Properties of the reduced semi-invariants of the interclass Mahalanobis distance and their application to pattern recognition

Properties of the reduced semi-invariants of the interclass Mahalanobis distance (RSIM) are developed and used for pattern recognition in this work. These properties are understood in terms of the parameters of the Gaussian N dimensional statistical populations used to compute the RSIM. Some graphical representations of the RSIM are presented which serve as a basic framework for the use of the RSIM in pattern recognition. The implementation of computer programs to calculate the RSIM is discussed in addition to a procedure to compute the central moments of the Mahalanobis distance from the RSIM which involves solving a linear Diophantine equation iteratively. The results of a recognition program utilizing the RSIM is then presented. This program represents a typical use of the RSIM in a pattern recognition system designed to characterize changes occurring to sets of statistical data with time. A summary of the usefulness of the RSIM is then given.