Compute Warping Path Area
Compute the area between the warping function and the diagonal (no-warping) path, in unit steps.
- an object of class
Above- and below- diagonal unit areas all count plus one (they
do not cancel with each other). The "diagonal" goes from one corner to
the other of the possibly rectangular cost matrix, therefore having a
M/N, not 1, as in
The computation is approximate: points having multiple correspondences are averaged, and points without a match are interpolated. Therefore, the area can be fractionary.
The area, not normalized by path length or else.
There could be alternative definitions to the area, including considering the envelope of the path.
ds<-dtw(1:4,1:8); plot(ds);lines(seq(1,8,len=4),col="red"); warpArea(ds) ## Result: 6 ## index 2 is 2 while diag is 3.3 (+1.3) ## 3 3 5.7 (+2.7) ## 4 4:8 (avg to 6) 8 (+2 ) ## -------- ## 6