Orthogonal Low Rank Tensor Approximation: Alternating Least Squares Method and Its Global Convergence

@article{Wang2015OrthogonalLR,
  title={Orthogonal Low Rank Tensor Approximation: Alternating Least Squares Method and Its Global Convergence},
  author={Liqi Wang and Moody T. Chu and Bo Yu},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2015},
  volume={36},
  pages={1-19}
}
With the notable exceptions of two cases---that tensors of order 2, namely, matrices, always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-1 approximation, it is known that high-order tensors may fail to have best low rank approximations. When the condition of orthogonality is imposed, even under the modest assumption of semiorthogonality where only one set of components in the decomposed rank-1 tensors is required to be mutually… 
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26 Citations

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This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank-k approximation of a real m×n matrix, A. This method…

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O C ] 9 D ec 2 01 9 LINEAR CONVERGENCE OF AN ALTERNATING POLAR DECOMPOSITION METHOD FOR LOW RANK ORTHOGONAL TENSOR APPROXIMATIONS

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An improved version of the classical APD, iAPD, of the alternating polar decomposition method is proposed, which exhibits an overall sublinear convergence with an explicit rate which is sharper than the usual Op1{kq for first order methods in optimization.

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