Segmentor3IsBack (version 1.2)

Segmentor: Segmentor

Description

The functions are used for change-point problems. Given a loss function (Poisson, Normal homoscedastic, Negative Binomial or Normal Heteroscedastic (with given constant mean)), the function Segmentor estimates the optimal segmentation with respect to the log-likelihood. The Segmentor gives estimates of the breakpoint locations as well as the loss function parameter of each segment.

Usage

Segmentor(data=numeric(), model=1, Kmax = 15, theta = numeric(), m = numeric())

Arguments

data

A vector of observations to be segmented. Must have no missing values.

model

Integer between 1 and 4 giving the modelisation of the observed data, 1: poisson (default), 2: normal-homoscedastic, 3: negative binomial or 4: normal-heteroscedastic

Kmax

The maximum number of segments wanted for the data. The Segmentor will find all optimal segmentations in 1 to Kmax segments.

theta

Needed only for the Negative Binomial distribution: the value of the inverse of the overdispersion parameter. If the user does not enter a value, the package uses a modified version of Johnson and Kotz's estimator where the mean is replaced by the median.

m

Needed only for Normal Heteroscedastic distribution: the value of the constant mean. If not entered, the function uses the empirical mean of the data.

Value

• model
  Emission distribution (Poisson, Normal Homoscedastic, Negative Binomial or Normal Heteroscedastic)
• breaks
  Matrix of size Kmax*Kmax of estimated change-point locations for each optimal segmentation in 1 to Kmax segments.
• parameters
  Matrix of size Kmax*Kmax which elements are the estimated parameters for each segment of the optimal segmentation. If model is Poisson or Normal, the parameter corresponds to the mean of the signal in each segment. If model is Negative binomial, the parameter corresponds to the success-probability of the signal in each segment. If model is normal heteroscedastic, the parameter is the variance assuming known mean.
• likelihood
  Vector of size Kmax of resulting negative log-likelihood for each optimal segmentation.
• overdispersion
  only if model = Negative Binomial, the value of the inverse of overdispersion used for the segmentation
• mean
  only if model = Normal Heteroscedastic, the value of the mean used for the segmentation

Details

ll{ Package: Segmentor3IsBack Type: Package Version: 1.1 Date: 2012-05-10 License: GPL (>= 2) }

References

Pruned dynamic programming for optimal multiple change-point detection: http://arxiv.org/abs/1004.0887

A Generic Implementation of the Pruned Dynamic Programing Algorithm: http://arxiv.org/abs/1204.5564

Johnson, Kotz & Kemp: Univariate Discrete Distributions

Examples

require(Segmentor3IsBack);
N=2000 
x=c(rpois(N,2.0),rpois(2*N,2.2),rpois(N,1.9));
res=Segmentor(data=x,Kmax=3);  
# Finds the optimal segmentation in 1, 2 and 3 segments with respect to the Poisson model.

y=c(rnbinom(N,prob=0.3,size=0.15),rnbinom(2*N,prob=0.1,size=0.15),rnbinom(N,prob=0.6,size=0.15))
res2=Segmentor(y, model=3,Kmax=10); 
#Finds the optimal segmentation in 1 to 10 segments with respect to the Negative Binomial model.