Multidimensional Scaling (MDS) is certainly an option to be considered.
Its suitability depends, of course, on the specific application.
In my case, which is conceptually similar to Martin's, that option was
discarded.
And I think I can explain why whith this single image:
http://www.geeitema.org/doc/guenmap/docs/distances.gif
Here, three types of distances between all pairs from a set of points
are compared.
The reference distance (red) is the "cost based" distance (or "water
distance"), which is the minimum distance measured within the
"permisible" region (i.e. "as the fish swims").
In black are represented the corresponding euclidean distances, while in
blue, the corresponding MDS distances (in 2D).
As you can see, the MDS approach corrects the "bias" in the long terrm.
However the variability around the "correct" value holds.
So, while it provides the best overall euclidean approximation, it does
not account for the behaviour due to the shape of the region.
Since the latter was what we was looking for, we discarded this approach.
One could try to use MDS with higher dimension. But it does not improve
things very much, specially if you have regions with "holes".
Distances in such regions don't have an euclidean representation
regardless of the dimension.
Bests
ƒacu.-
Greg Snow escribió:
Another approach that might be simpler (or it may oversimplify and not give
good results) is to compute the distances between your points as the fish swim,
then use multi dimensional scaling (cmdscale function or others) to get a set
of points that represent those distances and do the rest of your analysis on
the transformed points.
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