The Mahalanobis distance and its relationship to principal component scores
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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.
[1] P. Mahalanobis. On the generalized distance in statistics , 1936 .
[2] Ian Witten,et al. Data Mining , 2000 .
[3] R. Brereton. The chi squared and multinormal distributions , 2015 .