RE: measuring distance in grids

[Jack Buckley]

By an amazing coincidence, I happen to be reading about this very topic
vis-a-vis graph theory today. In Davidson (1983-Multidimensional Scaling in
the Wiley Probability series), "nonmetric" methods are discussed, in which
the simple Euclidean distance is transformed by a simple monotone function:

Euclidean: d[i,j] = sqrt(sum[d](x[i,d]-x[j,d])^2)   (where d is # of
dimensions, which is 2 for your grid)

"Nonmetric:" d[i,j] = f(sqrt(sum[d](x[i,d]-x[j,d])^2)

As Watts(1999-Small Worlds) points out, nonmetric is a misnomer. Such a
distance is every bit as metric as a Euclidean one. Nevertheless, the work
that you are replicating may have used some sort of tranformation on its
distances (perhaps they took the natural log of them or something).

This is probably unhelpful, but good luck!

Jack
___________________
Jack Buckley
Department of Political Science
State University of New York at Stony Brook
address@hidden
(631) 632-4353

"The generation of random numbers is too important to be left to
chance." -Robert Coveyou




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