Nonsupervised sequential classification and recognition of patterns

A Bayes approach to nonsupervised pattern recognition is given where -dimensional vector samples are received unclassified, i.e., any one of pattern sources , with corresponding probabilities of occurrence , caused each sample . The approach utilizes the fact that the cumulative distribution function (c.d.f.) of is a mixture c.d.f., . It is assumed that available a priori knowledge includes knowledge of and the family , where is characterized by a vector . In general, and are considered fixed but unknown, and conditional probability of error in deciding which source caused is minimized. When the functional form of in terms of is unknown, the family is taken to be the family of multinomial c.d.f.\´s--an application of the histogram concept to the nonsupervisory problem. Additional nonparameteric a priori knowledge about the family--such as is symmetrical, and/or differs from only by a translational vector--can be utilized in the Bayes solution.