An evaluation of some simple measures for detecting non-linear relationships between variables

Since the introduction of simple measures of linear relationship such as Pearson’s Correlation Coefficient, measures have been sought that will also describe non-linear relationships that may exist between a pair of variables. Currently there are a number of such methods, encompassing a range of sophistication and involving a range of computational effort. This work reports on some experiments with a computationally simple measure that operates using a division of input space into regularly spaced cells. The Distribution Area Ratio Correlation Coefficient (DARCC) compares the distribution of cells containing k points with a theoretical distribution. The method is described then evaluated by comparing the resulting correlation coefficient with the magnitude of added noise. Results show a good agreement between noise and DARCC for several synthesised datasets. The measure is also evaluated on some real datasets. DARCC is computationally very simple and has potential for datasets with a large number of variables where speed is important.