swh:1:snp:e75a8a2617c9395688cff068aec5b1e7448d2a41
Tip revision: fb9d711f03cd085124e022a5179b96dd48b48a1b authored by Toni Giorgino on 27 April 2013, 00:00:00 UTC
version 1.16
version 1.16
Tip revision: fb9d711
dtwDist.Rd
\name{dtwDist}
\alias{dtwDist}
\title{Compute a dissimilarity matrix}
\description{Compute the dissimilarity matrix between
a set of single-variate timeseries. }
\usage{
dtwDist(mx,my=mx,...)
# dist(mx,my=mx,method="DTW",...)
}
\arguments{
\item{mx}{numeric matrix, containing timeseries as rows}
\item{my}{numeric matrix, containing timeseries as rows (for cross-distance)}
\item{...}{arguments passed to the \code{\link{dtw}} call}
}
\value{
A square matrix whose element \code{[i,j]} holds the Dynamic Time Warp
distance between row \code{i} (query) and \code{j} (reference) of
\code{mx} and \code{my}, i.e. \code{dtw(mx[i,],my[j,])$distance}.
}
\details{
\code{dtwDist} computes a dissimilarity matrix, akin to
\code{\link{dist}}, based on the Dynamic Time Warping definition of a
distance between single-variate timeseries.
The \code{dtwDist} command is a synonym for the
\code{\link[proxy]{dist}} function of package \pkg{proxy}; the DTW
distance is registered as \code{method="DTW"} (see examples below).
The timeseries are stored as rows in the matrix argument \code{m}. In
other words, if \code{m} is an N * T matrix, \code{dtwDist} will build
N*N ordered pairs of timeseries, perform the corresponding N*N
\code{dtw} alignments, and return all of the results in a matrix. Each
of the timeseries is T elements long.
\code{dtwDist} returns a square matrix, whereas the \code{dist} object
is lower-triangular. This makes sense because in general the DTW
"distance" is not symmetric (see e.g. asymmetric step patterns). To
make a square matrix with the \code{\link[proxy]{dist}} function
sematics, use the two-arguments call as \code{dist(m,m)}. This will
return a square \code{crossdist} object. }
\note{
To convert a square cross-distance matrix (\code{crossdist} object) to
a symmetric \code{\link{dist}} object, use a suitable conversion
strategy (see examples).
}
\seealso{Other "distance" functions are: \code{\link{dist}},
\code{\link[vegan]{vegdist}} in package \code{vegan},
\code{\link[analogue]{distance}} in package \code{analogue}, etc.
}
\examples{
## Symmetric step pattern => symmetric dissimilarity matrix;
## no problem coercing it to a dist object:
m <- matrix(0,ncol=3,nrow=4)
m <- row(m)
dist(m,method="DTW");
# Old-fashioned call style would be:
# dtwDist(m)
# as.dist(dtwDist(m))
## Find the optimal warping _and_ scale factor at the same time.
## (There may be a better, analytic way)
# Prepare a query and a reference
query<-sin(seq(0,4*pi,len=100))
reference<-cos(seq(0,4*pi,len=100))
# Make a set of several references, scaled from 0 to 3 in .1 increments.
# Put them in a matrix, in rows
scaleSet <- seq(0.1,3,by=.1)
referenceSet<-outer(1/scaleSet,reference)
# The query has to be made into a 1-row matrix.
# Perform all of the alignments at once, and normalize the result.
dist(t(query),referenceSet,meth="DTW")->distanceSet
# The optimal scale for the reference is 1.0
plot(scaleSet,scaleSet*distanceSet,
xlab="Reference scale factor (denominator)",
ylab="DTW distance",type="o",
main="Sine vs scaled cosine alignment, 0 to 4 pi")
## Asymmetric step pattern: we can either disregard part of the pairs
## (as.dist), or average with the transpose
mm <- matrix(runif(12),ncol=3)
dm <- dist(mm,mm,method="DTW",step=asymmetric); # a crossdist object
# Old-fashioned call style would be:
# dm <- dtwDist(mm,step=asymmetric)
# as.dist(dm)
## Symmetrize by averaging:
(dm+t(dm))/2
## check definition
stopifnot(dm[2,1]==dtw(mm[2,],mm[1,],step=asymmetric)$distance)
}
\author{Toni Giorgino}
\keyword{ts}