Mahalonobis distance in R, error: system is computationally singular

mahalanobis uses the covariance matrix, cov, (more precisely the inverse of it) to transform the coordinate system, then compute Euclidian distance in the new coordinates. A standard reference is Duda & Hart "Pattern Classification and Scene Recognition"

Looks like your cov matrix is singular. Perhaps there are linearly-dependent columns in "dat" that are unnecessary? Setting the tolerance to zero won't help if the covariance matrix is truly singular. The first thing to do, instead, is look for columns that might be a rescaling of some other column, or might be just a sum of 2 or more other columns and remove them. Such columns are redundant for the mahalanobis distance.

BTW, since mahalanobis distance is effectively a rescaling and rotation, calling the scaling function looks superfluous - any reason why you want that?

The Mahalanobis distance requires you to calculate the inverse of the covariance matrix. The function mahalanobis internally uses solve which is a numerical way to calculate the inverse. Unfortunately, if some of the numbers used in the inverse calculation are very small, it assumes that they are zero, leading to the assumption that it is a singular matrix. This is why it specifies that they are computationally singular, because the matrix might not be singular given a different tolerance.

The solution is to set the tolerance for when it assumes that they are zero. Fortunately, mahalanobis allows you to pass this parameter (tol) to solve:

mahalanobis(dat,center=centroid,cov=cov(dat),tol=1e-20)
# [1] 24.215494 28.394913  6.984101 28.004975 11.095357 14.401967 ...