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

Abstract : 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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https://hal.univ-grenoble-alpes.fr/hal-03521267
Contributor : Guillaume Ginolhac Connect in order to contact the contributor
Submitted on : Tuesday, January 11, 2022 - 2:42:21 PM
Last modification on : Monday, May 16, 2022 - 5:08:51 PM
Long-term archiving on: : Tuesday, April 12, 2022 - 7:26:27 PM

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

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