Mutual Information on Tensors for Measuring the Nonlinear Correlations in Network Security

Correlation analysis has been proposed to measure the relationship among different variables, with application in multi-view dimension reduction. However, the existing methods usually are used by covariance in a linear way rather than the nonlinear effects being considered among multiple variables and only few works on nonlinear interaction of two variables have been considered. In this paper we propose a nonlinear analysis of multiple (more than two) variables based on mutual information for tensors analysis (MITA) firstly. In addition, we extend the mutual information matrix analysis directly to mutual information tensor analysis and show the mutual information formula for multiple variables theoretically. Experiment on multi-view dimension reduction, including attacking internet traffic detection, has been done to illustrate the effectiveness of the proposed method, especially in the case of low dimensional subspace.