Fpop: Fpop

In fpop: Segmentation using Optimal Partitioning and Functional Pruning

Description

Function calling the fpop algorithm, use functional pruning and optimal partionning to recover the best segmentation with respect to the L2 loss with a per change-point penalty of lambda. More precisely, this function computes the solution to argmin_m sum_i=1^n (x_i-m_i)^2 + lambda * sum_i=1^n-1 [1+I(m_i != m_i+1)], where the indicator function I counts the number of changes in the mean vector m, so the total penalty term is equivalent to the number of segments.

Usage

Fpop(x, lambda, mini = min(x), 
    maxi = max(x))

Arguments

x	A vector of double : the signal to be segmented
lambda	Value of the penalty
mini	Min value for the mean parameter of the segment
maxi	Max value for the mean parameter of the segment

Value

Named list with the following elements: input data (signal, n, lambda, min, max), path (best previous segment end up to each data point), cost (optimal penalized cost up to each data point, where loss is the square loss without the constant term and the penalty is lambda times the number of segments), t.est (vector of overall optimal segment ends), K (optimal number of segments), J.est (total un-penalized cost of optimal model, aka total square loss). To see how cost relates to J.est, see definition of J.est in the R source code for this function. (last cost = J.est - sum.of.squares + K*lambda)

Author(s)

Guillem Rigaill <[e-mail]> [aut, cre], Toby Hocking [aut], Robert Maidstone [aut], Michel Koskas [ctb], Paul Fearnhead [aut]

Examples

set.seed(1)
N <- 100
data.vec <- c(rnorm(N), rnorm(N, 2), rnorm(N))
fit <- Fpop(data.vec, N)
end.vec <- fit$t.est
change.vec <- end.vec[-length(end.vec)]
start.vec <- c(1, change.vec+1)
segs.list <- list()
for(seg.i in seq_along(start.vec)){
  start <- start.vec[seg.i]
  end <- end.vec[seg.i]
  seg.data <- data.vec[start:end]
  seg.mean <- mean(seg.data)
  segs.list[[seg.i]] <- data.frame(
    start, end,
    mean=seg.mean,
    seg.cost=sum((seg.data-seg.mean)^2))
}
segs <- do.call(rbind, segs.list)
plot(data.vec)
with(segs, segments(start-0.5, mean, end+0.5, mean, col="green"))
with(segs[-1,], abline(v=start-0.5, col="green", lty="dotted"))

Example output

Welcome to the fpop package.
This package implements the FPOP algorithm (http://arxiv.org/abs/1409.1842),
see the Fpop function.

fpop documentation built on April 9, 2020, 3:01 a.m.