Topological and Algebraic Properties of Chernoff Information between Gaussian Graphs

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Conference Proceeding

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In this paper, we want to find out the determining factors of Chernoff information in distinguishing a set of Gaussian graphs. We find that Chernoff information of two Gaussian graphs can be determined by the generalized eigenvalues of their covariance matrices. We find that the unit generalized eigenvalues do not affect Chernoff information and their corresponding dimensions do not provide information for classification purpose. In addition, we can provide a partial ordering using Chernoff information between a series of Gaussian trees connected by independent grafting operations. By exploiting relationship between generalized eigenvalues and Chernoff information, we can do optimal classification linear dimension reduction with least loss of information for classification. Key words: Gaussian graphs, Generalized eigenvalue, Chernoff information, Dimension reduction.

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2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018

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