| Autor: |
Chevallier, Emmanuel |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Geometric Science of Information. GSI 2023, Nielsen, F., Barbaresco, F., Aug 2023, Saint-Malo (FR), France. pp.444-451 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/978-3-031-38271-0_44 |
| Popis: |
We are interested in the distribution of Wishart samples after forgetting their scaling factors. We call such a distribution a projective Wishart distribution. We show that projective Wishart distributions have strong links with the affine-invariant geometry of symmetric positive definite matrices in the real case or Hermitian positive definite matrices in the complex case. First, the Fr{\'e}chet mean of a projective Wishart distribution is the covariance parameter, up to a scaling factor, of the corresponding Wishart distribution. Second, in the case of 2 by 2 matrices, the densities have simple expressions in term of the affine-invariant distance. |
| Databáze: |
arXiv |
| Externí odkaz: |
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