Mahalanobis Distance

Computes the squared Mahalanobis distance of all rows in x.

Usage

# S4 method for class 'CompositionMatrix'
mahalanobis(x, center, cov, ..., robust = TRUE, method = c("mve", "mcd"))

# S4 method for class 'ILR'
mahalanobis(x, center, cov, ..., robust = TRUE, method = c("mve", "mcd"))

Arguments

x

A CompositionMatrix or an ILR object.

center

A numeric vector giving the mean vector of the distribution. If missing, will be estimated from x.

cov

A numeric matrix giving the covariance of the distribution. If missing, will be estimated from x.

...

Extra parameters to be passed to MASS::cov.rob(). Only used if robust is TRUE.

robust

A logical scalar: should robust location and scatter estimation be used?

method

A character string specifying the method to be used. It must be one of "mve" (minimum volume ellipsoid) or "mcd" (minimum covariance determinant). Only used if robust is TRUE.

Value

A numeric vector.

See also

stats::mahalanobis()

Other statistics: aggregate(), condense(), covariance(), dist, margin(), mean(), pip(), quantile(), scale(), variance(), variance_total(), variation()

Author

N. Frerebeau

Examples

## Data from Aitchison 1986
data("hongite")

## Coerce to compositional data
coda <- as_composition(hongite)

## Mahalanobis distance
mahalanobis(coda)
#> 
#>        H1        H2        H3        H4        H5        H6        H7        H8 
#>  5.007867  1.515868  2.640239  0.733542 43.447199  7.290514 87.750750 55.482671 
#>        H9       H10       H11       H12       H13       H14       H15       H16 
#>  1.540124  9.858429  2.441832  6.315752  5.180475 34.016193  1.854172 24.280570 
#>       H17       H18       H19       H20       H21       H22       H23       H24 
#> 26.654962  1.847951  2.839573  5.322244  4.088381  1.715226  4.433984  3.373827 
#>       H25 
#> 19.346698