Multivariate Correlation Entropy and Law Discovery in Large Data Sets

Over the past several centuries, many important natural laws have been discovered by scientists, which have not only changed our viewpoints about nature but also affected our lives significantly. Today, automatic discovery of meaningful laws from data beyond two variables becomes an important task of our time. Here, we propose two multivariate correlation measures, namely, the multivariate correlation entropy (MCE) and the multivariate incorrelation entropy (MIE), which can be used to measure the strength of the correlation among multiple variables. Using MIE makes it possible to directly detect linear relations existing in large data sets. In addition, more complicated nonlinear multivariate laws can be discovered using a function dictionary.