A Contribution to the Schlesinger’s Algorithm Separating Mixtures of Gaussians

Abstract

This paper contributes to the statistical pattern recognition problem in which two classes of objects are considered and either of them is described by a mixture of Gaussian distributions. The components of either mixture are known, and unknown are only their weights. The class (state) of the object k is to be found at the mentioned incomplete a priori knowledge of the statistical model and the known observation x. The task can be expressed as a statistical decision making with non-random interventions. The task was formulated and solved first by Anderson and Bahadur [1] for a simpler case where each of two classes is described by a single Gaussian. The more general formulation with more Gaussians describing each of two classes was suggested by M.I. Schlesinger under the name generalized Anderson’s task (abbreviated GAT in the sequel). The linear solution to GAT was proposed in [5] and described recently in a more general context in a monograph [4].

This contribution provides (i) a formulation of GAT, (ii) a taxonomy of various solutions to GAT including their brief description, (iii) the novel improvement to one of its solutions by proposing better direction vector for next iteration, (iv) points to our implementation of GAT in a more general Statistical Pattern Recognition Toolbox (in MATLAB, public domain) and (v) shows experimentally the performance of the improvement (iii).