The Mahalanobis distance and its relationship to principal component scores

The Mahalanobis distance is one of the most common measures in chemometrics, or indeed multivariate statistics. It can be used to determine whether a sample is an outlier, whether a process is in control or whether a sample is a member of a group or not. In the article on the chi-squared and multinormal distributions, we discussed the role of the Mahalanobis distance in the chisquared distribution, although it is used in many other situations [1]. Although many people use this distance in chemometrics, it is poorly understood, especially its relationship to principal components analysis (PCA), another very common technique.