The Level of Similarity as a Functions Classification Measure

Abstract

Data processing in the essence of the notion of "Data Mining" may require procedures - algorithms for assessing the similarity between the resulting functions of the studied phenomena. A model for evaluating the level of similarity between two functions is proposed. According to the way of approaching the essence of the study regarding the differences between two functions, in this paper an algorithm is to be presented and discussed, based on which certain numerical values could be obtained. The respective values, following a synthesis, are to constitute a set of parameters included in a mathematical expression that numerically expresses the "distance" between two functions. The level of similarity of two functions will be considered to be a positive numerical value, and for the functions that coincide, according to the model, the respective value of the level will be "zero". The basic properties of functions will be considered through the lens of the fundamental notions involved in the procedures for researching functions in the field of mathematics. Certain numerical values (parameters) characteristics of the essence of some notions will be highlighted and used, such as: monotonicity intervals, critical points, inflection points, convexity, concavity, extreme values, values of first-order derivatives and second-order derivatives. The values obtained for each of the previously listed properties are supposed to be calculated for each function included in the similarity evaluation process. Depending on the set of values among those listed, various algorithms can be defined. For example, considering only the monotonic intervals, one algorithm could be created, and if the inflection points are also included, another algorithm will be obtained, with a different result. UDC: 004.421:324; JEL: C63, I21, I23, I25, I29.