Fpop {fpop}

Fpop

Description

Function calling the fpop algorithm, use functional pruning and optimal partioning 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 I(m_i != m_i+1), where the indicator function I counts the number of changes in the mean vector m.

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), t.est (vector of overall optimal segment ends), K (optimal number of segments), J.est (total un-penalized cost of optimal model). To see how cost relates to J.est, see definition of J.est in the R source code for this function.

Author(s)

Guillem Rigaill, Toby Dylan Hocking

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"))