optimizeParam: Estimate optimal delay, embedding dimension and radius for...

In crqa: Unidimensional and Multidimensional Methods for Recurrence Quantification Analysis

Estimate optimal delay, embedding dimension and radius for continuous time-series data

Description

Iterative procedure to examine the values of delay, embedding dimension and radius to compute recurrence plots of one, two, or more time-series.

Usage

optimizeParam(ts1, ts2, par, min.rec, max.rec)

Arguments

ts1	First time-series
ts2	Second time-series
par	A list of parameters needed for the optimization, refer to the Details section.
min.rec	The minimum value of recurrence accepted. Default = 2
max.rec	The maximum value of recurrence accepted. Default = 5

Details

The optimization can be applied both to uni-dimensional time-series (method = crqa), or multi-dimensional (method = mdcrqa)

The procedure is identical in both cases:

1) Identify a delay that accommodates both time-series by finding the local minimum where mutual information between them drops, and starts to level off. When one ts has a considerably longer delay indicated than the another, the function selects the longer delay of the two to ensure that new information is gained for both. When the delays are close to each other, the function computes the mean of the two delays.

2) Determine embedding dimensions by using false nearest neighbors and checking when it bottoms out (i.e., there is no gain in adding more dimensions). If the embedding dimension for the two ts are different the algorithm selects the higher embedding dimension of the two to make sure that both time series are sufficiently unfolded.

3) Determine radius yielding a recurrence rate between 2-5 To do so, we first determine a starting radius that yields approximately 25 We generate a sampled sequence of equally spaced possible radi from such radius till 0, using as unit for the sequence step, the standard deviation of the distance matrix divided by a scaling parameter (radiusspan). The larger this parameter, the finer the unit.

For uni-dimensional time-series, the user has to decide how to choose the value of average mutual information (i.e., typeami = mindip, the lag at which minimal information is observed, or typeami = maxlag, the maximum lag at which minimal information is observed) and the relative percentage of information gained in FNN, relative to the first embedding dimension, when higher embeddings are considered (i.e., fnnpercent). Then, as crqa is integrated in the optimizeParam to estimate the radius, most of the arguments are the same (e.g., mindiagline or tw).

For multidimensional series, the user needs to specify the right RQA method (i.e., method = "mdcrqa"). Then, for the estimation of the delay via AMI: (1) nbins the number of bins to compute the two-dimensional histogram of the original and delayed time series and (2) the criterion to select the delay (firstBelow to use the lowest delay at which the AMI function drops below the value set by the threshold argument, and localMin to use the position of the first local AMI minimum). The estimation of the embedding dimensions instead needs the following arguments: (1) maxEmb, which is the maximum number of embedding dimensions considered, (2) noSamples, which is the number of randomly drawn coordinates from phase-space used to estimate the percentage of false-nearest neighbors, (3) Rtol, which is the first distance criterion for separating false neighbors, and (4) Atol, which is the second distance criterion for separating false neighbors. The radius is estimated as before.

Value

It returns a list with the following arguments:

radius	The optimal radius value found
emddim	Number of embedding dimensions
delay	The lag parameter.

Note

As optimizeParam uses crqa to estimate the parameters: the additional arguments normalize, rescale, mindiagline, minvertline, whiteline, recpt should be supplied in the par list. Set up relatively large radiusspan (e.g. 100), for a decent coverage of radius values.

Author(s)

Moreno I. Coco ([e-mail]), James A. Dixon ([e-mail]) Sebastian Wallot, Max Planck Insitute for Empirical Aesthetics Dan Moenster, Aarhus University

References

Marwan, N., Carmen Romano, M., Thiel, M., and Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438(5), 237-329.

See Also

crqa, wincrqa

Examples

data(crqa) ## load the data

handset = handmovement[1:300, ] ## take less points

P1 = cbind(handset$P1_TT_d, handset$P1_TT_n) 
P2 = cbind(handset$P2_TT_d, handset$P2_TT_n)

par = list(method = "mdcrqa", metric = "euclidean", maxlag =  20, 
           radiusspan = 100, radiussample = 40, normalize = 0, 
           rescale = 4, mindiagline = 10, minvertline = 10, tw = 0, 
           whiteline = FALSE, recpt = FALSE, side = "both", 
           datatype = "continuous", fnnpercent  = NA,  
           typeami = NA, nbins  = 50, criterion = "firstBelow",
           threshold = 1, maxEmb = 20, numSamples = 500, 
           Rtol = 10, Atol = 2)

results = optimizeParam(P1, P2, par, min.rec = 2, max.rec = 5)
print(unlist(results))
           

crqa documentation built on June 22, 2024, 9:17 a.m.