I need to calculate the mahalanobis distance for a numerical dataset of 500 independent observations grouped in 12 groups (species). I know how to compare two matrices , but I do not understand how to calculate mahalanobis distance from my dataset i.e. between the 12 species. R documentation gives
mahalanobis(x, center, cov, inverted = FALSE, ...)
x is the matrix, cov is covariance matrix (cov(x))
but I do not understand how I can calculate the metric for the 12 groups
I found this question on mahalanobis but it does not answer really my question
Getting the distances is straigtforward if you organize your data in a 500 by 12 data.frame or matrix. To show you, first we create a data.frame with some toy data:
set.seed(1) # To ensure reproducibility of the random numbers
df <- data.frame(sapply(LETTERS[1:12], function(x) rnorm(500)))
# Adding some outliers
df[1,1] <- 20
df[200,5] <- 60
head(df)
# A B C D E F G H
# 1 20.0000000 0.07730312 1.13496509 0.8500435 -0.88614959 -1.8054836 0.7391149 0.5205997
# 2 0.1836433 -0.29686864 1.11193185 -0.9253130 -1.92225490 -0.6780407 0.3866087 0.3775619
# 3 -0.8356286 -1.18324224 -0.87077763 0.8935812 1.61970074 -0.4733581 1.2963972 -0.6236588
# 4 1.5952808 0.01129269 0.21073159 -0.9410097 0.51926990 1.0274171 -0.8035584 -0.5726105
# 5 0.3295078 0.99160104 0.06939565 0.5389521 -0.05584993 -0.5973876 -1.6026257 0.3125012
# 6 -0.8204684 1.59396745 -1.66264885 -0.1819744 0.69641761 1.1598494 0.9332510 -0.7074278
# I J K L
# 1 -1.1346302 1.5579537 -1.5163733 -1.1378698
# 2 0.7645571 -0.7292970 0.6291412 -0.9518105
# 3 0.5707101 -1.5039509 -1.6781940 1.6192595
# 4 -1.3516939 -0.5667870 1.1797811 0.1678136
# 5 -2.0298855 -2.1044536 1.1176545 -0.9081778
# 6 0.5904787 0.5307319 -1.2377359 1.3417959
where you have the 12 species called A-L. Organized in this way, you simply run the following line:
dist.sq <- mahalanobis(x = df, center = colMeans(df), cov = cov(df))
Remember, the function returns the square of the distances!
plot(sqrt(dist.sq))
I hope this helps.