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Higher order multi-dimension reduction methods via Einstein product
Alaeddine Zahir, Khalide Jbilou, Ahmed Ratnani
This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompass…
Quaternion tensor low rank Quaternion tensor low-rank approximation using a family of non-convex norms
Alaeddine Zahir, Ahmed Ratnani, Khalide Jbilou
In this paper, we propose a new approaches for low rank approximation of quaternion tensors \cite{chen2019low,zhang1997quaternions,hamilton1866elements}. The first method uses quas…
A rational Krylov methods for large scale linear multidimensional dynamical systems
Houda Barkouki, Khalide Jbilou
In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Kry…
Non-negative Einstein tensor factorization for unmixing hyperspectral images
Anas El Hachimi, Khalide Jbilou, Ahmed Ratnani
In this manuscript, we introduce a tensor-based approach to Non-Negative Tensor Factorization (NTF). The method entails tensor dimension reduction through the utilization of the Ei…