On a class of unsupervised estimation problems

The unsupervised estimation problem has received considerable attention during the last three years. The problem usually considered, however, is only one of a class of unsupervised estimation problems. In this paper, a "mixture approach" defined previously is used to define this class of unsupervised estimation problems, and state precisely the a priori knowledge used to define each problem. After using available a priori knowledge to construct precisely the mixture appropriate to the unsupervised problem, the parameters characterizing this particular unsupervised problem can be estimated, or a Bayes minimum conditional risk receiver can be constructed. The class of unsupervised estimation problems includes the following cases: unknown number of pattern classes, dependent observation vectors, nonstationary class probabilities, more than one vector observation taken with a single class active, lack of synchronization, and unsupervised learning control and communications.