README.md

In lpishchagina/FPOPapprox2D: FPOPapprox2D

FPOPapprox2D Vignette

Liudmila Pishchagina

April 1, 2021

Quick Start

FPOPapprox2D is an R package written in Rcpp/C++ and developed to detection changepoints using the Functional Pruning Optimal Partitioning method (FPOP) in p-variate time series of length n.

The package implements the following types of FPOP-pruning:

type = 1: ("intersection" of sets), approximation - "rectangle";

type = 2:("intersection" of sets)"minus"("union" of sets), approximation - "rectangle";

type = 3: (last disk)"minus"("union" of sets), approximation - "disk".

We present a basic use of the main functions of the FPOPapprox2D package.

We install the package from Github:

#devtools::install_github("lpishchagina/FPOPapprox2D")
library(FPOPapprox2D)

The function data_genDp

The data_genDp function simulates a p-variate time series of length n with the arguments:

p is the time series dimension.

n is the time series length.

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

The last element of chpts is always less than to the length of time series.

By default, chpts = NULL for the data without changepoints.

means matrix of successive means for the p-variate time series.

By default, means = matrix(0, ncol = 1, nrow = p) for the data without changepoints.

The length of each matrix row is equal to the length of chpts plus one.

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

set.seed(13)

size <- 1000

Data1 =  data_genDp(p = 2, n = size) 

Data2 =  data_genDp(p = 2, n = size, chpts = 500, means = matrix(c(0,0,1,1), nrow = 2), noise = 1) 

The function FPOPDp

The FPOPDp function returns the result of the segmentation of FPOP-method using the parameters:

data is the p-variate time series (matrix of real numbers with p-rows and n-columns).

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

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

type is a value defining the type of geometry for FPOP-pruning.

The type must be either 1, 2 or 3:

type = 1: ("intersection" of sets), approximation - "rectangle";

type = 2:("intersection" of sets)"minus"("union" of sets), approximation - "rectangle";

type = 3: (last disk)"minus"("union" of sets), approximation - "disk".

We choose a Gaussian cost.

library(base)

set.seed(13)

dim <-2

size <- 1000

sigma <- 1

beta <- 2 * sigma * dim * log(size)

Data1 =  data_genDp(p = dim, n = size) 

Data2 =  data_genDp(p = dim, n = size, chpts = 500, means = matrix(c(0,0,1,1), nrow = dim), noise = 1)

FPOPDp(Data1, penalty = beta, type = 1)

FPOPDp(Data1, penalty = beta, type = 2)

FPOPDp(Data1, penalty = beta, type = 3)

$chpts
numeric(0)

$means
$means[[1]]
[1] -0.0031129231  0.0008128666

$globalCost
[1] 5.172187e-231

FPOPDp(Data2, penalty = beta, type = 1)

FPOPDp(Data2, penalty = beta, type = 2)

FPOPDp(Data2, penalty = beta, type = 3)

$chpts
[1] 500

$means
$means[[1]]
[1] -0.01552099 -0.02517320

$means[[2]]
[1] 1.044882 0.975139


$globalCost
[1] -27.63102

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

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

means is the list of successive means for the p-variate time series.

globalCost is the overall Gaussian cost of the segmented data.

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lpishchagina/FPOPapprox2D documentation built on Dec. 21, 2021, 11:49 a.m.