Data Science: Similarity, Dissimilarity and Correlation Functions

The lecture presents a new, non-statistical approach to the analysis and construction of similarity, dissimilarity and correlation measures. The measures are considered as functions defined on an underlying set and satisfying the given properties. Different functional structures, relationships between them and methods of their construction are discussed. Particular attention is paid to functions defined on sets with an involution operation, where the class of (strong) correlation functions is introduced. The general methods constructing new correlation functions from similarity and dissimilarity functions are considered. It is shown that the classical correlation and association coefficients (Pearson’s, Spearman’s, Kendall’s, Yule’s Q, Hamann) can be obtained as particular cases.