CEGO (version 2.0.0)

distancePermutationEuclidean: 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 $r=sqrt(2*4*n*(n+1)*(2*n+1)/6)$ (if n is odd) or $r=sqrt(2*n*(2*n-1)*(2*n+1)/3)$ (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)