Recurrence Plot for binary variable?

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 Research field: Neuroscience/Psychology
Recurrence Plot for binary variable?
I was wondering, if it is possible to compute the RP also for a binary variable which alternates between 0 and 1? I'm really not sure, if the phase space reconstruction makes sense in such a case
 Norbert
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 Joined: Wed Jan 4, 2006 11:03
 Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
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 Location: Potsdam Institute for Climate Impact Research, Germany
Re: Recurrence Plot for binary variable?
Yes, this is possible. This is also called "recurrence on a nominal scale" or "symbolic recurrences". There are several studies already using this approach. The difference to the standard recurrence approach is that instead of a neighbourhood of some size ε a recurrence can now be defined by the exact match of x(i) and x(j). Embedding of such binary or symbolic series mean that we consider words of length m instead of reconstructing an mdimension phase space.
Here is some literature related to this variant of recurrence:
Here is some literature related to this variant of recurrence:
 C. Bandt, A. Groth, N. Marwan, M. C. Romano, M. Thiel, M. Rosenblum, J. Kurths: Analysis of Bivariate Coupling by Means of Recurrence, In: Mathematical Methods in Time Series Analysis and Digital Image Processing, Eds.: R. Dahlhaus and J. Kurths and P. Maas and J. Timmer, Springer, Berlin, Heidelberg, ISBN: 9783540756316, 153–182 (2008). DOI:10.1007/9783540756323_5
 R. V. Donner, U. Hinrichs, B. ScholzReiter: Symbolic recurrence plots: A new quantitative, European Physical Journal – Special Topics, 164(1), 85–104 (2008). DOI:10.1140/epjst/e2008008362
 P. Faure, A. Lesne: Recurrence plots for symbolic sequences, International Journal of Bifurcation and Chaos, 20(6), 1731–1749 (2010). DOI:10.1142/S0218127410026794
 P. beim Graben, A. Hutt: Detecting Recurrence Domains of Dynamical Systems by Symbolic Dynamics, Physical Review Letters, 110(15), 154101 (2013). DOI:10.1103/PhysRevLett.110.154101

 Senior
 Posts: 16
 Joined: Wed Feb 19, 2014 09:53
 Affiliation (Univ., Inst., Dept.): Univ. Bochum
 Location: Bochum, Germany
 Research field: Neuroscience/Psychology
Re: Recurrence Plot for binary variable?
Thank you!
Is this approach implemented in the matlab software (crqa), i.e. when I just compute the RR,LAM,DET asf. for a binary variable as normally done with my continuous variable?
Is this approach implemented in the matlab software (crqa), i.e. when I just compute the RR,LAM,DET asf. for a binary variable as normally done with my continuous variable?
 Norbert
 Expert
 Posts: 183
 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: Recurrence Plot for binary variable?
There is nothing to be implemented further. If you have only a binary time series, you just need to ensure that your threshold is smaller than 1. This will give the same results as using the identity relationship (i.e., threshold = 0).

 Senior
 Posts: 16
 Joined: Wed Feb 19, 2014 09:53
 Affiliation (Univ., Inst., Dept.): Univ. Bochum
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 Research field: Neuroscience/Psychology
Re: Recurrence Plot for binary variable?
Ok..thanks..just to be sure. I attached a screenshot of an analysis with a binary timeseries. Here, the treshold is 0.2 and I used euclidian norm. Is this correct? I assume I can interpret the values of RR, DET asf. in the same way as with a continuous variable?
 Attachments

 example.png (38.94 KiB) Viewed 10826 times
 Norbert
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 Posts: 183
 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: Recurrence Plot for binary variable?
I would suggest to use the option "nonorm" to avoid the centering and standardisation of the data.
When using embedding dimension of 1 the results should be the same for Euclidean and Maximum norm.
The interpretation is similar but be aware that there is no phase space trajectory. We could also consider a phase space that is highly discretised (due to the binary time series). The interpretation depends, of course, strongly on the kind of data and the considered system.
When using embedding dimension of 1 the results should be the same for Euclidean and Maximum norm.
The interpretation is similar but be aware that there is no phase space trajectory. We could also consider a phase space that is highly discretised (due to the binary time series). The interpretation depends, of course, strongly on the kind of data and the considered system.

 Senior
 Posts: 16
 Joined: Wed Feb 19, 2014 09:53
 Affiliation (Univ., Inst., Dept.): Univ. Bochum
 Location: Bochum, Germany
 Research field: Neuroscience/Psychology
Re: Recurrence Plot for binary variable?
I see . Thanks a lot!