win_pcm_th: A windows-based approach for multiple change-point detection...
In IDetect: Isolate-Detect Methodology for Multiple Change-Point Detection

Description Usage Arguments Details Value Author(s) See Also Examples

This function performs the windows-based variant of the Isolate-Detect methodology with the thresholding-based stopping rule in order to detect multiple change-points in the mean of a noisy data sequence, with noise that is Gaussian. It is particularly helpful for very long data sequences, as due to applying Isolate-Detect on moving windows, the computational time is reduced. See Details for a brief explanation of this approach and for the relevant literature reference.

1 2	win_pcm_th(xd, sigma = stats::mad(diff(xd)/sqrt(2)), thr_con = 1, c_win = 3000, w_points = 3, l_win = 12000)

`xd`	A numeric vector containing the data in which you would like to find change-points.
`sigma`	A positive real number. It is the estimate of the standard deviation of the noise in `xd`. The default value is the median absolute deviation of `xd` computed under the assumption that the noise is independent and identically distributed from the Gaussian distribution.
`thr_con`	A positive real number with default value equal to 1. It is used to define the threshold, which is equal to `sigma * thr_con * sqrt(2 * log(T))`, where `T` is the length of the data sequence `xd`.
`c_win`	A positive integer with default value equal to 3000. It is the length of each window for the data sequence in hand. Isolate-Detect will be applied in segments of the form `[(i-1) * c_win + 1, i * c_win]`, for i=1,2,...,K, where K depends on the length `T` of the data sequence.
`w_points`	A positive integer with default value equal to 3. It defines the distance between two consecutive end- or start-points of the right- or left-expanding intervals, respectively.
`l_win`	A positive integer with default value equal to 12000. If the length of the data sequence is less than or equal to `l_win`, then the windows-based approach will not be applied and the result will be obtained by the classical Isolate-Detect methodology based on thresholding.

The method that is implemented by this function is based on splitting the given data sequence uniformly into smaller parts (windows), to which Isolate-Detect, based on the threshold stopping rule (see pcm_th), is then applied. An idea of the computational improvement that this structure offers over the classical Isolate-Detect in the case of large data sequences is given in the supplement of “Detecting multiple generalized change-points by isolating single ones”, Anastasiou and Fryzlewicz (2018), preprint.

A numeric vector with the detected change-points.

Andreas Anastasiou, a.anastasiou@lse.ac.uk

pcm_th, which is the function that win_pcm_th is based on. Also, see ID_pcm and ID, which employ win_pcm_th. In addition, see win_cplm_th for the case of detecting changes in the slope of a piecewise-linear and continuous signal via thresholding.

single.cpt <- c(rep(4,1000),rep(0,1000))
single.cpt.noise <- single.cpt + rnorm(2000)
cpt.single.th <- win_pcm_th(single.cpt.noise)

three.cpt <- c(rep(4,4000),rep(0,4000),rep(-4,4000),rep(1,4000))
three.cpt.noise <- three.cpt + rnorm(16000)
cpt.three.th <- win_pcm_th(three.cpt.noise)