METHODS FOR DETERMINING SIMILARITY OF CATEGORICAL ORDERED DATA

Abstract

Context. The development of effective distance metrics and similarity measures for categorical features is an important task in data analysis, machine learning, and decision theory since a significant portion of object properties is described by non-numerical values. Typically, the dependence between categorical features may be more complex than simply comparing them for equality or inequality. Such attributes can be relatively similar, and to construct an effective model, it is necessary to consider this similarity when calculating distance or similarity measures.
 Objective. The aim of the study is to improve the efficiency of solving practical data analysis problems by developing mathematical tools for determining the similarity of objects based on categorical ordered features.
 Method. A distance based on weighted Manhattan distance and a similarity measure for determining the similarity of objects based on categorical ordinal features (i.e. a linear order with scales of preference considering the problem domain can be specified on the attribute value set) are proposed. It is proven that the distance formula satisfies the axioms of non-negativity, symmetry, triangle inequality, and upper bound, and therefore is a distance metric in the space of ranked categorical features. It is also proven that the similarity measure presented in the study satisfies the axioms of boundedness, symmetry, maximum and minimum similarity, and is described by a decreasing function.
 Results. The developed approach has been implemented in an applied problem of determining the degree of similarity between objects described by ordered categorical features.
 Conclusions. In this study, mathematical tools were developed to determine similarity between structured data described by categorical attributes that can be ordered based on a specific priority in the form of a ranking system with preferences. Their properties were analyzed. Experimental studies have shown the convenience and “intuitive understanding” of the logic of data processing in solving practical problems. The proposed approach can provide the opportunity to conduct new meaningful research in data analysis. Prospects for further research lie in the experimental use of the proposed tools in practical tasks and in studying their effectiveness.