but i'm not able to recognize such
linear scaling region in the plot.

example.jpg (79.96 KiB) Viewed 886 times

Any hint or help would be of great support for me.

Thank you very much
Best regards
Norbert
Expert
Posts: 191
Joined: Wed Jan 4, 2006 11:03
Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
Location: Potsdam, Germany
Location: Potsdam Institute for Climate Impact Research, Germany

### Re: pss function and other methods to find proper radius for CRQA

Hi,

I guess with "radius" you mean the recurrence threshold ε?

There are really many ideas out now to identify the "optimal" recurrence threshold ε. However, it really depends on the research question. If you like to compare two time series with CRP, it might be best to use simply the FAN approach and fix the percentage of recurrences (aka recurrence rate):

Code: Select all

crqa(timeseries1, timeseries2,m,t,0.05,[],'fan','normalize')
The approach you are aiming for, using this scaling region, does not make sense, in my opinion (in particular for CRPs).

Best
Norbert
gionaz
Junior
Posts: 2
Joined: Tue Sep 28, 2021 08:16
Affiliation (Univ., Inst., Dept.): University of Ferrara
Location: Città di Ferrara
Research field: Neuroscience

### Re: pss function and other methods to find proper radius for CRQA

Dear Prof. Marwan,

Yes, for radius I meant recurrence threshold ε. As for the research question i'm interested in analyzing the dynamics between two people performing the same movements at the same time. To this regard if I were interested to just the line of synchronization, inputting in the crqad function a lag = 0, what results of the structure should I consider, e.g. .RRp or .RRm?

Coming back to pss function, can we not compute the maximal phase space diameter of the two times series together?

Finally I found the scaling region 'method' in the Chapter 2 "Recurrence Quantification Analysis of Nonlinear Dynamical Systems" by Webber & Zbilut (here the open source link for the web book: https://www.nsf.gov/pubs/2005/nsf05057/nmbs/nmbs.pdf) but probably I misunderstood something.

Thanks again.

Best regards
Norbert
Expert
Posts: 191
Joined: Wed Jan 4, 2006 11:03
Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
Location: Potsdam, Germany
Location: Potsdam Institute for Climate Impact Research, Germany

### Re: pss function and other methods to find proper radius for CRQA

gionaz wrote: Mon Oct 4, 2021 10:29 Yes, for radius I meant recurrence threshold ε. As for the research question i'm interested in analyzing the dynamics between two people performing the same movements at the same time. To this regard if I were interested to just the line of synchronization, inputting in the crqad function a lag = 0, what results of the structure should I consider, e.g. .RRp or .RRm?
RRp is provides the RR for the "normal" embedding of the time series, like considering positive correlations. But sometimes, we might be more interested in anticorrelated behaviour. This would require to "flip" the second phase space trajectory. This is done and measured by RRm. Thus, if you are interested in positvely correlated synchronisation, use RRp, if you are interested in asynchronuous behaviour (anticorrelated sync), use RRm.
gionaz wrote: Mon Oct 4, 2021 10:29 Coming back to pss function, can we not compute the maximal phase space diameter of the two times series together?
This could surely be done, but it is not implemented in the CRP Toolbox.
gionaz wrote: Mon Oct 4, 2021 10:29 Finally I found the scaling region 'method' in the Chapter 2 "Recurrence Quantification Analysis of Nonlinear Dynamical Systems" by Webber & Zbilut (here the open source link for the web book: https://www.nsf.gov/pubs/2005/nsf05057/nmbs/nmbs.pdf) but probably I misunderstood something.
This work is rather old and several new approaches have been suggested and discussed since then. The selection of the threshold really depends on the research question. For your situation, the FAN approach seems to fit best.