dtwDist: Compute a dissimilarity matrix
In dtw: Dynamic time warping algorithms

Description Usage Arguments Details Value Note Author(s) See Also Examples

Compute the dissimilarity matrix between a set of single-variate timeseries.

1 2	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)