Tensor mutual information and its applications

Abstract

Correlation analysis has long been a question of great interest in measuring the relationship among different variables and has been applied in many fields, such as dimension reduction, classification, and so on. However, current methods of correlation analysis take into account the linear relationship between multiple variables and only few works on nonlinear interaction of two variables have been considered. In this article, we first present a nonlinear analysis method of multiple (two or more) variables based on mutual information for tensor analysis (MITA). In addition, we extend the mutual-information matrix analysis directly to MITA and show the multivariable mutual information formula based on Venn diagram. Experiments on multiview dimension reduction, including attacking internet traffic prediction, advertisement classification, and biometric structure prediction illustrate the effectiveness of the proposed method, especially in the case of low-dimensional subspace.