What is Mahalanobis Distance?

The Mahalanobis Distance is a multivariate form of the Euclidean Distance that accounts for correlation between dimensions. If the correlation between features is 0, the Mahalanobis Distance is equivalent to the Euclidean distance. The Mahalanobis Distance is frequently used in multivariate outlier detection, as it measures the distance of each observation to the mass of the distribution using its mean and correlation structure. For two vectors x and x’ and covariance matrix Σ, the Mahalanobis Distance is given by: