The unsupervised estimation problem has been conveniently formulated in terms of a mixture density. It has been shown that a criterion naturally arises whose maximum defines the Bayes minimum risk solution. This criterion is the expected value of the natural log of the mixture density. By making the assumptions that the component densities in the mixture are truncated Gaussian, the criterion has a greatly simplified form. This criterion can be used to resolve mixtures when the number of classes as well as the class covariances are unknown. In this paper a technique is presented where an assumed test covariance is supplied by an experimenter who uses a test function as a "portable magnifying glass" to examine data. Because the experimenter supplies the covariance and thus the test function, the technique is especially suited for interactive data analysis.

Two groups ofL-dimensional observations of sizeN_{1}andN_{2}are known to be random vector variables from two unknown probability distribution functions [1]. A method is discussed for obtaining anl-dimensional linear subspace of the observation space in which thel-variate marginal distributions are most separated, based on a nonparametric estimate of probability density functions and a distance criterion. The distance used essentially is theL_{2}norm of the difference between Parzen estimates of the two densities. An algorithm is developed that determines the subspace for which the distance between the two densities is maximized. Computer simulations are performed.