Compute the dissimilarity matrix between a set of single-variate timeseries.
numeric matrix, containing timeseries as rows
numeric matrix, containing timeseries as rows (for cross-distance)
arguments passed to the
dtwDist computes a dissimilarity matrix, akin to
based on the Dynamic Time Warping definition of a distance between
dtwDist command is a synonym for the
function of package proxy; the DTW distance is registered as
method="DTW" (see examples below).
The timeseries are stored as rows in the matrix argument
m. In other
m is an N * T matrix,
dtwDist will build NN ordered
pairs of timeseries, perform the corresponding NN
and return all of the results in a matrix. Each of the timeseries is T
dtwDist returns a square matrix, whereas the
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
proxy::dist() function sematics, use the two-arguments
dist(m,m). This will return a square
A square matrix whose element
[i,j] holds the Dynamic Time
Warp distance between row
i (query) and
j (reference) of
To convert a square cross-distance matrix (
crossdist object) to
dist() object, use a suitable conversion strategy
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## 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)
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