| Title: | Variable Penalty Dynamic Time Warping |
|---|---|
| Description: | Variable Penalty Dynamic Time Warping (VPdtw) for aligning chromatographic signals. With an appropriate penalty this method performs good alignment of chromatographic data without deforming the peaks (Clifford, D., Stone, G., Montoliu, I., Rezzi S., Martin F., Guy P., Bruce S., and Kochhar S.(2009) <doi:10.1021/ac802041e>; Clifford, D. and Stone, G. (2012) <doi:10.18637/jss.v047.i08>). |
| Authors: | David Clifford [aut],
Glenn Stone [aut],
Ethan Bass [ctb, cre] |
| Maintainer: | Ethan Bass <[email protected]> |
| License: | GPL-2 |
| Version: | 2.2.1 |
| Built: | 2024-11-04 21:42:58 UTC |
| Source: | https://github.com/ethanbass/VPdtw |
A dilation is a moving local maximum over a window of specific fixed width
specified by span. This dilation is computed first in one direction and then
in the other.
dilation(y, span)dilation(y, span)
y |
Signal (as a numeric vector). |
span |
An integer specifying the width of the moving window. |
A dilation is a method often used in mathematical morphology and image analysis (Soille 1999). This function is for vectors not matrices or images though applying it to rows and columns of a matrix will give the corresponding results.
An erosion of a vector or image can also be computed easily from this by computing the dilation of -1 times the vector and transforming back.
We recommend using a dilation to form a penalty for use in
VPdtw.
res |
Dilation of y with width specified by |
David Clifford
Soille, P. Morphological Image Analysis: Principles and Applications; Springer: New York, 1999.
## Example 1 - dilation of a signal data(reference) dref <- dilation(reference, 150) plot(reference, log = "y", type = "l") lines(dref, col = 2) ## Example 2 - dilation of an image BIN <- (volcano > 177) dBIN <- t(apply(BIN, 1, dilation, span = 5)) dBIN <- apply(dBIN, 2, dilation, span = 5) oldpar <- par(no.readonly = TRUE) par(mfrow=c(2, 2)) image(volcano) image(BIN) image(dBIN) par(oldpar)## Example 1 - dilation of a signal data(reference) dref <- dilation(reference, 150) plot(reference, log = "y", type = "l") lines(dref, col = 2) ## Example 2 - dilation of an image BIN <- (volcano > 177) dBIN <- t(apply(BIN, 1, dilation, span = 5)) dBIN <- apply(dBIN, 2, dilation, span = 5) oldpar <- par(no.readonly = TRUE) par(mfrow=c(2, 2)) image(volcano) image(BIN) image(dBIN) par(oldpar)
Plot VPdtw object
## S3 method for class 'VPdtw' plot( x, type = c("All", "Before", "After", "Shift", "Chromatograms"), xlim = NULL, ... )## S3 method for class 'VPdtw' plot( x, type = c("All", "Before", "After", "Shift", "Chromatograms"), xlim = NULL, ... )
x |
A VPdtw object generated by |
type |
What to plot. |
xlim |
Numeric vector specifying x-axis limits. |
... |
Additional arguments |
No return value, called for side effects.
Plots information about alignment according to value of type: either
unaligned query and reference ("Before"), aligned query and reference
("After"), shift at each index ("Shift"), a three-panel plot
containing all three of these options ("All"), or a two-panel plot with
unaligned and aligned query ("Chromatograms").
query <- c(1,5,4,3,9,8,5,2,6,5,4) reference <- c(rnorm(5), query, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 11 res <- VPdtw(reference, query, lambda, maxshift) plot(res)query <- c(1,5,4,3,9,8,5,2,6,5,4) reference <- c(rnorm(5), query, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 11 res <- VPdtw(reference, query, lambda, maxshift) plot(res)
Print VPdtw
## S3 method for class 'VPdtw' print(x, ...)## S3 method for class 'VPdtw' print(x, ...)
x |
A VPdtw object generated by |
... |
Additional argument. |
Numeric vector from the summary slot in the VPdtw
object specified by x.
query <- c(1,5,4,3,9,8,5,2,6,5,4) reference <- c(rnorm(5), query, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 11 res <- VPdtw(reference, query, lambda, maxshift) print(res)query <- c(1,5,4,3,9,8,5,2,6,5,4) reference <- c(rnorm(5), query, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 11 res <- VPdtw(reference, query, lambda, maxshift) print(res)
GC-MS chromatogram from a wine sample
A numeric vector of length 10018
This together with the query data are used in the VPdtw examples. The
alignment of these two signals is usually carried out on the log scale.
Plotting of this signal is best done also on the log scale (see example
below).
Amalia Berna, Stephen Trowell, CSIRO Food Futures Flagship
Amalia Z. Berna, Stephen Trowell, David Clifford, Wies Cynkar, Daniel Cozzolino, Geographical origin of Sauvignon Blanc wines predicted by mass spectrometry and metal oxide based electronic nose, Analytica Chimica Acta, Volume 648, Issue 2, 26 August 2009, Pages 146-152, ISSN 0003-2670, DOI: 10.1016/j.aca.2009.06.056. Keywords: Sauvignon Blanc; Electronic nose; Gas chromatography-mass spectrometry; Prediction
data(reference) data(query) plot(reference, log="y", type="l", main = "Gas Chromatogram", ylab = "log(intensity)", lwd = 2, col = 1) lines(query, col = 2)data(reference) data(query) plot(reference, log="y", type="l", main = "Gas Chromatogram", ylab = "log(intensity)", lwd = 2, col = 1) lines(query, col = 2)
Use variable penalty dynamic time warping to align one (or many) query signal(s) to a master signal. Penalties are incurred whenever a non-diagonal move is taken.
VPdtw( reference, query, penalty = 0, maxshift = 50, Reference.type = c("random", "median", "mean", "trimmed") )VPdtw( reference, query, penalty = 0, maxshift = 50, Reference.type = c("random", "median", "mean", "trimmed") )
reference |
Reference signal, NULL or a vector, see details. |
query |
Query signal, a vector or matrix, see details |
penalty |
Penalty term, a vector of same length as reference (not checked) or a matrix. See details. Default is 0 repeated to the length of reference |
maxshift |
Maximum allowable shift, an integer |
Reference.type |
Choices for |
Performs variable penalty dynamic time warping of query to
reference. Sakoe Chiba dtw used with width maxshift.
The basic operation aligns a query vector to a reference
vector.
If reference is not specified and query is a matrix then the
reference is created based on the value of Reference.type. The
four choices are random, median, mean and
trimmed. These choose a column of query at random as a
reference, or the piecewise median, mean or trimmed mean (with
trim = 0.1) with missing values removed.
If query is a matrix and penalty is a vector then the same
penalty is used to align each column of query to the
reference. Different alignment paths are chosen for each column of
the query matrix.
If query is a vector and penalty is a matrix then the
query is aligned to the reference several times, using each
column of the penalty matrix in turn as the penalty for the
alignment.
If query and penalty are matrices then nothing happens. If you
wish to align many query vectors and test many penalty vectors at the same
time then do the appropriate looping (over queries, or penalties) outside of
VPdtw.
xVals |
For plotting everything to correct index |
reference |
reference vector used by VPdtw expanded by NAs for plotting. |
query |
query passed to VPdtw |
penalty |
penalty passed to VPdtw |
warpedQuery |
result of alignment, same class as query |
shift |
shifts required to achieve alignment |
summary |
Summary information about the alignment. Used for
|
information |
Information about the alignment. Used for
|
David Clifford, Glenn Stone
Alignment Using Variable Penalty Dynamic Time Warping by Clifford, D; Stone, G; Montoliu, I; et al. Analytical Chemistry Volume: 81 Issue: 3 Pages: 1000-1007 Published: 2009
Also check out the dtw package by Toni Giorgino which
covers many variations of dynamic time warping.
## Citation citation("VPdtw") ## Basic Examples of zero-penalty DTW ## Example of exact fit in the middle query <- c(1,5,4,3,9,8,5,2,6,5,4) reference <- c(rnorm(5), query, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 11 res <- VPdtw(reference, query, lambda, maxshift) plot(res) res ## Example of exact fit on one side reference <- c(1,5,4,3,9,8,5,2,6,5,4) query <- c(rnorm(5), reference) reference <- c(reference, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 6 res <- VPdtw(reference, query, lambda, maxshift) plot(res) res ## Example of exact fit on the other side reference <- c(1,5,4,3,9,8,5,2,6,5,4) query <- c(reference, rnorm(5)) reference <- c(rnorm(5), reference) lambda <- rep(0, length(reference)) maxshift <- 6 res <- VPdtw(reference, query, lambda, maxshift) plot(res) res ## Example of exact fit except where one query gets dropped and its all on one side reference <- c(1,5,4,3,9,8,5,2,6,5,4) query <- c(reference[1:5], 20, reference[6:11]) reference <- c(rnorm(5), reference) query <- c(query, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 6 res <- VPdtw(reference, query, lambda, maxshift) plot(res) res ## Examples that use penalty term. Examples with long signals data(reference) data(query) ## Do alignment on log scale reference <- log(reference) query <- log(query) ## VPdtw result <- VPdtw(reference=reference[1:2500], query = query[1:2500], penalty = dilation(reference[1:2500], 150)/4, maxshift=150) plot(result) result ## Zero penalty DTW result2 <- VPdtw(reference = reference[1:2500], query = query[1:2500], penalty = rep(0, length(reference)), maxshift = 150) plot(result2) ## Try both penalties at the same time penalty <- dilation(reference, 350)/5 penalty <- cbind(penalty, rep(0, length(penalty))) result <- VPdtw(reference, query, penalty = penalty, maxshift = 350) plot(result, "After") plot(result, "Shift") result ## All three plots at once plot(result)## Citation citation("VPdtw") ## Basic Examples of zero-penalty DTW ## Example of exact fit in the middle query <- c(1,5,4,3,9,8,5,2,6,5,4) reference <- c(rnorm(5), query, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 11 res <- VPdtw(reference, query, lambda, maxshift) plot(res) res ## Example of exact fit on one side reference <- c(1,5,4,3,9,8,5,2,6,5,4) query <- c(rnorm(5), reference) reference <- c(reference, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 6 res <- VPdtw(reference, query, lambda, maxshift) plot(res) res ## Example of exact fit on the other side reference <- c(1,5,4,3,9,8,5,2,6,5,4) query <- c(reference, rnorm(5)) reference <- c(rnorm(5), reference) lambda <- rep(0, length(reference)) maxshift <- 6 res <- VPdtw(reference, query, lambda, maxshift) plot(res) res ## Example of exact fit except where one query gets dropped and its all on one side reference <- c(1,5,4,3,9,8,5,2,6,5,4) query <- c(reference[1:5], 20, reference[6:11]) reference <- c(rnorm(5), reference) query <- c(query, rnorm(5)) lambda <- rep(0, length(reference)) maxshift <- 6 res <- VPdtw(reference, query, lambda, maxshift) plot(res) res ## Examples that use penalty term. Examples with long signals data(reference) data(query) ## Do alignment on log scale reference <- log(reference) query <- log(query) ## VPdtw result <- VPdtw(reference=reference[1:2500], query = query[1:2500], penalty = dilation(reference[1:2500], 150)/4, maxshift=150) plot(result) result ## Zero penalty DTW result2 <- VPdtw(reference = reference[1:2500], query = query[1:2500], penalty = rep(0, length(reference)), maxshift = 150) plot(result2) ## Try both penalties at the same time penalty <- dilation(reference, 350)/5 penalty <- cbind(penalty, rep(0, length(penalty))) result <- VPdtw(reference, query, penalty = penalty, maxshift = 350) plot(result, "After") plot(result, "Shift") result ## All three plots at once plot(result)