Re‐evaluating the role of the Mahalanobis distance measure

It is shown that the sum of squares of the standardised scores of all non‐zero principal components (PCs) equals the squared Mahalanobis distance. A new distance measure, the reduced Mahalanobis distance, is explored in which the number of PCs retained is less than the full rank model. It is illustrated by both one‐class and two‐class classifiers. Linear discriminant analysis can be employed as a soft model, and principal component analysis using the pooled variance‐covariance matrix is introduced as an intermediate view between conjoint and disjoint models allowing linear discriminant analysis to be used on these reduced rank models. By choosing the most discriminatory PCs, it can be shown that the reduced Mahalanobis distance has superior performance over the full rank model for discriminating via soft models.