Mahalanobis Distance

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

$D_{M}(X)={\sqrt {(X-\mathrm {M} )^{T}\Sigma ^{-1}(X-\mathrm {M} )}}$

where

• X is a vector of observations
• $\Sigma$ is the covariance matrix
• $\mathrm {M}$ is the mean vector

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

See Also

• Discriminant Analysis
• Divergence Statistic