Pairwise Mahalanobis distance in R

Question

I'm trying to calculate a Mahalanobis-type pairwise distance matrix in R. I have 33 individuals, each with 10 variables. The idea is to get a distance matrix D, where

$$D_{i,j}=(\mathbf{X}_i-\mathbf{X}_j)W^{-1}(\mathbf{X}_i-\mathbf{X}_j)^T$$

However I haven't been able build proper code for it.

Answer 1

Here is the code to do it:

library("MASS")
library("ICSNP")

x0<-mvrnorm(33,1:10,diag(c(seq(1,1/2,l=10)),10))
x1<-pair.diff(x0) #C-implementation.
dM<-mahalanobis(x1,rep(0,10),var(x1))

Following Roman Luštrik's suggestion, here are more details. The OP asked for pairwise Mahalanobis distance, which are multivariate U-statistics of distance. I have first seen them mentionned in Croux et al. 94 (below equation 6.4) but i'm sure others such as Oja have explored this concept.

Answer 2

The following worked for me in similar example where R is a dataframe of 54 individuals and 8 variables. Mahalanobis distance Ma between individuals X1 and X2 can be computed as ff:

# express difference (X1-X2) as atomic row vector
d <- as.matrix(X1-X2)[1,] 

# find inverse of covariance matrix
Sx <- solve(cov(R))

# Mahalanobis calculation forced in two steps
Ma <- (d %\*% Sx) %\*% d

Answer 3

You could try the gendistance function in the nbpMatching package

Here's a short example modified from the help page, with two variables instead of 10:

df <- data.frame(id=1:33, val1=rnorm(33), val2=rnorm(33))
df.dist <- gendistance(df, idcol=1)
df.dist$dist

The distance matrix will have a 34th row/column-- this is for use in matching, and you can ignore it.