Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE SYMMETRIZED LOG-DETERMINANT DIVERGENCE

  • SEJONG KIM (Department of Mathematics, Chungbuk National University) ;
  • VATSALKUMAR N. MER (Institute for Industrial and Applied Mathematics, Chungbuk National University)
  • Received : 2024.02.23
  • Accepted : 2024.07.07
  • Published : 2024.07.30
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Abstract

We see fundamental properties of the log-determinant α-divergence including the convexity of weighted geometric mean and the reversed sub-additivity under tensor product. We introduce a symmetrized divergence and show its properties including the boundedness and monotonicity on parameters. Finally, we discuss the barycenter minimizing the weighted sum of symmetrized divergences.

Keywords

Acknowledgement

We thank to anonymous reviewers for valuable comments.

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