PeakSegFPOP | R Documentation |
Find the optimal change-points using the Poisson loss and the
PeakSeg constraint. For N data points, the functional pruning
algorithm is O(N log N) time and memory. It recovers the exact
solution to the following optimization problem. Let Z be an
N-vector of count data (count.vec
, non-negative integers), let W
be an N-vector of positive weights (weight.vec
), and let penalty
be a non-negative real number. Find the N-vector M of real numbers
(segment means) and (N-1)-vector C of change-point indicators in
-1,0,1 which minimize the penalized Poisson Loss,
penalty*sum_[i=1]^[N_1] I(c_i=1) + sum_[i=1]^N
w_i*[m_i-z_i*log(m_i)], subject to constraints: (1) the first
change is up and the next change is down, etc (sum_[i=1]^t c_i in
0,1 for all t<N-1), and (2) the last change is down
0=sum_[i=1]^[N-1] c_i, and (3) Every zero-valued change-point
variable has an equal segment mean after: c_i=0 implies
m_i=m_[i+1], (4) every positive-valued change-point variable may
have an up change after: c_i=1 implies m_i<=m_[i+1], (5) every
negative-valued change-point variable may have a down change
after: c_i=-1 implies m_i>=m_[i+1]. Note that when the equality
constraints are active for non-zero change-point variables, the
recovered model is not feasible for the strict inequality
constraints of the PeakSeg problem, and the optimum of the PeakSeg
problem is undefined.
PeakSegFPOP(count.vec,
weight.vec = rep(1,
length(count.vec)),
penalty = NULL)
count.vec |
integer vector of length >= 3: non-negative count data to segment. |
weight.vec |
numeric vector (same length as |
penalty |
non-negative numeric scalar: |
List of model parameters. count.vec
, weight.vec
, n.data, penalty
(input parameters), cost.mat (optimal Poisson loss), ends.vec
(optimal position of segment ends, 1-indexed), mean.vec (optimal
segment means), intervals.mat (number of intervals stored by the
functional pruning algorithm). To recover the solution in terms of
(M,C) variables, see the example.
Toby Dylan Hocking <toby.hocking@r-project.org> [aut, cre]
## Use the algo to compute the solution list.
library(PeakSegOptimal)
data("H3K4me3_XJ_immune_chunk1", envir=environment())
by.sample <-
split(H3K4me3_XJ_immune_chunk1, H3K4me3_XJ_immune_chunk1$sample.id)
n.data.vec <- sapply(by.sample, nrow)
one <- by.sample[[1]]
count.vec <- one$coverage
weight.vec <- with(one, chromEnd-chromStart)
penalty <- 1000
fit <- PeakSegFPOP(count.vec, weight.vec, penalty)
## Recover the solution in terms of (M,C) variables.
change.vec <- with(fit, rev(ends.vec[ends.vec>0]))
change.sign.vec <- rep(c(1, -1), length(change.vec)/2)
end.vec <- c(change.vec, fit$n.data)
start.vec <- c(1, change.vec+1)
length.vec <- end.vec-start.vec+1
mean.vec <- rev(fit$mean.vec[1:(length(change.vec)+1)])
M.vec <- rep(mean.vec, length.vec)
C.vec <- rep(0, fit$n.data-1)
C.vec[change.vec] <- change.sign.vec
diff.vec <- diff(M.vec)
data.frame(
change=c(C.vec, NA),
mean=M.vec,
equality.constraint.active=c(sign(diff.vec) != C.vec, NA))
stopifnot(cumsum(sign(C.vec)) %in% c(0, 1))
## Compute penalized Poisson loss of M.vec and compare to the value reported
## in the fit solution list.
n.peaks <- sum(C.vec==1)
rbind(
n.peaks*penalty + PoissonLoss(count.vec, M.vec, weight.vec),
fit$cost.mat[2, fit$n.data])
## Plot the number of intervals stored by the algorithm.
FPOP.intervals <- data.frame(
label=ifelse(as.numeric(row(fit$intervals.mat))==1, "up", "down"),
data=as.numeric(col(fit$intervals.mat)),
intervals=as.numeric(fit$intervals.mat))
library(ggplot2)
ggplot()+
theme_bw()+
theme(panel.margin=grid::unit(0, "lines"))+
facet_grid(label ~ .)+
geom_line(aes(data, intervals), data=FPOP.intervals)+
scale_y_continuous(
"intervals stored by the\nconstrained optimal segmentation algorithm")
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