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

 cpt.np R Documentation

## Identifying Changes using a Nonparametric Cost Function

### Description

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

### Usage

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

### Arguments

 `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". `verbose` Logical value. If TRUE then progress will be reported when penalty=CROPS. Default value is TRUE.

### Details

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.

### Value

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 changes, the number of segmentations and the value of the cost at that penalty value. `changepoints` The optimal changepoints for the different penalty values starting with the lowest penalty value.

Kaylea Haynes

### References

\insertRef

Haynes2017changepoint.np

\insertRef

Killick2012changepoint.np

\insertRef

Haynes2015changepoint.np

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.

### Examples

```
#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.
plot(out)

#Example 2 uses the heart rate data .

data(HeartRate)
cptHeartRate <- cpt.np(HeartRate, penalty = "CROPS", pen.value = c(5,200),
method="PELT", test.stat="empirical_distribution",
class=TRUE,minseglen=2,
nquantiles =4*log(length(HeartRate)))
plot(cptHeartRate, diagnostic = TRUE)
plot(cptHeartRate, ncpts = 11)

```

changepoint.np documentation built on Oct. 21, 2022, 1:07 a.m.