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We show how to develop sampling-based alternating least squares (ALS) algorithms for decomposition of tensors into any tensor network (TN) format.
The expression of a tensor or a polyadic as a sum of products
F. L. Hitchcock · 1927
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Implications of factor analysis of three-way matrices for measurement of change
L. R. Tucker · 1963
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Columbia object image library (COIL-100)
S. A. Nene, S. K. Nayar, and H. Murase · 1996
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Sampling algorithms for ℓ 2 \ell_{2} regression and applications
P. Drineas, M. W. Mahoney, and S. Muthukrishnan · 2006
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Relative-error CUR matrix decompositions
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Tensor decompositions and applications
T. G. Kolda and B. W. Bader · 2009
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Faster least squares approximation
P. Drineas, M. W. Mahoney, S. Muthukrishnan, and T. Sarlós · 2011
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Randomized algorithms for matrices and data
M. W. Mahoney · 2011
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Tensor-train decomposition
I. V. Oseledets · 2011
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Sketching as a tool for numerical linear algebra
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SPALS: Fast alternating least squares via implicit leverage scores sampling
D. Cheng, R. Peng, Y. Liu, and I. Perros · 2016
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Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions
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C. Li and Z. Sun · 2020
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MATLAB Tensor Toolbox, Version 3.2.1
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A sampling-based method for tensor ring decomposition
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Subquadratic Kronecker regression with applications to tensor decomposition
M. Fahrbach, T. Fu, and M. Ghadiri · 2022
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Practical leverage-based sampling for low-rank tensor decomposition
B. W. Larsen and T. G. Kolda · 2022
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Cost-efficient Gaussian tensor network embeddings for tensor-structured inputs
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Tensor networks for dimensionality reduction and large-scale optimization: Part 2 applications and future perspectives
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Y. Ji, Q. Wang, X. Li, and J. Liu · 2019
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J. Kossaifi, Y. Panagakis, A. Anandkumar, and M. Pantic · 2019
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Randomized tensor ring decomposition and its application to large-scale data reconstruction
L. Yuan, C. Li, J. Cao, and Q. Zhao · 2019
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Randomized algorithms for fast computation of low-rank tensor ring model
S. Ahmadi-Asl, A. Cichocki, A. H. Phan, M. G. Asante-Mensah, F. Mousavi, I. Oseledets, and T. Tanaka · 2020
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NCON: A tensor network contractor for MATLAB
R. N. Pfeifer, G. Evenbly, S. Singh, and G. Vidal
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Faster identification of optimal contraction sequences for tensor networks
R. N. C. Pfeifer, J. Haegeman, and F. Verstraete
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L. Ma and E. Solomonik · 2022
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More efficient sampling for tensor decomposition with worst-case guarantees
O. A. Malik · 2022
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