| dtw {dtw} | R Documentation |
Compute Dynamic Time Warp and find optimal alignment between two time series.
dtw(x, y=NULL,
dist.method="Euclidean",
step.pattern="s",
window.type="none",
keep.internals=FALSE,
distance.only=FALSE,
... )
is.dtw(d)
x |
query vector or local cost matrix |
y |
template vector, unused if x given as cost matrix |
dist.method |
pointwise (local) distance function. See
dist in package proxy |
step.pattern |
step pattern. Character "s" (symmetric1), "a"
(asymmetric), or a stepPattern object describing the
local warping steps allowed with their cost (see stepPattern) |
window.type |
windowing function. Character: "none", "itakura", "sakoechiba", "slantedband", or a function (see details). |
keep.internals |
don't discard the cumulative cost matrix and other internal structures |
distance.only |
only compute distance (no backtrack, faster) |
d |
an arbitrary R object |
... |
additional arguments, passed to window.type |
The function performs Dynamic Time Warp (DTW) and computes the optimal
alignment between two time series x and y, given as
numeric vectors. The ``optimal'' alignment minimizes the sum of
distances between aligned elements. Lengths of x and y
may differ.
The (local) distance between elements of x (query) and y
(template) is computed passing x and y to the
dist function in package proxy
with the method dist.method.
Multivariate time series and arbitrary distance metrics can be handled
by supplying a local-distance matrix. Element [i,j] of the
local-distance matrix is understood as the distance between element
x[i] and y[j]. The distance matrix has therefore
n=length(x) rows and m=length(y) columns (see note
below).
Several common variants of DTW are supported via the
step.pattern argument, which defaults to symmetric1
(White-Neely). Most common step patterns are pre-defined, plus the
user can write their own. See stepPattern for details.
Windowing is supported by supplying a name into the window.type
argument (abbreviations allowed) between the built-in types:
"none""sakoechiba""slantedband""itakura"
window.type can also be an user-defined windowing function.
See dtwWindowingFunctions for all available windowing
functions, details on user-defined windowing, and a discussion of the
(mis)naming of the "Itakura" parallelogram as a global constraint.
Some windowing functions may require parameters, such as the
window.size argument.
A native (fast, compiled) version of the function is normally available. If it is not, an interpreted equivalent will be used as a fall-back, with a warning.
is.dtw tests whether the argument is of class dtw.
An object of class dtw with the following items:
distance |
the computed distance not normalized. Normalization depends on the chosen step pattern. |
N,M |
query and template length |
call |
the function call that created the object |
index1 |
matched elements: indices in x |
index2 |
corresponding mapped indices in y |
stepPatterns |
the stepPattern object used for the computation |
costMatrix |
if keep.internals=TRUE, the cumulative
cost matrix |
directionMatrix |
if keep.internals=TRUE, the
directions of steps that would be taken at each alignment pair
(integers indexing step patterns) |
Cost matrices (both input and output) have query elements row-wise (first index), and template elements column-wise (second index). They print according to the usual convention, with indexes increasing down- and rightwards. Many DTW papers and tutorials show matrices according to plot-like conventions, i.e. template index growing upwards. This may be confusing.
Toni Giorgino
Sakoe, H.; Chiba, S., Dynamic programming algorithm optimization for spoken word recognition,
Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on ,
vol.26, no.1, pp. 43-49, Feb 1978 URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1163055
dtwDist, for iterating dtw over a set of timeseries;
dtwWindowingFunctions, for windowing and global constraints;
stepPattern, step patterns and local constraints;
plot.dtw, plot methods for DTW objects.
To generate a local distance matrix, the functions
dist in package proxy,
distance in package analogue,
outer may come handy.
## A noisy sine wave as query
idx<-seq(0,6.28,len=100);
query<-sin(idx)+runif(100)/10;
## A cosine is for template; sin and cos are offset by 25 samples
template<-cos(idx)
plot(template); lines(query,col="blue");
## Find the best match
alignment<-dtw(query,template);
## Display the mapping, AKA warping function - may be multiple-valued
## Equivalent to: plot(alignment,type="alignment")
plot(alignment$index1,alignment$index2,main="Warping function");
## Confirm: 25 samples off-diagonal alignment
lines(1:100-25,col="red")
#########
##
## Subsetting allows warping and unwarping of
## timeseries according to the warping curve.
## See first example below.
##
## Most useful: plot the warped query along with template
plot(template)
lines(query[alignment$index1]~alignment$index2,col="blue")
## Plot the (unwarped) query and the inverse-warped template
plot(query,type="l",col="blue")
points(template[alignment$index2]~alignment$index1)
#########
##
## Contour plots of the cumulative cost matrix
## similar to: plot(alignment,type="density") or
## dtwPlotDensity(alignment)
## See more plots in ?plot.dtw
##
## keep = TRUE so we can look into the cost matrix
alignment<-dtw(query,template,keep=TRUE);
contour(alignment$costMatrix,col=terrain.colors(100),x=1:100,y=1:100,
xlab="Query (noisy sine)",ylab="Template (cosine)");
lines(alignment$index1,alignment$index2,col="red",lwd=2);
#########
##
## An hand-checkable example
##
ldist<-matrix(1,nrow=6,ncol=6); # Matrix of ones
ldist[2,]<-0; ldist[,5]<-0; # Mark a clear path of zeroes
ldist[2,5]<-.01; # Forcely cut the corner
ds<-dtw(ldist); # DTW with user-supplied local
# cost matrix
da<-dtw(ldist,step="a"); # Also compute the asymmetric
plot(ds$index1,ds$index2,pch=3); # Symmetric: alignment follows
# the low-distance marked path
points(da$index1,da$index2,col="red"); # Asymmetric: visiting
# 1 is required twice
ds$distance;
da$distance;