Abstract of Mariya Ishteva

The best low multilinear rank approximation of tensors: computation and applications
The multilinear rank of a higher-order tensor is a direct generalization of column and row rank of a matrix. In this talk we discuss the best low multilinear rank approximation. Given a higher-order tensor, we are looking for another tensor, as close as possible to the original one and with multilinear rank bounded by given numbers. This approximation is used for dimensionality reduction and signal subspace estimation in many fields, including higher-order statistics, biomedical signal processing and telecommunications. Its computation is not as straightforward as in the matrix case. Moreover, standard optimization algorithms face a difficulty caused by an invariance property of the cost function. We remove the invariance by working on quotient matrix manifolds.


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)