Data analysis and decision-making with logical regularities in the form of half-planes

The intellectual analysis of data through solving recognition problems with the teacher is considered. As a tool for extracting new knowledge from databases, it is proposed to use logical regularities in the form of half-planes. Three methods for analyzing the initial and latent features are described on the basis of: Fisher’s criterion; The relationship of intra-class similarity and the interclass difference defined through the Lagrange function; Criterion for calculating the optimal boundary between values from different classes. A methodology is proposed for selecting informative sets of features taking into account these methods of analysis. The mapping of various descriptions of objects onto the numerical axis was considered. It is proved that using the optimal boundary between classes on the numerical axis as a threshold for a linear decision function increases the generalizing ability in recognition. This effect is explained by the rejection of the assumption of a normal distribution of sample data when choosing a threshold. The proposed technology for data analysis is in demand in the development of intelligent systems.