The RSA toolbox presents a time series segmentation technique for the detection of metastable states (aka "recurrence domains").
There are essentially two ways to apply:
In the file lorenzepl.m
(lines 34–41), RSA is applied to a single time series (from the Lorenz attractor).
% carry out RSA!
% recommended 1st attempt
% for probing ball size sampling
s = rsa(y, 100, 100, 'show', 1);
This invokes the RSA for data set y
, with 100 threshold samples of the full range of state space (100%). The 'show'
option plots the utility function based on a Markov chain optimization procedure. It is recommended to change the second parameter first, e.g., replacing 100 to 20 (i.e., 20% of data range), through
s = rsa(y, 100, 20, 'show', 1);
In this way, one should be able to reduce redundant threshold values. After this, it is recommended to increase the threshold sampling, e.g.,
s = rsa(y, 500, 20);
Setting
ds = 500;
pr = 20;
leads then to the default Markov chain optimization
s = rsa(y, ds, pr); % default: Markov optimization
Another possibility is entropy optimization:
s = rsa(y, ds, pr, 'optim', 'uniform'); % entropy optimization
One can also change the norm from Euclidian (default) to, e.g., cosine similarity:
s = rsa(y, ds, pr, 'norm', 'cos'); % default Markov + cosine similarity
Additionally, in the file ensemblelorenzepl.m
(lines 44–50), RSA can be applied to an ensemble of time series (e.g., obtained from cutting a long series into short segments, or from multiple realizations of measurements), with optional Hausdorff clustering in state space.
% carry out RSA!
s = ensemblersa(y, datasamp, prorange); % default
% s = ensemblersa(y, datasamp, prorange, 'cluster', thres);
% including Hausdorff clustering
% additional Hausdorff clustering
sc = hdcluster(y, s, thres);
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beim Graben, P. & Hutt, A. (2013). Detecting recurrence domains of dynamical systems by symbolic dynamics. Physical Review Letters, 110, 154101.
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beim Graben, P. & Hutt, A. (2015). Detecting event-related recurrences by symbolic analysis: Applications to human language processing. Philosophical Transactions of the Royal Society London, A373, 201400897.
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beim Graben, P., Sellers, K. K., Fröhlich, F. & Hutt, A. (2016). Optimal estimation of recurrence structures from time series. EPL, 114, 38003
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Tosic, T., Sellers, K. K., Fröhlich, F., Fedotenkova, M., beim Graben, P., & Hutt, A. (2016). Statistical frequency-dependent analysis of trial-to-trial variability in single time series by recurrence plots. Frontiers in Systems Neuroscience, 9, 184.
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Hutt, A. & beim Graben, P. (2017). Sequences by metastable attractors: interweaving dynamical systems and experimental data. Frontiers in Applied Mathematics and Statistics, 3, 11.
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beim Graben, P., Jimenez-Marin, A., Diez, I., Cortes, J. M., Desroches, M., & Rodrigues, S. (2019). Metastable brain resting state dynamics. Frontiers in Computational Neuroscience, 13, 62.
(C) Peter beim Graben, BCCN 2023