distancePermutationManhattan {CEGO}

Manhattan Distance for Permutations

Description

Manhattan distance for permutations, scaled to values between 0 and 1:

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

where n is the length of the permutations x and y, and scaling factor r=(n^2-1)/2 (if n is odd) or r=((n^2)/2 (if n is even).

Usage

distancePermutationManhattan(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)

Examples

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