Volume 62, pp. 22-57, 2024.

Quasi-orthogonalization for alternating non-negative tensor factorization

Lars Grasedyck, Maren Klever, and Sebastian Krämer


Low-rank tensor formats allow for efficient handling of high-dimensional objects. In many applications, it is crucial to preserve the non-negativity in the approximation, for instance, by constraining all cores to be non-negative. Common alternating strategies reduce the high-dimensional problem to a sequence of low-dimensional subproblems but often suffer from slow convergence and persistence in local minima. In order to counteract this, we propose a new quasi-orthogonalization strategy as an intermediate step between the alternating minimization steps that preserves non-negativity. It allows one to improve the expressivity in each individual factor by modifying the current factorization within the equivalence class representing the same tensor.

Full Text (PDF) [816 KB], BibTeX

Key words

non-negative factorization, orthogonalization, $M$-matrices, low-rank tensors, alternating least-squares, high-dimensional problems

AMS subject classifications

15-06, 65F06, 65D40

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