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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 22-57, 2024/07/03
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.
Keywords: non-negative factorization, orthogonalization, -matrices, low-rank tensors, alternating least-squares, high-dimensional problems