Mahalanobis Distance

Abstract

The Mahalanobis distance is the distance from X to the quantity μ defined as: d 2 M (X, μ) = (X − μ) t −1 (X − μ). This distance is based on the correlation between variables or the variance-covariance matrix. It differs from the Euclidean distance in that it takes into account the correlation of the data set and does not depend on the scale of measurement. Mahalanobis distance is widely used in cluster analysis and other classification methods. HISTORY The Mahalanobis distance was introduced by Mahalanobis, P.C. in 1936. MATHEMATICAL ASPECTS If μ i denotes E(X i), then by definition the expected value of X = (X 1 ,. .. , X p) vector: E[X] = μ =