Geometric structures and deviations on James' symmetric positive-definite matrix bicone domain
Symmetric positive-definite (SPD) matrix datasets play a central role across numerous scientific disciplines, including signal processing, statistics, finance, computer vision, information theory, and machine learning among others. The set of SPD matrices forms a cone which can be viewed as a global coordinate chart of the underlying SPD manifold. Rich differential-geometric structures may be defined on the SPD cone manifold. Among the most widely used geometric frameworks on this manifold are the affine-invariant Riemannian structure and the dual information-geometric log-determinant barrier structure, each associated with dissimilarity measures (distance and divergence, respectively). I...
| Authors | Jacek Karwowski, Frank Nielsen |
|---|---|
| Primary category | stat.ML |
| Published | 3 March 2026 |
| Last updated at source | 3 March 2026 |
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