Measuring and Discovering Correlations in Large Data Sets

The unknown laws of nature and society are always hidden among massive data in the form of correlation [1-3], such as the relationship between air quality and the developing level of industry, the associations between economic growth and various factors, and so on [4-6]. A medium-sized database may contain hundreds of variables and tens of thousands of hidden correlations. The efficiency of discoverring the desired correlations depends on the method of correlation assessment. The most commonly used method is the ancient correlation coefficient Pearson's r [7], but it captures only linear relationships and its usefulness is greatly reduced when relationships are nonlinear [8]. In the context of information theory, mutual information (MI) can treat linear and nonlinear relationships relatively fairly, and it seems like to be the most promising solution after Pearson's r [9-11].