Euclidean Distance for Permutations
Euclidean distance for permutations, scaled to values between 0 and 1:
d(x,y) = 1/r * sqrt(∑_{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).
distancePermutationEuclidean(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)
x <- 1:5 y <- c(5,1,2,3,4) distancePermutationEuclidean(x,y) p <- replicate(10,sample(1:5),simplify=FALSE) distanceMatrix(p,distancePermutationEuclidean)
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