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Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

Abstract : Symmetric Positive Definite (SPD) matrices have been usedin many fields of medical data analysis. Many Riemannian metrics havebeen defined on this manifold but the choice of the Riemannianstructurelacks a set of principles that could lead one to choose properly the met-ric. This drives us to introduce the principle of balanced metrics that re-late the affine-invariant metric with the Euclidean and inverse-Euclideanmetric, or the Bogoliubov-Kubo-Mori metric with the Euclidean and log-Euclidean metrics. We introduce two new families of balanced metrics,the mixed-power-Euclidean and the mixed-power-affine metrics and wediscuss the relation between this new principle of balanced metrics and the concept of dual connection in information geometry.
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Contributor : Yann Thanwerdas <>
Submitted on : Monday, September 9, 2019 - 3:20:51 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:59 PM
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Yann Thanwerdas, Xavier Pennec. Exploration of Balanced Metrics on Symmetric Positive Definite Matrices. GSI 2019 - 4th conference on Geometric Science of Information, Aug 2019, Toulouse, France. pp.484--493, ⟨10.1007/978-3-030-26980-7_50⟩. ⟨hal-02158525⟩

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