FD (version 1.0-12.3)

mahaldis: Mahalanobis Distance

Description

mahaldis measures the pairwise Mahalanobis (1936) distances between individual objects.

Usage

mahaldis(x)

Value

an object of class dist.

Arguments

x

matrix containing the variables. NAs are not tolerated.

Author

Pierre Legendre

http://adn.biol.umontreal.ca/~numericalecology/

Ported to FD by Etienne Laliberté.

Details

mahaldis computes the Mahalanobis (1936) distances between individual objects. The Mahalanobis distance takes into account correlations among variables and does not depend on the scales of the variables.

mahaldis builds on the fact that type-II principal component analysis (PCA) preserves the Mahalanobis distance among objects (Legendre and Legendre 2012). Therefore, mahaldis first performs a type-II PCA on standardized variables, and then computes the Euclidean distances among (repositioned) objects whose positions are given in the matrix \(\mathbf{G}\). This is equivalent to the Mahalanobis distances in the space of the original variables (Legendre and Legendre 2012).

References

Legendre, P. and L. Legendre (2012) Numerical Ecology. 3nd English edition. Amsterdam: Elsevier.

See Also

mahalanobis computes the Mahalanobis distances among groups of objects, not individual objects.

Examples

mat <- matrix(rnorm(100), 50, 20)

ex1 <- mahaldis(mat)

# check attributes
attributes(ex1)