Learning to recognize patterns without a teacher

An important problem in pattern recognition or signal detection is the recognition of a pattern that is completely characterized statistically except for a finite set of unknown parameters. If a machine is required to solve such a problem on a number of occasions, it is possible to take advantage of this repetition. One can design a machine that will extract more and more of the pertinent information about these unknown parameters as it recognizes the patterns and readjusts itself to be more selective to them; the machine improves in performance as it gains experience on the problem. This paper presents a model suitable for many such problems and evolves a solution in the form of a machine that "learns" to solve the problem without external aid. Such machines are said to "learn without a teacher." The Bayes solution to the model problem requires the computation of the a posteriori probability density of the unknown parameters. A recursive equation for this density is derived. This equation describes the structure of a relatively simple system of finite size that may be realized in a delay-feedback form. The application of the model and the synthesis of a learning system are illustrated by the derivation of a receiver for the detection of signals of unknown amplitude in white Gaussian noise.