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Communication Dans Un Congrès Année : 2021

On-line Kronecker Product Structured Covariance Estimation with Riemannian geometry for t-distributed data

Résumé

The information geometry of the zero-mean tdistribution with Kronecker-product structured covariance matrix is derived. In particular, we obtain the Fisher information metric which shows that this geometry is identifiable to a product manifold of S ++ p (positive definite symmetric matrices) and sS ++ p (positive definite symmetric matrices with unit determinant). From this result, we obtain the geodesics and the Riemannian gradient. Finally, this geometry makes it possible to propose an on-line covariance matrix estimation algorithm well adapted to large datasets. Numerical experiments show that optimal results are obtained for a reasonable number of data.
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Dates et versions

hal-03521267 , version 1 (11-01-2022)

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Citer

Florent Bouchard, Arnaud Breloy, Ammar Mian, Guillaume Ginolhac. On-line Kronecker Product Structured Covariance Estimation with Riemannian geometry for t-distributed data. The 29th European Signal Processing Conference (EUSIPCO 2021), Aug 2021, Dublin, Ireland. pp.856-859, ⟨10.23919/EUSIPCO54536.2021.9616101⟩. ⟨hal-03521267⟩
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