A nonlinear correlation measure for multivariable data set

The paper states that the mutual information carried by the rank sequences that are obtained from the original two sequences is a good measure of nonlinear correlation. Based on that, the nonlinear correlation information entropy (NCIE) is proposed for measuring the general relationship of a multivariable data set. NCIE uses a number in the closed interval [0, 1] to indicate the nonlinear correlation degree of the concerned multivariable data set, with 0 and 1 denotes the weakest and the strongest relationship, respectively. Data sets generated from an autoregressive model, a nonlinear chaotic Lorenz system, and a logistic function as known correlation sequences are analyzed using the proposed NCIE. The results testify the suitableness and correctness of the proposed concepts as nonlinear correlation measure.