mahalanobis {stats} R Documentation

## Mahalanobis Distance

### Description

Returns the squared Mahalanobis distance of all rows in `x` and the vector mu = `center` with respect to Sigma = `cov`. This is (for vector `x`) defined as

D^2 = (x - μ)' Σ^-1 (x - μ)

### Usage

```mahalanobis(x, center, cov, inverted = FALSE, ...)
```

### Arguments

 `x` vector or matrix of data with, say, p columns. `center` mean vector of the distribution or second data vector of length p or recyclable to that length. If set to `FALSE`, the centering step is skipped. `cov` covariance matrix (p x p) of the distribution. `inverted` logical. If `TRUE`, `cov` is supposed to contain the inverse of the covariance matrix. `...` passed to `solve` for computing the inverse of the covariance matrix (if `inverted` is false).

`cov`, `var`

### Examples

```require(graphics)

ma <- cbind(1:6, 1:3)
(S <-  var(ma))
mahalanobis(c(0, 0), 1:2, S)

x <- matrix(rnorm(100*3), ncol = 3)
stopifnot(mahalanobis(x, 0, diag(ncol(x))) == rowSums(x*x))
##- Here, D^2 = usual squared Euclidean distances

Sx <- cov(x)
D2 <- mahalanobis(x, colMeans(x), Sx)
plot(density(D2, bw = 0.5),
main="Squared Mahalanobis distances, n=100, p=3") ; rug(D2)
qqplot(qchisq(ppoints(100), df = 3), D2,
main = expression("Q-Q plot of Mahalanobis" * ~D^2 *
" vs. quantiles of" * ~ chi^2))
abline(0, 1, col = 'gray')
```

[Package stats version 3.6.0 Index]