The selection of logical patterns for constructing a decision rule of recognition

We investigate an aspect of the construction of logical recognition algorithms - selection of patterns in the set of found patterns in the data. We consider the recognition problem for objects described by binary attributes and divided into two classes. In consequence of performance the procedure of searching patterns on the training set (a set of input data) a number of patterns has been found. The question is to select some patterns from their total number to form a decision rule. That can not only reduce the size of the decision rule, but also improve recognition. One way to make a selection of patterns is to select a subset of patterns that is needed to cover all objects of the training sample. This problem is formulated as an optimization problem. The resulting optimization model represents a problem of conditional pseudo-Boolean optimization, in which the objective function and the constraints functions are unimodal monotone pseudo-Boolean functions. Another way is to make the selection of such patterns, which when used together will increase separating capacity of the decision rule. As a criterion for the formation of the decision rule is considered the width of the separation margin. One more way is to select supporting objects and on their basis to form the rules. The selection of logical patterns, which is made in accordance with the proposed approach, can significantly reduce the number of patterns and simplify the decision rule, almost without compromising the accuracy of recognition. This makes the decision rule clearer, and the results more interpretable. It is necessary to support decision making for recognition.