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Séminaire du département Images et Signal du 15/11/2013 à 14h00

 

Kronecker PCA: a covariance decomposition for high dimensional data

Intervenant : Alfred HERO, University of Michigan

Lieu : Salle Mont-Blanc

 

Résumé :

Kronecker covariance decompositions can be interpreted as a generalization of the matrix singular value decomposition (SVD) where the components are Kronecker product matrices. While these components are not orthogonal, the number of Kronecker components, called the Kronecker separation rank, of the decomposition plays a similar role as the rank in low rank covariance matrix approximation. We obtain high dimensional convergence rates  on the approximation error of the Kronecker decomposition under a Wishart sample covariance model as a function of the number of free variables p and the number of independent samples n. We illustrate the power of Kronecker covariance decompositions for spatio-temporal data applications in sensor networks and video processing.


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