Pairwise Squared Generalized Mahalanobis Distances

Function to calculate the squared generalized Mahalanobis distance between all pairs of rows in a data frame with respect to a covariance matrix. The element of the i-th row and j-th column of the distance matrix is defined as $$D_{ij}^2 = (\bold{x}_i - \bold{x}_j)' \bold{\Sigma}^{-1} (\bold{x}_i - \bold{x}_j)$$

D2.dist(data, cov, inverted = FALSE)

Arguments

data	a data frame or matrix of data (n x p).
cov	a variance-covariance matrix (p x p).
inverted	logical. If FALSE (default), cov is supposed to be a variance-covariance matrix.

Value

An object of class "dist".

References

Mahalanobis, P. C. (1936) On the generalized distance in statistics. Proceedings of The National Institute of Sciences of India, 12:49-55.

Author

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

See also

dist, singh

Examples

# Manly (2004, p.65-66)
x1 <- c(131.37, 132.37, 134.47, 135.50, 136.17)
x2 <- c(133.60, 132.70, 133.80, 132.30, 130.33)
x3 <- c(99.17, 99.07, 96.03, 94.53, 93.50)
x4 <- c(50.53, 50.23, 50.57, 51.97, 51.37)
x <- cbind(x1, x2, x3, x4)
Cov <- matrix(c(21.112,0.038,0.078,2.01, 0.038,23.486,5.2,2.844,
  0.078,5.2,24.18,1.134, 2.01,2.844,1.134,10.154), 4, 4)
D2.dist(x, Cov)
#>            1          2          3          4
#> 2 0.09103867                                 
#> 3 0.90451337 0.73086040                      
#> 4 1.88407643 1.59779871 0.44281866           
#> 5 2.69996452 2.17905736 0.91121818 0.21984612

# End (not run)