A finite algorithm to compute rank-1 tensor approximations

Abstract : We propose a non iterative algorithm, called SeROAP (Sequential Rank-One Approximation and Projection), to estimate a rank-1 approximation of a tensor in the real or complex field. Our algorithm is based on a sequence of singular value decompositions followed by a sequence of projections onto Kronecker vectors. For three-way tensors, we show that our algorithm is always at least as good as the state-of-the-art truncation algorithm, ST-HOSVD (Sequentially Truncated Higher-Order Singular Value Decomposition), in terms of approximate error. Thus, it gives a good starting point to iterative rank-1 tensor approximation algorithms. By means of computational experiments, it also turns out that for $4$-th order tensors, SeROAP yields a better approximation with high probability when compared to the standard THOSVD (Truncated Higher-Order Singular Value Decomposition) algorithm.
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IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2016, 23 (7), pp.959-963. 〈http://ieeexplore.ieee.org/document/7473918/〉. 〈10.1109/LSP.2016.2570862〉
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Soumis le : jeudi 21 décembre 2017 - 16:24:34
Dernière modification le : lundi 9 avril 2018 - 12:22:48

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Alex Pereira da Silva, Pierre Comon, André De Almeida. A finite algorithm to compute rank-1 tensor approximations. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2016, 23 (7), pp.959-963. 〈http://ieeexplore.ieee.org/document/7473918/〉. 〈10.1109/LSP.2016.2570862〉. 〈hal-01385538〉

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