Recently I have started looking for the definition of normalized Euclidean distance between two real vectors u and v. So far, I have discovered two apparently unrelated definitions:
I am familiar with the context of the Wikipedia definition. However, I am yet to discover any context for the Wolfram.com definition:
NormalizedSquaredEuclideanDistance[u,v] is equivalent to 1/2*Norm[(u-Mean[u])-(v-Mean[v])]^2/(Norm[u-Mean[u]]^2+Norm[v-Mean[v]]^2)
I simplified the above expression to the following:
NormalizedSquaredEuclideanDistance[u,v] = 0.5*Var(u - v)/[Var(u) + Var(v)]
(where Var(x) denotes the variance of x)
The intuitive meaning of this definition is not very clear. Any help on this will be appreciated.
Thanks and regards,