Mahalanobis Distance

Mahalanobis distance measures the distance between a point and a distribution. It takes into account the correlations of the data set and is scale-invariant.

Defined as:

$$D^2=(x-\mu {)}^T{S}^{-1}(x-\mu )$$

where:

• $x$ is a vector of the point whose distance from the distribution is being measured
• $\mu$ is the mean vector of the distribution
• $S$ is the covariance matrix of the distribution
• $S^{-1}$ is the inverse of the covariance matrix