OUTLINE OF THE GENERAL THEORY OF SIMILARITY, CORRELATION AND ASSOCIATION MEASURES: FUNCTIONAL APPROACH

The presentation discusses recent results obtained by speaker in analysis of similarity, correlation and association measures studied in statistics, pattern classification, data mining etc. These measures considered as functions defined on underlying set and satisfying some simple sets of properties. The methods of transformation of these functions and construction of these functions on specific domain will be discussed. General methods of construction of correlation functions from similarity and/or dissimilarity functions will be considered. The known correlation coefficients (Pearson, Spearman, Kendal, Yule Q) can be obtained as particular cases. The proposed methods can be used for constructing new similarity measures and correlation coefficients on different domains. Examples will be considered.