Revision

**f3fa0a2ccb9bde3782d3555dfc9ebd3381d1757f**authored by Toni Giorgino on**30 November 2007, 00:00:00 UTC**, committed by Gabor Csardi on**30 November 2007, 00:00:00 UTC****1 parent**8635857

dtw.Rd

```
\name{dtw}
\alias{dtw}
\alias{is.dtw}
\title{Dynamic Time Warp}
\description{
Compute Dynamic Time Warp
and find optimal alignment between two time series.
}
\usage{
dtw(x, y=NULL, distance.function=euclideanSquared, step.pattern="s",
window.type="none", keep.internals=FALSE, ...)
is.dtw(d)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{x}{ query vector OR local cost matrix }
\item{y}{ template vector, or unused if cost matrix given }
% \item{partial}{ ~~Describe \code{partial} here~~ }
\item{distance.function}{ pointwise distance function. See e.g. \code{\link{dtwDistanceFunctions}} }
\item{step.pattern}{ step pattern. Char: "s" (symmetric), "a"
(asymmetric), or step matrix containing the allowed
steps with their cost (see \code{\link{stepPattern}})}
\item{window.type}{ windowing function, character or function. Char: "none",
"itakura", "sakoechiba", "slantedband". Function: boolean of two arguments.}
\item{keep.internals}{don't discard the cumulative cost matrix and other
internal structures}
\item{d}{an arbitrary R object}
\item{...}{additional arguments, passed to \code{window.function}}
}
\details{
The function performs Dynamic Time Warp (DTW) and computes the optimal
alignment between two time series \code{x} and \code{y}, given as
numeric vectors. The ``optimal'' alignment minimizes the sum of
distances between aligned elements. Lengths of \code{x} and \code{y} may be different.
The (local) distance between elements of \code{x} (query) and \code{y}
(template) is computed through the supplied \code{distance.function}
(see \code{\link{dtwDistanceFunctions}}).
Multivariate time series and complex distance functions can be handled
by supplying a local-distance
matrix. Element \code{[i,j]} of the
local-distance matrix is understood as the distance between element \code{x[i]} and
\code{y[j]}. The distance matrix has therefore \code{n=length(x)} rows and
\code{m=length(y)} columns (see note below).
To generate a local distance matrix, the functions \code{outer}
and \code{\link[pkg:analogue]{distance}} in package
\pkg{analogue} may come handy.
Several common variants of DTW are supported via the \code{step.pattern}
argument, which defaults to \code{symmetric}. Most common
step patterns are supported and pre-defined matrices; the
user can write their own. See
\code{\link{stepPattern}} for details.
Windowing is supported by supplying a name into the \code{window.type}
argument (abbreviations allowed) between the built-in types:
\itemize{
\item{\code{"none"}}{No windowing (default)}
\item{\code{"sakoechiba"}}{A band around main diagonal}
\item{\code{"slantedband"}}{A band around slanted diagonal}
\item{\code{"itakura"}}{So-called Itakura parallelogram}
}
\code{window.type} can also be user-defined windowing function.
See \code{\link{dtwWindowingFunctions}} for
all available windowing functions, details on user-defined windowing,
and a discussion of the (mis)naming of the "Itakura" parallelogram
as a global constraint.
Some windowing functions may require parameters, such as the
\code{window.size} argument.
A native (fast, compiled) version of the function is normally available.
If it is not, an interpreted equivalent will be used as
a fall-back, with a warning.
\code{is.dtw} tests whether the argument is of class \code{dtw}.
}
\value{
An object of class \code{dtw} with the following items:
\item{distance}{the computed distance \emph{not normalized}. Normalization
depends on the chosen step pattern.}
\item{index1}{matched elements: indices in \code{x}}
\item{index2}{corresponding mapped indices in \code{y}}
\item{stepPatterns}{the \code{stepPattern} object used for the computation}
\item{costMatrix}{if \code{keep.internals=TRUE}, the cumulative
cost matrix}
\item{directionMatrix}{if \code{keep.internals=TRUE}, the
directions of steps that would be taken at each alignment pair
(integers indexing step patterns)}
}
\references{
Sakoe, H.; Chiba, S., \emph{Dynamic programming algorithm optimization for spoken word recognition,}
Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on ,
vol.26, no.1, pp. 43-49, Feb 1978 URL: \url{http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1163055} \cr
}
\author{Toni Giorgino }
\note{Cost matrices (both input and output) have query elements row-wise
(first index), and template elements column-wise (second index). They
print according to the usual convention, with indexes increasing down and right. Many
DTW papers and tutorials show matrices according to plot-like conventions, i.e.
one index growing upwards. This may be confusing.
}
\seealso{
\code{\link{outer}},\code{\link[pkg:analogue]{distance}};
\code{\link{dtwWindowingFunctions}}, windowing and global constraints;
\code{\link{stepPattern}}, step patterns and local constraints
including slope;
\code{\link{plot.dtw}}, the plot method for DTW objects.
}
\examples{
## A noisy sine wave as query
idx<-seq(0,6.28,len=100);
query<-sin(idx)+runif(100)/10;
## A cosine is for template; sin and cos are offset by 25 samples
template<-cos(idx)
plot(template); lines(query);
## Find the best match (approx 1sec on Pentium 4)
## keep = TRUE so we can make a density plot later on
alignment<-dtw(query,template,keep=TRUE);
## Display the mapping
plot(alignment$index1,alignment$index2);
## That's all: 25 samples off-diagonal alignment
lines(1:100-25,col="red")
## Contour plots of the global cost
## A profile of the cumulative distance matrix
## similar to: plot(alignment,type="density") or dtwPlotDensity(alignment)
contour(alignment$costMatrix,col=terrain.colors(100),x=1:100,y=1:100,
xlab="Query (noisy sine)",ylab="Template (cosine)");
lines(alignment$index1,alignment$index2,col="red",lwd=2);
## More plots on dtw.plot!
#########
## An hand-checkable example
ldist<-matrix(1,nrow=6,ncol=6); # Matrix of ones
ldist[2,]<-0; ldist[,5]<-0; # Mark a clear path of zeroes
ldist[2,5]<-.01; # Forcely cut the corner
ds<-dtw(ldist); # DTW with user-supplied local cost matrix
da<-dtw(ldist,step="a"); # Also compute the asymmetric
plot(ds$index1,ds$index2,pch=3); # Symmetric: alignment follows the marked path
points(da$index1,da$index2,col="red"); # Asymmetric: visiting 1 is required twice
ds$distance;
da$distance;
}
\concept{Dynamic Time Warp}
\concept{Dynamic programming}
\concept{Align timeseries}
\concept{Minimum cumulative cost}
\keyword{ ts }
\keyword{ optimize }
```

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