Lee Distance for Permutations
Usually a string distance, with slightly different definition. Adapted to permutations as:
d(x,y) = ∑_{i=1}^n min(|x_i - y_i|), n- |x_i - y_i|)
where n is the length of the permutations x and y.
distancePermutationLee(x, y)
x |
first permutation (integer vector) |
y |
second permutation (integer vector) |
numeric distance value
d(x,y)
, scaled to values between 0 and 1 (based on the maximum possible distance between two permutations)
Lee, C., "Some properties of nonbinary error-correcting codes," Information Theory, IRE Transactions on, vol.4, no.2, pp.77,82, June 1958
x <- 1:5 y <- c(5,1,2,3,4) distancePermutationLee(x,y) p <- replicate(10,sample(1:5),simplify=FALSE) distanceMatrix(p,distancePermutationLee)
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