On the logical analysis of partially ordered data in the supervised classification problem

The importance of this study is caused by the existence of applied machine learning problems that cannot be adequately solved in the classical statement of the logical data analysis. Based on a generalization of basic concepts, a scheme for synthesizing correct supervised classification procedures is proposed. These procedures are focused on specifying partial order relations on sets of feature values. It is shown that the construction of classification procedures requires a key intractable discrete problem to be solved. This is the dualization problem over products of partially ordered sets. The matrix formulation of this problem is given. The effectiveness of the proposed approach to the supervised classification problem is illustrated on model data.