dtw (version 1.4-3)

dtw: Dynamic Time Warp

Description

Compute Dynamic Time Warp and find optimal alignment between two time series.

Usage

dtw(x, y=NULL,
         dist.method="Euclidean",
         step.pattern="s",
         window.type="none",
         keep.internals=FALSE,
         distance.only=FALSE,
         ... )
is.dtw(d)

Arguments

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

Value

• 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)

code

dtw

concept

• Dynamic Time Warp
• Dynamic programming
• Align timeseries
• Minimum cumulative cost
• Distance

Details

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"

{No windowing (default)} "sakoechiba"{A band around main diagonal} "slantedband"{A band around slanted diagonal} "itakura"{So-called Itakura parallelogram}

References

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

See Also

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.

Examples

## 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;