Nomograms for comparing the corrective abilities of binary and ternary neurons used in multicriteria testing of the hypothesis of small sample data independence

Abstract

Background. The purpose of the research is to obtain a numerical estimate of the effect of the transition from ordinary binary neurons with two output states “0”, “1” to neurons with three output states “-1”, “0”, “1”. Materials and methods. As an example, a neural network is considered that generalizes three classical statistical criteria for testing the hypothesis of independence of small samples of 22 experiments. The Pearson- Edgeworth-Edleton test (1890-1900), the Kenoway test (1965) and the modified Nelson test (1983) were used. For these criteria, artificial neurons equivalent to them with binary and ternary quantizes have been constructed. As a result, we get a binary and ternary output code with a threefold code redundancy. The folding of these codes makes it possible to correct the errors present in them. Through the implementation of the summarization of correlation matrices, a forecast of the quality of the made neural network decisions was created for a situation where 21 statistical criteria for testing the independence hypothesis will be used. A nomogram is given that allows one to estimate the gain in the transition from ordinary binary neurons to ternary neurons. Results. The ternary selfcorrecting output code of the neural network in terms of its corrective ability turned out to be one and a half times more powerful in comparison with its binary counterpart. The latter is explained by the increase in the amount of information available for analysis and the greater information content of data on error syndromes. Conclusions. It has been suggested that the effect of increasing the growth of the corrective ability of ternary neurons compared to binary neurons will increase as the number of artificial neurons that combine the currently known statistical criteria for joint use increases.

Keywords

• artificial neurons
• binary neurons
• ternary neurons
• ternary quantizes