dtwDist {dtw} | R Documentation |
Compute the dissimilarity matrix between a set of single-variate timeseries.
dtwDist(mx,my=mx,...) # dist(mx,my=mx,method="DTW",...)
mx |
numeric matrix, containing timeseries as rows |
my |
numeric matrix, containing timeseries as rows (for cross-distance) |
... |
arguments passed to the dtw call |
dtwDist
computes a dissimilarity matrix, akin to
dist
, based on the Dynamic Time Warping definition of a
distance between single-variate timeseries.
The dtwDist
command is a synonym for the
dist
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 words, if m
is an N * T matrix, dtwDist
will build
N*N ordered pairs of timeseries, perform the corresponding N*N
dtw
alignments, and return all of the results in a matrix. Each
of the timeseries is T elements long.
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 with the dist
function
sematics, use the two-arguments call as dist(m,m)
. This will
return a square crossdist
object.
A square matrix whose element [i,j]
holds the Dynamic Time Warp
distance between row i
(query) and j
(reference) of
mx
and my
, i.e. dtw(mx[i,],my[j,])$distance
.
To convert a square cross-distance matrix (crossdist
object) to
a symmetric dist
object, use a suitable conversion
strategy (see examples).
Toni Giorgino
Other "distance" functions are: dist
,
vegdist
in package vegan
,
distance
in package analogue
, etc.
## Symmetric step pattern => symmetric dissimilarity matrix; ## no problem coercing it to a dist object: m <- matrix(0,ncol=3,nrow=4) m <- row(m) dist(m,method="DTW"); # Old-fashioned call style would be: # dtwDist(m) # as.dist(dtwDist(m)) ## Find the optimal warping _and_ scale factor at the same time. ## (There may be a better, analytic way) # Prepare a query and a reference query<-sin(seq(0,4*pi,len=100)) reference<-cos(seq(0,4*pi,len=100)) # Make a set of several references, scaled from 0 to 3 in .1 increments. # Put them in a matrix, in rows scaleSet <- seq(0.1,3,by=.1) referenceSet<-outer(1/scaleSet,reference) # The query has to be made into a 1-row matrix. # Perform all of the alignments at once, and normalize the result. dist(t(query),referenceSet,meth="DTW")->distanceSet # The optimal scale for the reference is 1.0 plot(scaleSet,scaleSet*distanceSet, xlab="Reference scale factor (denominator)", ylab="DTW distance",type="o", main="Sine vs scaled cosine alignment, 0 to 4 pi") ## Asymmetric step pattern: we can either disregard part of the pairs ## (as.dist), or average with the transpose mm <- matrix(runif(12),ncol=3) dm <- dist(mm,mm,method="DTW",step=asymmetric); # a crossdist object # Old-fashioned call style would be: # dm <- dtwDist(mm,step=asymmetric) # as.dist(dm) ## Symmetrize by averaging: (dm+t(dm))/2 ## check definition stopifnot(dm[2,1]==dtw(mm[2,],mm[1,],step=asymmetric)$distance)