Mahalanobis distance

Summary

The Mahalanobis distance measures how far a point lies from the centre of a multivariate distribution. Its units are adapted to the spread and the correlations of the distribution. It is the Euclidean distance after the data are transformed so that the covariance matrix becomes the identity. It is used to detect outliers and in linear discriminant analysis. The density of a multivariate normal distribution is constant on the sets of constant Mahalanobis distance.