Possibilities of analysis of nominative signs in tasks of information security

Abstract

Using various examples, the article demonstrates and discusses the possibilities of testing hypotheses and applying information measures to identify and assess the strength of the connection of nominative features in classification problems in the analysis of information security. The main type of presentation of the initial data in this scale is a contingency table of nominative features or an "object-feature" table, from which frequencies of coincidence of feature categories and a contingency table can be obtained. Using this table, it is easy to test the hypothesis of independence or homogeneity of features. An alternative approach to this analysis is considered based on the Kullback statistics, which is the average discriminating information in favor of the hypothesis of the dependence of features. In particular cases, the hypothesis of the symmetry of square tables is of practical interest, which can also be tested on the basis of information measures and criteria. An example of the processing of dichotomous data of the "yes-no" type according to the Cochran test is shown. The paper discusses ways to measure the strength of the connection of features. Illustrative examples of calculating measures based on chi-square statistics and directed measures are considered. The possibilities of various information characteristics are discussed in the form of a relative decrease in the entropy of one feature with a known other, or in the form of a weighted average amount of information falling on different categories of a feature. These measures are useful for comparative analysis of nominative features in decision-making problems. Shannon's informativeness index, Kullback-Leibler divergence, and a measure of pairwise differentiation of protection efficiency classes according to the laws of distribution of the corresponding categories of a feature are used. The classical procedures for testing hypotheses and approaches based on information characteristics are consistently compared. The methods and examples considered in the work cover many urgent problems of information security associated with nominative features.