Distance-based approaches to pattern recognition via embedding

The most popular separation criterion of establishing rules for discrimination and recognition (classification) of patterns is the Fisher discriminant (separation) ratio. The approach proposed by Fisher assumes equality of population covariance matrices, but does not explicitly require multivariate normality. However, optimal classification performance of Fisher's discriminant function can only be expected when multivariate normality is present as well, since only good discrimination can ensure good allocation. In practice, we often are in need of analyzing input data samples, which are not adequate for Fisher's classification rule, such that the distributions of the groups are not multivariate normal or covariance matrices of those are different or there are strong multi-nonlinearities. In this paper, distance-based approaches for pattern classification (recognition) via embedding are proposed which allow one to classify, say, radar clutter into one of several major categories, including bird, weather, and target classes. These approaches do not require the arbitrary selection of priors as in the Bayesian classifier and represent the Improved pattern recognition (classification) procedures that allows one to take into account the cases which are not adequate for Fisher's classification rule. Moreover, they allow one to classify sets of multivariate observations, where each of the sets contains more than one observation. For the cases, which are adequate for Fisher's classification rule, the proposed approaches give the results similar to that of Fisher's classification rule. For illustration, a numerical example is given.