distancePermutationLee {CEGO}

Lee Distance for Permutations

Description

Usually a string distance, with slightly different definition. Adapted to permutations as:

d(x,y) = \sum_{i=1}^n min(|x_i - y_i|), n- |x_i - y_i|)

where n is the length of the permutations x and y.

Usage

distancePermutationLee(x, y)

Arguments

x

first permutation (integer vector)

y

second permutation (integer vector)

Value

numeric distance value

d(x,y)

, scaled to values between 0 and 1 (based on the maximum possible distance between two permutations)

References

Lee, C., "Some properties of nonbinary error-correcting codes," Information Theory, IRE Transactions on, vol.4, no.2, pp.77,82, June 1958

Examples

x <- 1:5
y <- c(5,1,2,3,4)
distancePermutationLee(x,y)
p <- replicate(10,sample(1:5),simplify=FALSE)
distanceMatrix(p,distancePermutationLee)