In lpishchagina/OptPartitioning2D: Optimal Partitioning and PELT algorithm

OptPartitioning2D Vignette

Liudmila Pishchagina

January 27, 2021

Quick Start

OptPartitioning2D is an R package written in Rcpp/C++ and developed to change-point detection in 2 bivariate time-series.

The package implements two algorithms: Optimal Partitioning and PELT-algorithm.

We present a basic use of the main functions of the OptPartitioning2D package.

We install the package from Github:

#devtools::install_github("lpishchagina/OptPartitioning2D")
library(OptPartitioning2D)

The function GenData2D

The GenData2D function simulates a bivariate time series with the arguments:

n is a time series length.

changepoints is a changepoint vector that gives the last index of each segment.

The last element of changepoints always equals to the length of time series Data.

means1 is a vector of means for the first univariate time series.

The length of this vector is equal to the length of changepoints.

means2 is a vector of means for the second univariate time series.

The length of this vector is equal to the length of changepoints.

noise1 is a variance of the first univariate time series(by default it is equal to 1).

noise2 is a variance of the second univariate time series(by default it is equal to 1).

n <- 100
Data <- GenData2D(n, changepoints = c(20, 40, 60, 80, 100), means1 = c(0, 1, 0, 1, 0), means2 = c(1, 2, 3, 4, 5), noise1 = 1,  noise2 = 1)

The function OptPart2D

The OptPart2D function returns the result of the segmentation using the parameters:

data1 is the first univariate time series.

data2 is the second univariate time series.

penalty is a value of penalty (a non-negative real number).

The penalty here equals to a classic 2*(noise^2)*log(n).

type is a parameter defining the algorithm of segmentation.

The type must be either "null" or "pruning".

We use Optimal Partitioning algorithm when type = "null" and PELT-algorithm when type = "pruning".

We choose a gaussian cost.

OptPart <- OptPart2D(Data[1,], Data[2,], penalty = 2 * log(n) , type="null")

OptPELT <- OptPart2D(Data[1,], Data[2,], penalty = 2 * log(n) , type="pruning")

## OptPart$changepoints
## [1]  19  34  60  80 100
##
## OptPart$means1
## [1] -0.1017971  1.6048117  0.1004500  1.2940562  0.1666548
##
## OptPart$means2
## [1] 1.416380 1.581436 2.816486 3.890411 4.845932
## OptPart$globalCost
## [1] 210.8269

## OptPELT$changepoints
## [1]  19  34  60  80 100
##
## OptPELT$means1
## [1] -0.1017971  1.6048117  0.1004500  1.2940562  0.1666548
##
## OptPELT$means2
## [1] 1.416380 1.581436 2.816486 3.890411 4.845932
##
## OptPELT$globalCost
## [1] 210.8269

changepoints is a vector of the inferred changepoints.

means1 is a vector of the inferred means for the first univariate time series.

means2 is a vector of the inferred means for the second univariate time series.

globalCost is the overall gaussian cost of the segmented data.

The function PlotOptPart2D

The function PlotOptPart2D plots a graph for each univariate time series of the bivariate series.

The graph shows the univariate time series, the estimated values of means and the inferred segments.

The function PlotOptPart2D uses the parameters:

data is the bivariate time series.

changepoints is a vector of the inferred changepoints.

means1 is a vector of the inferred means for the first univariate time series.

means2 is a vector of the inferred means for the second univariate time series.

PlotOptPart2D(data = Data, changepoints = c(20, 40, 60, 80, 100), means1 = c(0, 1, 0, 1, 0), means2 = c(1, 2, 3, 4, 5))

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lpishchagina/OptPartitioning2D documentation built on Feb. 9, 2021, 9:17 p.m.