On the Matrices of Pairwise Frequencies of Categorical Attributes for Objects Classification

Abstract

This paper proposes two new algorithms for classifying objects with categorical attributes. These algorithms are derived from the assumption that the attributes of different object classes have different probability distributions. One algorithm classifies objects based on the distribution of the attribute frequencies, and the other classifies objects based on the distribution of the pairwise attribute frequencies described using a matrix of pairwise frequencies. Both algorithms are based on the method of invariants, which offers the simplest dependencies for estimating the probabilities of objects in each class by an average frequency of their attributes. The estimated object class corresponds to the maximum probability. This method reflects the sensory process models of animals and is aimed at recognizing an object class by searching for a prototype in information accumulated in the brain. Because these matrices may be sparse, the solution cannot be determined for some objects. For these objects, an analog of the k-nearest neighbors method is provided in which for each attribute value, the class to which the majority of the k-nearest objects in the training sample belong is determined, and the most likely class value is calculated. The efficiencies of these two algorithms were confirmed on five databases.