distancePermutationEuclidean {CEGO} | R Documentation |

## 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)
```

[Package

*CEGO*version 2.4.3 Index]