Detecting manifold dependences of multivariate data with total correlation

Abstract

Discovering dependences between variables has a significant impact on the performance of exploration on large datasets. Many useful measures have been presented to identify interesting dependences for pairs of variables, but few for triplets. Here, we proposed a novel measure of dependence for three-variable relationships: the maximal total correlation coefficient (MTCC). With a score roughly equaling the determination coefficient $R^2$ , MTCC captures a wide range of trivariate one-dimensional manifold dependences, including many common space curves. Applying MTCC to datasets in global health and major-league baseball, we identify a number of almost unknown manifold dependences, especially an impressive superposition of three trivariate relationships.