cpt.np: Identifying Changes using a Nonparametric Cost Function
In JRichards1995/Changepoint.np: Methods for Nonparametric Changepoint Detection

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

Calculates the optimal positioning and number of changepoints for data given a user specified cost function and penalty.

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cpt.np(data, penalty = "MBIC", pen.value = 0, method = "PELT",
  test.stat = "empirical_distribution", class = TRUE, minseglen = 1,
  nquantiles = 10)

`data`	A vector, ts object or matrix containing the data within which you wish to find a changepoint. If the data is a matrix, each row is considered as a separate dataset.
`penalty`	Choice of "None", "SIC", "BIC", "MBIC", AIC", "Hannan-Quinn", "Manual" and "CROPS" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. If CROPS is specified, the penalty range is contained in the pen.value parameter; note this is a vector of length 2 which contains the minimum and maximum penalty value. Note CROPS can only be used if the method is "PELT". The predefined penalties listed DO count the changepoint as a parameter, postfix a 0 e.g."SIC0" to NOT count the changepoint as a parameter.
`pen.value`	The value of the penalty when using the Manual penalty option. A vector of length 2 (min,max) if using the CROPS penalty.
`method`	Currently the only method is "PELT".
`test.stat`	The assumed test statistic/distribution of the data. Currently only "empirical_distribution".
`class`	Logical. If TRUE then an object of class cpt is returned.
`minseglen`	Positive integer giving the minimum segment length (number of observations between changes), default is the minimum allowed by theory.
`nquantiles`	The number of quantiles to calculate when test.stat = "empirical_distribution".

This function is used to find multiple changes in a data set using the changepoint algorithm PELT with a nonparametric cost function based on the empirical distribution. A changepoint is denoted as the first observation of the new segment.

If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are returned. For class=FALSE the structure is as follows.

If data is a vector (single dataset) then a vector/list is returned depending on the value of method. If data is a matrix (multiple datasets) then a list is returned where each element in the list is either a vector or list depending on the value of method.

If method is PELT then a vector is returned containing the changepoint locations for the penalty supplied. If the penalty is CROPS then a list is returned with the elements:

`cpt.out`	A data frame containing the value of the penalty value where the number of segmentations chages, the number of segmentations and the value of the cost at that penalty value.
`changepoints`	The optimal changepoints for the different penalty values startings with the lowest penalty value.

Kaylea Haynes

PELT with an Empirical Distribution cost function: Haynes K, Fearnhead P, Eckley I A (2016) A computationally efficient nonparametric approach for changepoint detection, Statistics and Computed (accepted)

PELT Algorithm: Killick R, Fearnhead P, Eckley I A (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590-1598

CROPS: Haynes K, Eckley I A, Fearnhead P (2015) Computationally Efficient Changepoint Detection for a Range of Penalties, JCGS, To Appear

PELT in parametric settings: cpt.mean for changes in the mean, cpt.var for changes in the variance and cpt.meanvar for changes in the mean and variance.

#Example of a data set of length 1000 with changes in location
#(model 1 of Haynes, K et al. (2016)) with the empirical distribution cost function.

set.seed(12)

J <- function(x){
   (1+sign(x))/2
 }

n <- 1000
tau <- c(0.1,0.13,0.15,0.23,0.25,0.4,0.44,0.65,0.76,0.78,0.81)*n
h <- c(2.01, -2.51, 1.51, -2.01, 2.51, -2.11, 1.05, 2.16, -1.56, 2.56, -2.11)
sigma <- 0.5
t <- seq(0,1,length.out = n)
data <- array()
for (i in 1:n){
   data[i] <- sum(h*J(n*t[i] - tau)) + (sigma * rnorm(1))
}

out <- cpt.np(data, penalty = "SIC",method="PELT",test.stat="empirical_distribution",
             class=TRUE,minseglen=2, nquantiles =4*log(length(data)))
cpts(out)

#returns 100 130 150 230 250 400 440 650 760 780 810 as the changepoint locations.

#Example 2 uses the heart rate data . 

cptHeartRate <- cpt.np(HeartRate, penalty = "Manual", pen.value = 50, method="PELT",
 test.stat="empirical_distribution",class=TRUE,minseglen=2, nquantiles =4*log(length(HeartRate)))