caa a22 4500 60619942X CHVBK 20210128100938.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s11045-013-0269-9 doi (NATIONALLICENCE)springer-10.1007/s11045-013-0269-9 Tucker factorization with missing data with application to low- $$n$$ n -rank tensor completion [Elektronische Daten] [Marko Filipović, Ante Jukić] The problem of tensor completion arises often in signal processing and machine learning. It consists of recovering a tensor from a subset of its entries. The usual structural assumption on a tensor that makes the problem well posed is that the tensor has low rank in every mode. Several tensor completion methods based on minimization of nuclear norm, which is the closest convex approximation of rank, have been proposed recently, with applications mostly in image inpainting problems. It is often stated in these papers that methods based on Tucker factorization perform poorly when the true ranks are unknown. In this paper, we propose a simple algorithm for Tucker factorization of a tensor with missing data and its application to low- $$n$$ n -rank tensor completion. The algorithm is similar to previously proposed method for PARAFAC decomposition with missing data. We demonstrate in several numerical experiments that the proposed algorithm performs well even when the ranks are significantly overestimated. Approximate reconstruction can be obtained when the ranks are underestimated. The algorithm outperforms nuclear norm minimization methods when the fraction of known elements of a tensor is low. Springer Science+Business Media New York, 2013 Tucker factorization nationallicence Tensor completion nationallicence Low- $$n$$ n -rank tensor nationallicence Missing data nationallicence Filipović Marko Rudjer Bošković Institute, Bijenička 54, 10000, Zagreb, Croatia aut Jukić Ante Department of Medical Physics and Acoustics, University of Oldenburg, 26111, Oldenburg, Germany aut Multidimensional Systems and Signal Processing Springer US; http://www.springer-ny.com 26/3(2015-07-01), 677-692 0923-6082 26:3<677 2015 26 11045 https://doi.org/10.1007/s11045-013-0269-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11045-013-0269-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Filipović Marko Rudjer Bošković Institute, Bijenička 54, 10000, Zagreb, Croatia aut NATIONALLICENCE 700 1- Jukić Ante Department of Medical Physics and Acoustics, University of Oldenburg, 26111, Oldenburg, Germany aut NATIONALLICENCE 773 0- Multidimensional Systems and Signal Processing Springer US; http://www.springer-ny.com 26/3(2015-07-01), 677-692 0923-6082 26:3<677 2015 26 11045