Unidimensional and Multidimensional Methods for Recurrence Quantification Analysis

Description

Auto, Cross and Multi-dimensional recurrence quantification analysis. Different methods for computing recurrence, cross vs. multidimensional or profile iti.e., only looking at the diagonal recurrent points, as well as functions for optimization and plotting are proposed. in-depth measures of the whole cross-recurrence plot, Please refer to by Coco and Dale (2014) <doi:10.3389/fpsyg.2014.00510> and Wallot (2018) <doi: 10.1080/00273171.2018.1512846> for further details about the method.

Details

crqa: Core recurrence function, which examines recurrent structures of a single rqa, two crqa, or multidimensional time-series mdcrqa, which are time-delayed and embedded in higher dimensional space. The approach compares the phase space trajectories of the time-series in the same phase-space when delays are introduced. A distance matrix between the time-series, delayed and embedded is calculated. Several measures representative of the underlying dynamics of the system are extracted.

drpfromts: Method to explore the diagonal profile of the recurrence plot (Auto, Cross, or Multi-dimensional). It returns the recurrence for different delays, the maximal recurrence observed and the delay at which it occurred.

lorenzattractor: An implementation of the Lorenz dynamical system, which describes the motion of a possible particle, which will neither converge to a steady state, nor diverge to infinity; but rather stay in a bounded but 'chaotically' defined region, i.e., an attractor.

mdDelay:Estimates time delay for embedding of a multi-dimensional dataset.

mdFnn: Computes the percentage of false nearest neighbors for multidimensional time series as a function of embedding dimension.

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

piecewiseRQA: This is a convenience function which breaks down the computation of large recurrence plots into a collection of smaller recurrence plots. It can ease speed and memory issues if an appropriate size for the block is found.

plotRP: A convenience function to plot the RP matrix returned by the crqa.

simts: A simple algorithm for producing a time-series that drives a second time-series using parameters, which change independent and conditional probability of an event to occur.

wincrqa: A recurrence plot is computed in overlapping windows of a certain size for a number of delays smaller than the size of the window; and measures of it extracted.

windowdrp: A recurrence plot is computed in overlapping windows of a specified size for a number of delays smaller than the size of the window. In every window, the recurrence value for the different delays is calculated. A mean is then taken across the delays to obtain a recurrence value in that particular window.

Author(s)

Moreno I. Coco moreno.cocoi@gmail.com Dan Monster danm@econ.au.dk Giuseppe Leonardi g.leonardi@vizja.pl Rick Dale rdale@ucla.edu Sebastian Wallot sebastian.wallot@ae.mpg.de

References

Webber Jr, C. L., and Zbilut, J. P. (2005). Recurrence quantification analysis of nonlinear dynamical systems. Tutorials in contemporary nonlinear methods for the behavioral sciences, 26-94.

Marwan, N., and Kurths, J. Nonlinear analysis of bivariate data with cross recurrence plots. Physics Letters A 302.5 (2002): 299-307.

Coco, M. I., Monster, D., Leonardi, G., Dale, R., & Wallot, S. (2021). Unidimensional and Multidimensional Methods for Recurrence Quantification Analysis with crqa. R Journal, 13(1).

Examples

# use the available data
data(crqa) 

listener = eyemovement$listener
narrator = eyemovement$narrator

delay = 1; embed = 1; rescale = 0; radius = .1;
normalize = 0; mindiagline = 2; minvertline = 2;
tw = 0; whiteline = FALSE; recpt = FALSE; side = "both"
method = 'crqa'; metric = 'euclidean';  
datatype = "categorical"

ans = crqa(narrator, listener, delay, embed, rescale, radius, normalize, 
           mindiagline, minvertline, tw, whiteline, recpt, side, method, metric, 
           datatype)

print(ans[1:10]) ## last argument of list is the recurrence plot

Eye-movement categorical time-series

Description

Three time series (1250 observations) organised as columns and simulating data from: a periodical sine wave, one of the dimensions of the Lorenz attractor and a white noise signal.

Usage

Figure_1

Format

A data frame with 1250 rows and 3 columns:

sinus

A periodical sine wave

lorenz

One dimension of a Lorenz attractor

wnoise

White noise

A unidimensional sinusoidal time series

Description

A unidimensional sinusoidal time series

Usage

Figure_2

Format

A data frame with 45 rows and 1 column:

V1

A unidimensional sinusoidal time series

Simulated time series of the three dimensions from the Lorenz system

Description

Simulated time series of the three dimensions from the Lorenz system

Usage

Figure_3

Format

A data frame with 2048 rows and 3 columns:

V1

First dimension of the Lorenz system

V2

Second dimension of the Lorenz system

V3

Third dimension of the Lorenz system

Figure_6

Description

Speed (time in seconds) and memory (peak RAM in MB) performance of crqa() and piecewiseRQA() for simulated data of increasing size (from 3000 to 7000 data points), compared in blocks of different sizes (from 1000 to 6500 in increments of 500)

Usage

Figure_6

Format

A data frame with 28 rows and 2 variables:

speed

The time in seconds to perform a crqa() analysis

memory

The peak MB occupied in the RAM to perform a crqa() analysis

typeRQA

Whether the analysis contained all data points (full) or was computed piecewise (piece)

datapoint

The number of datapoints

blocksize

The dimension of the block

Auto, cross and multidimensional recurrence measures of one, two or multiple time-series, time-delayed and embedded in higher dimensional space

Description

Core recurrence function, which examines recurrent structures of a single (rqa), two (crqa), or multidimensional time-series (mdcrqa), which are time-delayed and embedded in higher dimensional space. The approach compares the phase space trajectories of the time-series in the same phase-space when delays are introduced. A distance matrix between the time-series, delayed and embedded is calculated. Several measures representative of the underlying dynamics of the system are extracted (explained below).

Usage

crqa(ts1, ts2, delay, embed, rescale, radius, normalize,
mindiagline, minvertline, tw, whiteline, recpt, side, method,
metric, datatype)

Arguments

Details

We recommend setting whiteline = FALSE, as the current version of the library does not make use of such information to extract recurrence measures.

Value

If a recurrence plot (RP) can be calculated and hence recurrence observed the function will returna a list with different measures extracted. Otherwise, the values for the output arguments will be either 0 or NA.

Note

Original bits of this code were translated from a Matlab version provided by Rick Dale, and created during the Non-Linear Methods for Psychological Science summer school held at the University of Cincinnati in 2012. The multi-dimensional method for the crqa function has been written together with Sebastian Wallot (sebastian.wallot at aesthetics.mpg.de )

Author(s)

Moreno I. Coco (moreno.cocoi@gmail.com)

References

Coco, M. I., and Dale, R. (2014). Cross-recurrence quantification analysis of categorical and continuous time series: an R package. Frontiers in psychology, 5, 510.

Wallot, S. (2018). Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) a method for quantifying correlation between multivariate time-series. Multivariate behavioral research, 1-19

See Also

spdiags, simts

Examples

# use the available data
data(crqa) 

listener = eyemovement$listener
narrator = eyemovement$narrator

delay = 1; embed = 1; rescale = 0; radius = .1;
normalize = 0; mindiagline = 2; minvertline = 2;
tw = 0; whiteline = FALSE; recpt = FALSE; side = "both"
method = 'crqa'; metric = 'euclidean';  
datatype = "categorical"

ans = crqa(narrator, listener, delay, embed, rescale, radius, normalize, 
           mindiagline, minvertline, tw, whiteline, recpt, side, method,
           metric, datatype)

print(ans[1:11]) ## last argument of list is the recurrence plot

Diagonal recurrence profile

Description

Method to explore the diagonal profile of the recurrence plot (Auto, Cross, or Multi-dimensional). It returns the recurrence for different delays, the maximal recurrence observed and the delay at which it occurred.

Usage

 drpfromts(ts1, ts2, windowsize, radius,
delay, embed, rescale, normalize, mindiagline, minvertline, tw,
whiteline, recpt, side, method, metric, datatype) 

Arguments

Value

A list with the following arguments:

Author(s)

Moreno I. Coco (moreno.cocoi@gmail.com)

See Also

windowdrp

Examples

# use the available data
data(crqa) 

listener = eyemovement$listener
narrator = eyemovement$narrator

res = drpfromts(narrator, listener, windowsize = 100,
                 radius = 0.001, delay = 1, embed = 1, rescale = 0,
                 normalize = 0, mindiagline = 2, minvertline = 2,
                 tw = 0, whiteline = FALSE, recpt = FALSE, 
                 side = 'both', method = 'crqa', 
                 metric = 'euclidean', datatype = 'continuous')

 profile = res$profile

 plot(seq(1,length(profile),1), profile, type = "l", lwd = 5,
     xaxt = "n", xlab = "Lag", ylab = "Recurrence")

Eye-movement categorical time-series

Description

A two-columns dataset of eye-movement fixation scan-pattern, which are temporal sequences of fixated objects.

Usage

eyemovement

Format

A data frame with 1000 rows and 2 variables:

listener

the listener time series

narrator

the narrator time series

References

Richardson, D. C., and Dale, R. (2005). Looking to understand: The coupling between speakers and listeners eye movements and its relationship to discourse comprehension. Cognitive Science, 29, 39-54.

Continuous series of hand movements

Description

Hand-movement velocity profiles of two participants (P1 and P2) for the dominant (d) and non-dominant (n) hand.

Usage

handmovement

Format

A dataframe of 5799 observations.

P1_TT_d

Participant 1 dominant hand

P1_TT_n

Participant 1 non-dominant hand

P2_TT_d

Participant 2 dominant hand

P2_TT_n

Participant 2 non-dominant

References

Wallot, S., Mitkidis, P., McGraw, J. J. and Roepstorff, A. (2016). Beyond synchrony: joint action in a complex production task reveals beneficial effects of decreased interpersonal synchrony. PloS one, 11(12), e0168306.

Simulate the Lorenz Attractor

Description

An implementation of the Lorenz dynamical system, which describes the motion of a possible particle, which will neither converge to a steady state, nor diverge to infinity; but rather stay in a bounded but 'chaotically' defined region, i.e., an attractor.

Usage

lorenzattractor(numsteps, dt, sigma, r, b)

Arguments

Value

It returns a matrix with the 3 dimensions of the Lorenz

Author(s)

Moreno I. Coco (moreno.cocoi@gmail.com)

References

Lorenz, Edward Norton (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20(2) 130-141.

Examples

## initialize the parameters
numsteps = 2 ^ 11; dt = .01; sigma = 10; r = 28; b = 8/3;

res = lorenzattractor(numsteps, dt, sigma, r, b)

Find optimal delay from a multi-dimensional dataset.

Description

Estimates time delay for embedding of a multi-dimensional dataset.

Usage

 mdDelay(data, nbins, maxlag, criterion, threshold) 

Arguments

Value

It returns the recurrence phi-coefficient profile for state k for all delays considered

Author(s)

Sebastian Wallot, Max Planck Insitute for Empirical Aesthetics Dan Moenster, Aarhus University, Moreno I. Coco, University of East London

References

Wallot, S., and Moenster, D. (2018). Calculation of average mutual information (AMI) and false-nearest neighbors (FNN) for the estimation of embedding parameters of multidimensional time -series in Matlab. Front. Psychol. - Quantitative Psychology and Measurement

See Also

mdFnn, optimizeParam

Examples

nbins = 10; maxlag = 10; criterion = "firstBelow"; threshold = exp(-1)

data(crqa) ## load the data

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

mdDelay(handset, nbins, maxlag, criterion, threshold)

Find optimal embedding dimension of a multi-dimensional dataset.

Description

Computes the percentage of false nearest neighbors for multidimensional time series as a function of embedding dimension.

Usage

 mdFnn(data, tau, maxEmb, numSamples, Rtol, Atol) 

Arguments

Value

It returns the percentage of false neighbors for each embedding.

Author(s)

Sebastian Wallot, Max Planck Insitute for Empirical Aesthetics Dan Moenster, Aarhus University, Moreno I. Coco, University of East London

References

Kennel, M. B., Brown, R., & Abarbanel, H. D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical review A, 45, 3403. Wallot, S., and Moenster, D. (2018). Calculation of average mutual information (AMI) and false-nearest neighbors (FNN) for the estimation of embedding parameters of multidimensional time-series in Matlab. Front. Psychol. - Quantitative Psychology and Measurement

See Also

mdDelay, optimizeParam

Examples

tau = 1; maxEmb = 10; numSamples = 500; Rtol = 10; Atol = 2

data(crqa) ## load the data

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

mdFnn(handset, tau, maxEmb, numSamples, Rtol, Atol)

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

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:

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 (moreno.cocoi@gmail.com), James A. Dixon (james.dixon@uconn.edu) 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))
           

Compute recurrence plots for long time-series data series using a block (piece-wise) method.

Description

This is a convenience function which breaks down the computation of large recurrence plots into a collection of smaller recurrence plots. It can ease speed and memory issues if an appropriate size for the block is found.

Usage

piecewiseRQA(ts1, ts2, blockSize, delay, embed, rescale, radius,
normalize, mindiagline, minvertline, tw, whiteline, recpt, side, 
method, metric, datatype, typeRQA, windowsize)

Arguments

Details

It is important to estimate the size of the block that may maximize the speed of the computation. We suggest to monitor how speed and memory usage changes as a result of increasing the time-series and the block size. We also recommend setting whiteline = FALSE, as the current version of the library does not make use of such information to extract measures of recurrence.

Value

If an RP can be calculated and recurrence is found, the piecewiseRQA will return exactly the same measures as crqa() if the typeRQA is set to 'full' and drpdfromts() if the typeRQA is set to 'diagonal'. Please refer to the help file for those two functions for details about the measures.

Author(s)

Moreno I. Coco (moreno.cocoi@gmail.com) based on Matlab code by Sebastian Wallot

See Also

crqa, spdiags, simts

Examples

## Uncomment and run locally

## generate some data using pracma

# ts1 = seq(0.1, 200, .1)
# ts1 = sin(ts1) + linspace(0, 1,length(ts1));

# ts2 = ts1

## initialize the parameters
# blockSize = 100; delay  = 15; embed  = 2; rescale = 0; radius = 0.5;
# normalize = 0; mindiagline = 2; minvertline = 2;
# tw = 1; whiteline = FALSE; recpt = FALSE; side = 'both'
# method = "crqa"; metric = 'euclidean'; datatype = "continuous"
# typeRQA = "full"; windowsize = NA

# pieceRP = piecewiseRQA(ts1, ts2, blockSize, delay, embed, rescale,
#                       radius, normalize, mindiagline, minvertline,
#                       tw, whiteline, recpt, side,
#                       method, metric, datatype, typeRQA, 
#                       windowsize)
                       
# print(unlist(pieceRP[1:10]))
                       

Plot a recurrence matrix

Description

Given a recurrence plot object (RP) returned from the function crqa(), visualize it.

Usage

plot_rp(rp_matrix,
        title = "",
        xlabel = "Time",
        ylabel = "Time",
        pcolour = "black",
        geom = c("tile", "point", "void"),
        flip_y = FALSE)

Arguments

Details

The argument geom is a character denoting what type of ggplot2 geom is used to plot the points in the recurrence plot. Allowed values are "tile", "point" and "void". The latter produces an empty plot, so the user is required to add their own geom to the output. See example below.

Value

A ggplot2 plot.

Author(s)

Mønster, D. danm@econ.au.dk

See Also

This plotting solution as substituted what was previously plotRP() available till version crqa.2.0.5

Examples

# Here is a very short example based on these two time series
ts_1 <-  c(0, 0, 1, 1, 0, 0, 2, 2, 1, 1)
ts_2 <-  c(1, 1, 2, 2, 0, 0, 1, 2, 2, 1)

# Create the cross recurrence matrix
short_rec <-  crqa(ts_1, ts_2, 
                   delay = 1, embed = 1, radius = 0.001,
                   rescale = 1, method = "crqa")

# Extract the cross recurrence matrix
small_rp <-  short_rec$RP

# Make a cross recurrence plot with blue tiles
plot_rp(small_rp, pcolour  = "blue", geom = "tile")

# Make a cross recurrenbce plot with blue points
plot_rp(small_rp, pcolour  = "blue", geom = "point")

## Uncomment below if you want to have more example. Not runnable because
## of CRAN, globally unavailable function plus timing constraint to check vignette.

# Neither of the two plots above may be suitable
# Using geom = "void" we can add a custumized geom, here blue tiles
# that are smaller than the default width and height
# plot_rp(small_rp, geom = "void") +
#  geom_tile(fill = "blue", height = 0.75, width = 0.75)

# Another custom geom uses tiles with a border colour
# plot_rp(small_rp, geom = "void") +
#  geom_tile(fill = "blue", colour = "pink", linewidth = 1)

# Use the eyemovement dataset to create a cross-recurrence plot
# large_crqa <- crqa(eyemovement$narrator, eyemovement$listener,
#                delay = 1, embed = 1, radius = 0.001,
#                method = "crqa", metric = "euclidean", datatype = "continuous")

# Extract the recurrence matrix from the result
# large_rp <- large_crqa$RP

# Create a recurrence plot using defaults
# plot_rp(large_rp)

# The same recurrence plot with flipped y axis and using geom_point()
# plot_rp(large_rp, flip_y = TRUE, geom = "point", title = "Flipped y axis") 

# Add axes labels, a title and extra plot elements
# Note that we can add to the output, here added the line of synchonization
# using ggplot2's geom_abline() function.
# plot_rp(large_rp, 
#        xlabel = "Narrator",
#        ylabel = "Listener",
#        title = "Coloured tiles with line of synchronization",
#        pcolour = "blue") +
#  geom_abline(intercept = 0, slope = 1)

Simulate dichotomous binary time-series

Description

A simple algorithm for producing a time-series that drives a second time-series (1 for event occurrence; 0 otherwise) using parameters, which change independent and conditional probability of an event to occur.

Usage

 simts(BL1, BL2, BLR1, BLR2, BL2C1, tsL) 

Arguments

Value

A matrix with two-rows, where the first row is the 'driving' time-series and the second row is the second time-series. The columns are the number of simulated points as selected by the argument tsL.

Author(s)

Rick Dale and Moreno I. Coco (moreno.cocoi@gmail.com)

Examples

## set up parameters

BL1 = .08; BL2 = .05; BLR1 = .5; BLR2 = .5;
BL2C1 = .33; tsL = 100

ts = simts(BL1, BL2, BLR1, BLR2, BL2C1, tsL)

Extract diagonal matrices

Description

Extracts all nonzero diagonals from the m-by-n matrix A. B is a min(m,n)-by-p matrix whose columns are the p nonzero diagonals of A.

Usage

 spdiags(A) 

Arguments

Details

Compared to the original Matlab implementation: 1) it does not handle the case with more than one input, and 2) (m > n) matrices give the B matrix columns in a different order, but the d vector of indices will also be changed accordingly, so the set of columns is OK, just ordered differently

Value

Note

For computational efficiency spdiags is actually computed using a Fortan implementation (jspd.f)

Author(s)

John C. Nash (nashjc@uottawa.ca)

Examples

dta <- c(0, 5, 0, 10, 0, 0, 0, 0, 6, 0, 11, 0, 3, 0, 0,
7, 0, 12, 1, 4, 0, 0, 8, 0, 0, 2, 5, 0, 0, 9)

A1 <- matrix(dta, nrow=5, ncol=6, byrow=TRUE)

print(A1)
res1 <- spdiags(A1)
print(res1) 

Categorical sequence of words

Description

A simple text of the nursery rhyme, \'the wheels on the bus\'

Usage

text

Format

A vector of 120 words

References

Verna Hills (1939). The Wheels on the bus. American Childhood (25), 56

Windowed Recurrence Measures

Description

A recurrence plot is computed in overlapping windows of a certain size for a number of delays smaller than the size of the window; and measures of it extracted.

Usage

wincrqa(ts1, ts2, windowstep, windowsize, delay, embed, 
radius, rescale, normalize, mindiagline, minvertline, tw, whiteline, 
recpt, side, method, metric, datatype, trend)

Arguments

Value

It returns a matrix where the rows are the different windows explored, and the columns are the recurrence measures observed in that particular window. Refer to crqa for the values returned.

Note

If no-recurrence is found in a window, that window will not be saved, and a message about it will be warned. TREND is implemented following a solution proposed by Norbert Marwan, and translated here in R, for those who have asked him. He, however, warns that this measure might strongly depend on the chosen settings to calculate crq. Relying blindly on such measure can, therefore, produce misleading results. Also, we enabled the possibility to input directly a RP with recpt = T, and so extract the measures. This implies that it will not be the same as by conducting phase-space reconstruction on subsets of the time series. So, please, make sure why you are doing it and why.

Author(s)

Moreno I. Coco (moreno.cocoi@gmail.com) Alexandra Paxton alexandra.paxton@uconn.edu

See Also

crqa

Examples

data(crqa) 

listener = eyemovement$listener[1:200]
narrator = eyemovement$narrator[1:200]

# NB, the parameters for windowsize and windowstep are large to allow
# faster running time, please set them carefully in your analysis. 

delay = 1; embed = 1; rescale = 0; radius = 0.001;
normalize = 0; mindiagline = 2; minvertline = 2;
tw = 0; whiteline = FALSE; recpt = FALSE; side = "both"
method = 'crqa'; metric = 'euclidean';  
datatype = "continuous"; 
windowsize =  100; windowstep = 50
trend = FALSE

ans = wincrqa(listener, narrator, windowstep, windowsize, delay, embed,
                    radius, rescale, normalize, mindiagline, minvertline,
                    tw, whiteline, recpt, side, method, metric, 
                    datatype, trend)

## other recurrence measures are available in ans
profile = as.numeric(ans$RR) 

plot(profile, type = 'l')

Windowed Recurrence Profile

Description

A recurrence plot is computed in overlapping windows of a specified size for a number of delays smaller than the size of the window. In every window, the recurrence value for the different delays is calculated. A mean is then taken across the delays to obtain a recurrence value in that particular window.

Usage

windowdrp(ts1, ts2, windowstep, windowsize, lagwidth,
radius, delay, embed, rescale, normalize, mindiagline, minvertline,
tw, whiteline, recpt, side, method, metric, datatype)

Arguments

Value

It returns a list of arguments where:

Author(s)

Moreno I. Coco (moreno.cocoi@gmail.com) and Rick Dale (rdale@ucmerced.edu)

References

Boker, S. M., Rotondo, J. L., Xu, M., and King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological Methods, 7(3), 338.

See Also

drpfromts

Examples

# use the available data
data(crqa) 

listener = eyemovement$listener
narrator = eyemovement$narrator

# NB, the parameters for windowsize and windowstep are large to allow
# faster running time, please set them carefully in your analysis. 

delay = 1; embed = 1; rescale = 1; radius = 0.001;
normalize = 0; mindiagline = 2; minvertline = 2;
tw = 0; whiteline = FALSE; recpt = FALSE; side = "both"
method = 'crqa'; metric = 'euclidean';  
datatype = "continuous"; windowsize =  100; 
lagwidth = 10; windowstep = 200

ans = windowdrp(narrator, listener, windowstep, windowsize, lagwidth, 
                radius, delay, embed, rescale, normalize, 
                mindiagline, minvertline, tw, 
                whiteline, recpt, side, method, metric, 
                datatype)


profile = ans$profile; maxrec = ans$maxrec; maxlag = ans$maxlag

plot(profile, type = 'l')