dtw (version 1.22-3)

# dtwDist: Compute a dissimilarity matrix

## Description

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

## Usage

`dtwDist(mx, my = mx, ...)`

## Arguments

mx

numeric matrix, containing timeseries as rows

my

numeric matrix, containing timeseries as rows (for cross-distance)

...

arguments passed to the `dtw()` call

## Value

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`.

## Details

`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 `proxy::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 NN ordered pairs of timeseries, perform the corresponding NN `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 `proxy::dist()` function sematics, use the two-arguments call as `dist(m,m)`. This will return a square `crossdist` object.

## Examples

```# NOT RUN {

## 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)

# }
```