R: Parametric Time Warping

ptw {ptw} | R Documentation

## 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, ...)
    ## S3 method for class 'ptw'
    summary(object, ...)
    ## S3 method for class '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
`x, object` | an object of class "ptw"

### 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) 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:

1. One sample and one reference: this obviously leads to one warping function regardless of the setting of `warp.type`.

2. Several samples, all warped to the same single reference, each with its own warping function: this is the default behaviour (`warp.type = "individual"`)

3. Several samples, warped to an equal number of references (pair-wise), with their own warping functions: this is the default behaviour (`warp.type = "individual"`)

4. Several samples, warped to one reference, with one warping function (`warp.type = "global"`)

5. Several samples, warped to an equal number of references (pair-wise), with one warping function (`warp.type = "global"`)

### 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
`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"

### Author(s)

Jan Gerretzen, Ron Wehrens

### 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.

### See Also

`WCC`, `RMS`, `select.traces`, `gaschrom`, `lcms`

### Examples

    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 = "RMS", init.coef = c(0, 1, 0, 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))
    t(sapply(gaschrom.st.ptw.list, coef))

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

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

    gaschrom.ptw <- ptw(ref, samp, warp.type = "global",
                        optim.crit = "WCC", init.coef = c(0, 1, 0))
    summary(gaschrom.ptw)

    ## #############################
    ## several samples on several references: one, global warping
    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)

    ## End(Not run)

    ## #############################
    ## Example of a three-way data set
    # first bring all samples to the same scale
    data(lcms)
    ## Not run:
    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)

    ## End(Not run)

    ## ###########################
    ## 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)

[Package ptw version 1.9-12 Index]