Mahalanobis Distance

From Open Risk Manual

Definition

The Mahalanobis Distance of an observation of random vector X that is sampled from a multivariate distribution is a measure of its "distance" from the mean of the distribution

Formula

D_M(X) = \sqrt{(X - \Mu)^T \Sigma^{-1} (X - \Mu)}

where

  • X is a vector of observations
  • \Sigma is the covariance matrix
  • \Mu is the mean vector

If the covariance matrix is the identity matrix, the Mahalanobis distance reduces to the Euclidean distance


See Also