An interpretation of Mahalanobis distance in the dual space

摘要

Using the concept of a dual space, nk-dimensional vectors can be viewed as k points in an n-dimensional co-ordinate system. The relationships between the basic statistical properties of a k-variate sample and the geometrical properties of such a space are developed and the concept extended to two samples drawn from different populations, with derivation of the geometrical meaning of Mahalanobis distance. This geometrical approach provides valuable insight into why different feature subsets may or may not have high discriminatory potential, and shows that clustering in the dual space, or its subspaces, does not necessarily yield an effective feature selection technique.