Multivariate generalization of Kendall's Tau (Tau-N) using paired orthants

Multivariate correlation analysis plays an important role in various fields such as statistics and big data analytics. In this paper, it is presented a new non-parametric measure of rank correlation between more than two variables from the multivariate generalization of the Kendall's Tau coefficient (Tau-N). This multivariate correlation analysis not only evaluates the inter-relatedness of multiple variables, but also determine the specific tendency of the tested data set. Additionally, it is discussed how the discordant concept would have some limitations when applied to more than two variables, for which reason this methodology has been developed based on the new concept paired orthants. In order to test the proposed methodology, different N-tuple sets (from two to six variables) have been evaluated.