geomcp {changepoint.geo}

Multivariate changepoint detection via two geometric mappings

Description

Implements the GeomCP algorithm (Grundy et al. 2020). This algorithm performs two geometric mappings on multivariate time series based on the Euclidean distance and principle angle between each time vector and a pre-specified reference vector. The univariate changepoint detection method PELT, (Killick et al. 2012), is then performed on the two mappings to identify changepoints which correspond to those in the original multivariate time series.

Usage

geomcp(X, penalty = "MBIC", pen.value = 0, test.stat = "Normal", msl = 2,
       nquantiles = 1,MAD=FALSE,ref.vec='Default',ref.vec.value=0)

Arguments

X

A matrix containing the data which is of size n by p. Each row is a new time point and each column is a different series.

penalty

Penalty choice for univariate changepoint analysis of mappings. Choice of "MBIC", "SIC", "BIC", "Hannan-Quinn","Manual". If "Manual" is specified, the manual penalty is contained in the pen.value parameter.

pen.value

The value of the penalty when using the "Manual" penalty option - this can be a numeric value or text giving the formula to use, see cpt.meanvar for more details.

test.stat

The assumed test statistic/distribution of the mapped data. Currently only "Normal" and "Empirical" are supported.

msl

Positive integer giving the minimum segment length (no. of observations between changes), default is 1.

nquantiles

Only required for test.stat="Empirical". Number of quantiles used in estimating the empirical likelihood.

MAD

Logical. If TRUE transforms each series by subtracting the median of the series and dividing by the median absolute deviation.

ref.vec

Choice of "Default" or "Manual". If "Default" is specified the vector of ones is used as the reference vector. If "Manual" is selected, the manual reference vector is contained in the ref.vec.value parameter.

ref.vec.value

The vector that is used as the reference vector for calculating distances and angles from.

Details

This function centralizes all time vectors using the given reference vector and then performs the distance and angle mappings from the reference vector. The univariate changepoint method PELT is then used to detect changepoints in the distance and angle mappings which correspond to changes in the multivariate time series.

Value

An object of S4 class "cpt.geo" is returned. The slots dist.cpts and ang.cpts return the changepoints identified in each measure.

Author(s)

Thomas Grundy

References

Grundy T, Killick R, Mihalyov G (2020). “High-dimensional changepoint detection via a geometrically inspired mapping.” Stat Comput, 0(0). doi:10.1007/s11222-020-09940-y.

Killick R, Fearnhead P, Eckley IA (2012). “Optimal detection of changepoints with a linear computational cost.” J. Am. Stat. Assoc., 107(500), 1590–1598.

See Also

cpt.geo,plot-methods

Examples

##Variance change in all series
set.seed(1)
X <- rbind(matrix(rnorm(100*50),ncol=50),matrix(rnorm(100*50,0,2),ncol=50))
ans <- geomcp(X)
summary(ans)
plot(ans)

##Mean change in 50% of series with a manual reference vector and non-parametric univariate 
##changepoint detection using 10 quantiles with a BIC penalty and min seg length of 5
set.seed(1)
Y <- rbind(matrix(rnorm(100*20),ncol=20),cbind(matrix(rnorm(100*10),ncol=10),
					       matrix(rnorm(100*10,1),ncol=10)))
res <- geomcp(Y,penalty='Manual',pen.value=30,test.stat='Empirical',nquantiles=10,ref.vec='Manual',
	      ref.vec.value=seq(1,10,length.out=20),msl=5)
summary(res)
plot(res)

##Different plot types for above example
#Plots mappings and changepoints
plot(res,plot.type='mappings') 
#Heatmap of data with changepoints not shown
plot(res,plot.type='full.data',changepoints=FALSE,scale.series=TRUE)
#Specific series with mappings and changepoints shown.
plot(res,plot.type='series',show.series=c(1,5,10),add.mappings=TRUE)