Description Usage Arguments Details Value Author(s) References See Also Examples
This function detects multiple change-points in the cross-covariance structure of a multivariate time series using a thresholding based procedure. It also, wherever possible, returns the relevant, transformed time series where each change-point was detected. See Details for a brief explanation.
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X |
A numerical matrix representing the multivariate time series, with the columns representing its components. |
approach |
A character string, which defines the metric to be used in order to detect the change-points. If approach = “euclidean”, which is also the default value, then the L_2 metric will be followed for the detection. If approach = “infinity”, then the L_{∞} metric will be used for the detection. |
th_max |
A positive real number with default value equal to 2.25. It is
used to define the threshold if the L_{∞} metric is chosen in
|
th_sum |
A positive real number with default value equal to 0.65. It is
used to define the threshold if the L_2 metric is chosen in
|
pointsgen |
A positive integer with default value equal to 10. It defines the distance between two consecutive end- or start-points of the right- or left-expanding intervals, respectively; see Details for more information. |
scales |
Negative integers for wavelet scales, with a small negative integer representing a fine scale. The default value is equal to -1. |
preaverage_gen |
A logical variable with default value equal to
|
scal_gen |
A positive integer number with default value equal to 3. It
is used to define the way we pre-average the given data sequence only if
|
min_dist |
A positive integer number with default value equal to 1. It is used in order to provide the minimum distance acceptable between detected change-points if such restrictions apply. |
The time series X_t is of dimensionality p and we are
looking for changes in the cross-covariance structure between the
different time series components
X_{t}^{(1)}, X_{t}^{(2)}, ..., X_{t}^{(p)}. We first use a
wavelet-based approach for the various given scales in scales
in order to transform the given time series X_t to a multiplicative
model Y_{t}^{(k)} = σ^{(k)}_t (Z_t^{(k)})^2; t=1,2,…,T; k = 1,2,…,d,
where Z_t^{(k)} is a sequence of standard normal random variables,
E(Y_t^{(k)}) = σ_t^{(k)}, and d is the new
dimensionality, which depends on the value given in scales
.
The function has been extensively tested on fMRI data, hence, its parameters
have been tuned for this data type. The function might not work well in other
structures, such as time series that are negatively serially correlated.
A list with the following components:
changepoints | The locations of the detected change-points. |
no.of.cpts | The number of the detected change-points. |
time_series | A list with two components that indicates which combinations |
of time series are responsible for each change-point detected. See the outcome | |
values time_series_indicator and most_important of the function
|
|
match.cpt.ts for more information.
|
If the minimum distance between the detected change-points is less than
the value given in min_dist
, then only the number and the locations of
the “pruned” change-points are returned.
Andreas Anastasiou, anastasiou.andreas@ucy.ac.cy
“Cross-covariance isolate detect: a new change-point method for estimating dynamic functional connectivity”, Anastasiou et al (2020), preprint <doi:10.1101/2020.12.20.423696>.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | set.seed(111)
A <- matrix(rnorm(20*400), nrow = 400) ## No change-point
M1 <- detect.th(A, approach = 'euclidean', scales = -1)
M2 <- detect.th(A, approach = 'infinity', scales = -1)
M1
M2
set.seed(111)
num.nodes <- 40 # number of nodes
etaA.1 <- 0.95
etaA.2 <- 0.05
pcor1 <- GeneNet::ggm.simulate.pcor(num.nodes, etaA = etaA.1)
pcor2 <- GeneNet::ggm.simulate.pcor(num.nodes, etaA = etaA.2)
n <- 100
data1 <- GeneNet::ggm.simulate.data(n, pcor1)
data2 <- GeneNet::ggm.simulate.data(n, pcor2)
X1 <- rbind(data1, data2) ## change-point at 100
N1 <- detect.th(X1, approach = 'euclidean', scales = -1)
N2 <- detect.th(X1, approach = 'infinity', scales = -1)
N1$changepoints
N1$time_series
N2$changepoints
N2$time_series
|
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