Dynamic Time Warping Distance

Given two time series - a query \(X = (X_1,X_2,\ldots,X_N)\) and a reference \(Y = (Y_1,Y_2,\ldots,Y_M)\), riem.dtw computes the most basic version of Dynamic Time Warping (DTW) distance between two series using a symmetric step pattern, meaning no window constraints and others at all. Although the scope of DTW in Euclidean space-valued objects is rich, it is scarce for manifold-valued curves. If you are interested in the topic, we refer to dtw package.

Usage

riem.dtw(riemobj1, riemobj2, geometry = c("intrinsic", "extrinsic"))

Arguments

riemobj1

a S3 "riemdata" class for \(M\) manifold-valued data along the curve.

riemobj2

a S3 "riemdata" class for \(N\) manifold-valued data along the curve.

geometry

(case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry.

Value

the distance value.

Validation status

This retained legacy interface is experimental. Its full numerical and statistical contract has not been independently verified across supported inputs. See riem-method-contracts and the installed contract table for method-specific assumptions, restrictions, and evidence scope.

Examples

# \donttest{
#-------------------------------------------------------------------
#                          Curves on Sphere
#
#  curve1 : y = 0.5*cos(x) on the tangent space at (0,0,1)
#  curve2 : y = 0.5*sin(x) on the tangent space at (0,0,1)
# 
#  we will generate two sets for curves of different sizes.
#-------------------------------------------------------------------
## GENERATION
clist = list()
for (i in 1:10){ # curve type 1
  vecx = seq(from=-0.9, to=0.9, length.out=sample(10:50, 1))
  vecy = 0.5*cos(vecx) + rnorm(length(vecx), sd=0.1)
  mats = cbind(vecx, vecy, 1)
  clist[[i]] = wrap.sphere(mats/sqrt(rowSums(mats^2)))
}
for (i in 1:10){ # curve type 2
  vecx = seq(from=-0.9, to=0.9, length.out=sample(10:50, 1))
  vecy = 0.5*sin(vecx) + rnorm(length(vecx), sd=0.1)
  mats = cbind(vecx, vecy, 1)
  clist[[i+10]] = wrap.sphere(mats/sqrt(rowSums(mats^2)))
}

## COMPUTE DISTANCES
outint = array(0,c(20,20))
outext = array(0,c(20,20))
for (i in 1:19){
  for (j in 2:20){
    outint[i,j] <- outint[j,i] <- riem.dtw(clist[[i]], clist[[j]], 
                                           geometry="intrinsic")
    outext[i,j] <- outext[j,i] <- riem.dtw(clist[[i]], clist[[j]],
                                           geometry="extrinsic")
  }
}

## VISUALIZE
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2), pty="s")
image(outint[,20:1], axes=FALSE, main="intrinsic DTW Distance")
image(outext[,20:1], axes=FALSE, main="extrinsic DTW Distance")

par(opar)
# }