# Mahalanobis Distance

### Description

`mahaldis`

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

### Usage

1 | ```
mahaldis(x)
``` |

### Arguments

`x` |
matrix containing the variables. |

### 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 *G*. This is equivalent to the Mahalanobis distances in the space of the original variables (Legendre and Legendre 2012).

### Value

an object of class `dist`

.

### Author(s)

Pierre Legendre pierre.legendre@umontreal.ca

http://www.bio.umontreal.ca/legendre/indexEn.html

Ported to FD by Etienne Laliberté.

### 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

1 2 3 4 5 6 | ```
mat <- matrix(rnorm(100), 50, 20)
ex1 <- mahaldis(mat)
# check attributes
attributes(ex1)
``` |