Measures of Correlation for Multiple Variables

Multivariate correlation analysis plays an important role in various fields such as statistics, economics, and big data analytics. In this paper, we propose a pair of measures, multivariate correlation coefficient (MCC) and multivariate uncorrelation coefficient (MUC), to measure the strength of the correlation and uncorrelation (lack of correlation) among multiple variables. Pearson's correlation coefficient is a special case of multivariate correlation for two variables. Based on the proposed MUC, a compact formula for linear decomposition is also presented in this paper. The experiment results show that the proposed MCC is an effective measure for multivariate correlation, and a new explanation of determinant is also made from the view of multivariate correlation.