Some recognizers for stochastic time-varying patterns with additive noise are studied. As in binary communication channels with fading, it is supposed that the fluctuation of a pattern (or signal) may be approximated by a stationary Gaussian autoregressive process with known parameters. Each measurement belongs to either of two classes: the pattern plus noise or noise alone. Under these assumptions, optimum dichotomizers with supervized learning are discussed. To the nonsupervised problems, the decision-directed approach and the modified-decision-directed approach are applied. Also some experimental results are presented.

A method of classifying patterns using fuzzy relations is described. To start with, we give a suitable value of the measure of subjective similarity to each pair of patterns that is taken from the population of patterns to be classified. Then a similitude between any two patterns is calculated by using the composition of a fuzzy relation. The similitude induces an equivalence relation. Consequently, we can classify the present population of the patterns into some classes by the equivalence relation. An experiment of the classification of portraits has been performed to test the method proposed here.