Metric correctness of pairwise comparisons in intelligent data analysis

Abstract

Abstract In modern data analysis and machine learning, data are often represented in the form of pairwise comparisons of the elements of the data set. The pairwise comparisons immediately correspond to the similarity or dissimilarity of objects under investigation, and such a situation regularly arises in the domains of image and signal analysis, bioinformatics, expert evaluation, etc. The practical pairwise comparison functions may be incorrect in terms of potentially using them as scalar products or distances. In contrast to other approaches, we develop in this paper a technique based on the so-called metric approach, which proposes to modify the values of empirical functions so as to get scalar products or distances. The methods for obtaining the correct matrices of pairwise comparisons and for improving their conditionality are developed here.