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Computing Distribution Overlap - Nearest Neighbour

We  are trying to explore and solve a problem where two data clouds  (dis-
tributions)  in  hyperspace need to be compared. We consider the  need  to
compute  the /overlap/ between the two clouds, but the problem is hard be-
cause we deal with a high dimensional space (>100 dims) and a small number
n of sample points (100<~n<~1000).

Is  there any known approach for doing this? Could anybody please point us
to a paper on the subject? So far we have computed the Euclidean and shuf-
fle  distance  between each point that forms one cloud with each point  in
the other cloud.

Many thanks,

Roy

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