distancePermutationEuclidean {CEGO}

Euclidean Distance for Permutations

Description

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

d(x,y) = \frac{1}{r} \sqrt(\sum_{i=1}^n (x_i - y_i)^2)

where n is the length of the permutations x and y, and scaling factor r=sqrt(2*4*c*(c+1)*(2*c+1)/6) with c=(n-1)/2 (if n is odd) or r=sqrt(2*c*(2*c-1)*(2*c+1)/3) with c=n/2 (if n is even).

Usage

distancePermutationEuclidean(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)
distancePermutationEuclidean(x,y)
p <- replicate(10,sample(1:5),simplify=FALSE)
distanceMatrix(p,distancePermutationEuclidean)