Mahalanobis distance measure problem

HCA is a common tool that is used to determine the natural grouping of objects, based on their multivariate responses [75]. In PAT, this method can be used to determine natural groupings of samples or variables in a data set. Like the classification methods discussed above, HCA requires the specification of a space and a distance measure. However, unlike those methods, HCA does not involve the development of a classification rule, but rather a linkage rule, as discussed below. For a given problem, the selection of the space (e.g., original x variable space, PC score space) and distance measure (e.g.. Euclidean, Mahalanobis) depends on the specific information that the user wants to extract. For example, for a spectral data set, one can choose PC score space with Mahalanobis distance measure to better reflect separation that originates from both strong and weak spectral effects. 

Problem 4.8 Classification of Pottery from Pre-classical Sites in Italy, Using Euclidean and Mahalanobis Distance Measures... 

To avoid this waste of time and money, and also to use those samples that have the largest spread of variations not only in those variables whose values are known but also in those variables that we may not even know exist but that have an effect on the spectrum, what is needed is a method of selecting samples that has certain characteristics. Those characteristics are as follows (a) It is based on measurements of the optical data only, and (b) it selects the samples that show the most differences in the spectra. An algorithm based on Gauss-Jordan reduction has been developed to overcome this problem [7], and here we present an approach based on the Mahalanobis distance concept. 

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