Semi-invariants of the interclass Mahalanobis distance
Rafael C. Gonzalez, C. G. Wagner · IEEE Transactions on Systems Man and Cybernetics · 1984
A new closed-form expression for the semi-invariants of the interclass Mahalanobis distance is derived. Typically, in the analysis of two multivariate Gaussian populations with different covariance matrices, simultaneous diagonalization of these matrices is required. The semi-invariants are given directly in terms of the mean vectors and inverse covariance matrices by the results established. In addition, a new iterative algorithm is derived for computing the moments of the interclass Mahalanobis distance from the semi-invariants.