Topological and Algebraic Properties of Chernoff Information between Gaussian Graphs

In this paper, we want to find out the determiningfactors of Chernoff information in distinguishing a set of Gaus-sian graphs. We find that Chernoff information of two Gaussiangraphs can be determined by the generalized eigenvalues of theircovariance matrices. We find that the unit generalized eigenvaluedoesn’t affect Chernoff information and its corresponding di-mension doesn’t provide information for classification purpose.In addition, we can provide a partial ordering using Chernoffinformation between a series of Gaussian trees connected byindependent grafting operations. With the relationship betweengeneralized eigenvalues and Chernoff information, we can dooptimal linear dimension reduction with least loss of informationfor classification.