ptw: Parametric Time Warping

Description

The main functions of the ptw package, performing parametric time warping of one or more samples. Features in the samples are optimally aligned with features in the reference(s). One may align a single sample to a single reference, several samples to a single reference, and several samples to several references. In the latter case, the number of references and samples should be equal. One may require that all samples are warped with the same warping function, or one may allow individual warpings for all samples.

Usage

ptw(ref, samp, selected.traces,
    init.coef = c(0, 1, 0), try = FALSE,
    warp.type = c("individual", "global"),
    optim.crit = c("WCC", "RMS"),
    mode = c("forward", "backward"),
    smooth.param = ifelse(try, 0, 1e05),
    trwdth = 20, trwdth.res = trwdth,
    verbose = FALSE, ...)
stptw(ref, samp, init.coef = c(0, 1, 0),
      trwdth = 20, trwdth.res = trwdth, 
      nGlobal = ifelse(length(init.coef) > 3, 5, 0),
      ...)
# S3 method for ptw
summary(object, …)
# S3 method for ptw
print(x, …)

Arguments

ref

reference. Either a vector (containing one reference signal) or a matrix (one reference per row). If more than one reference is specified, the number of reference signals must equal the number of sample signals.

samp

sample. A vector (containing one sample signal) or a matrix (one sample per row).

selected.traces

optional vector containing the row numbers to use from ref (if more than one reference signal is specified) and samp.

init.coef

starting coefficients. The first number is the zeroth-order coefficient (i.e., a constant shift); further numbers indicate linear, quadratic, ... stretches. The default is to start from the identity warping using a quadratic function (c(0, 1, 0))

try

if try = TRUE, ptw does not optimize the warping but returns a ptw object containing the warping for init.coef. Default: FALSE

warp.type

default is to treat samples and references as single entities and align them individually and independently. Using the argument warp.type = "global" leads to one alignment function; the samples are warped simultaneously to the reference(s). Also see details

optim.crit

either "WCC" or "RMS". In both cases, the optimal value of the alignment leads to a value of 0. For "WCC", this means that 1 - WCC is optimized rather than WCC (where the optimal value equals 1)

mode

either "forward" or "backward": the latter was the original implementation, basically for a point i in the original signal predicting the point j in the signal that would be in position i in the warped signal. The interpretation of the coefficients is counterintuitive. Therefore the default is "forward", simply predicting the location (time) in the warped signal of a particular point. Apart from possible numerical optimisation issues, both warpings should give the same net result.

smooth.param

smoothing parameter for smoothing the reference and sample when optim.crit equals "RMS". If no smoothing is required, set this to 0. The default is to use smoothing in the optimization mode, and no smoothing otherwise

trwdth

the width of the triangle in the WCC criterion during the optimization, given as a number of data points. Default: 20

trwdth.res

the width of the triangle in the WCC calculation in the calculation of the quality of the final result. Default: equal to trwdth

verbose

logical, default is FALSE. Whether to give output during the optimisation, which may be useful for large data sets

...

further arguments to optim

nGlobal

for stick optimisations with more than three coefficients, a more powerful optimisation method is used (nloptr: in such cases nGlobal indicates the number of times this method is employed.

x, object

an object of class "ptw"

Value

A list of class "ptw" containing:

reference

the reference(s) used as input

sample

the sample(s) used as input

warped.sample

the warped sample

warp.coef

the warping coefficients

warp.fun

the warped indices (not for stptw)

crit.value

the value of the chosen criterion, either "WCC" or "RMS"

optim.crit

the chosen criterion, either "WCC" or "RMS"

warp.type

the chosen type of warping, either "individual" or "global"

Details

Function ptw and friends is meant for profile data, where intensities have been recorded at regular time points; function stptw is meant for lists of peaks, for instance obtained after peak-picking the profile data. The latter option is less flexible (Euclidean distance and backward warping have not been implemented, and only global alignment is possible) but is much faster, especially for larger data sets.

In the optimization mode (try = FALSE), the function optimizes the warping coefficients using the chosen criterion (either "WCC" or "RMS"). For "RMS", the data are smoothed before the optimization, but the quality of the final warping is measured on the unsmoothed data. For "WCC", the warping is performed using trwdth as the triangle width, but the quality of the final solution is measured using trwdth.res.

If try = TRUE is used as an argument, the function does not start an optimization, but just calculates the warping for the given warp function (init.coef); if smooth.param is larger than zero for the RMS criterion, the RMS of the smoothed patterns is calculated. The WCC criterion uses trwidth.res as the triangle width in this case.

Five situations can be distinguished:

One sample and one reference: this obviously leads to one warping function regardless of the setting of warp.type.
Several samples, all warped to the same single reference, each with its own warping function: this is the default behaviour (warp.type = "individual")
Several samples, warped to an equal number of references (pair-wise), with their own warping functions: this is the default behaviour (warp.type = "individual")
Several samples, warped to one reference, with one warping function (warp.type = "global")
Several samples, warped to an equal number of references (pair-wise), with one warping function (warp.type = "global")

References

Eilers, P.H.C. (2004) "Parametric Time Warping", Analytical Chemistry, 76 (2), 404 -- 411.

Bloemberg, T.G., et al. (2010) "Improved parametric time warping for Proteomics", Chemometrics and Intelligent Laboratory Systems, 104 (1), 65 -- 74.

Examples

Run this code

# NOT RUN {
data(gaschrom)
ref <- gaschrom[1,]
samp <- gaschrom[16,]
gaschrom.ptw <- ptw(ref, samp)
summary(gaschrom.ptw)

## same with sticks (peak lists)
refst <- gaschrom.st[1]
sampst <- gaschrom.st[16]
gaschrom.st.ptw <- stptw(refst, sampst, trwdth = 100)
summary(gaschrom.st.ptw)

# }
# NOT RUN {
## comparison between backward and forward warping
gaschrom.ptw <- ptw(ref, samp, init.coef = c(0, 1, 0, 0), mode = "backward")
summary(gaschrom.ptw)
gaschrom.ptw <- ptw(ref, samp, init.coef = c(-10, 1, 0, 0), mode = "forward")
summary(gaschrom.ptw)

## #############################
## many samples warped on one reference
ref <- gaschrom[1,]
samp <- gaschrom[2:16,]
gaschrom.ptw <-
  ptw(ref, samp, warp.type = "individual", verbose = TRUE,
      optim.crit = "WCC",  trwdth = 100, init.coef = c(0, 1, 0))
summary(gaschrom.ptw)

## "individual" warping not implemented for sticks; do separate warpings
## instead
refst <- gaschrom.st[1]
sampst <- gaschrom.st[2:16]
gaschrom.st.ptw.list <-
  lapply(sampst,
         function(smpl)
           stptw(refst, list(smpl), trwdth = 100, init.coef = c(0, 1, 0)))
t(sapply(gaschrom.st.ptw.list,  "[[", "warp.coef"))
t(sapply(gaschrom.st.ptw.list,  "[[", "crit.value"))

## #############################
## several samples on several references individually
ref <- gaschrom[1:8,]
samp <- gaschrom[9:16,]
gaschrom.ptw <-
  ptw(ref, samp, warp.type = "individual",
      optim.crit = "WCC", trwdth = 100, init.coef = c(0, 1, 0))
summary(gaschrom.ptw)

## stick version
gaschrom.st.ptw.list <-
  mapply(function(x, y)
         stptw(list(x), list(y), trwdth = 100, init.coef = c(0, 1, 0)),
         gaschrom.st[1:8], gaschrom.st[9:16],
         SIMPLIFY = FALSE)
t(sapply(gaschrom.st.ptw.list, coef))

## #############################
## several samples on several references: one, global warping
gaschrom.ptw <- ptw(ref, samp, warp.type = "global",
                    optim.crit = "WCC", init.coef = c(0, 1, 0))
summary(gaschrom.ptw)

refst <- gaschrom.st[1:8]
sampst <- gaschrom.st[9:16]
gaschrom.st.ptw <- stptw(refst, sampst, trwdth=100, init.coef = c(0, 1, 0))
summary(gaschrom.st.ptw)

## #################################################################
## Example of a three-way data set#
## #################################################################

## first bring all samples to the same scale
data(lcms)
lcms.scaled <- aperm(apply(lcms, c(1,3), 
                           function(x) x/mean(x) ), c(2,1,3))
## add zeros to the start and end of the chromatograms
lcms.s.z <- aperm(apply(lcms.scaled, c(1,3), 
                        function(x) padzeros(x, 250) ), c(2,1,3))


## define a global 2nd degree warping
warp1 <- ptw(lcms.s.z[,,2], lcms.s.z[,,3], warp.type="global")
warp.samp <- warp1$warped.sample
warp.samp[is.na(warp.samp)] <- 0
## refine by adding 5th degree warpings for individual chromatograms
warp2 <- ptw(lcms.s.z[,,2], warp.samp, init.coef=c(0,1,0,0,0,0))
warp.samp2 <- warp2$warped.sample
warp.samp2[is.na(warp.samp2)] <- 0
## compare TICs
layout(matrix(1:2,2,1, byrow=TRUE))
plot(colSums(lcms.s.z[,,2]), type="l", ylab = "",
     main = "TIC: original data")
lines(colSums(lcms.s.z[,,3]), col=2, lty=2)
plot(colSums(lcms.s.z[,,2]), type="l", ylab = "",
     main = "TIC: warped data")
lines(colSums(warp.samp2), lty=2, col=2)

## ###########################
## stick version of this warping - note that the peaks have been picked
## from the scaled profiles. Note that here we need to take list
## elements: every sample is a list of mz channels.
warp1.st <- stptw(lcms.pks[[2]], lcms.pks[[3]], trwdth = 100)
summary(warp1.st)
# }

Run the code above in your browser using DataLab