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References

General Tensor Decomposition

  • Tensor decompositions (CP, Tucker): T. G. Kolda and B. W. Bader, "Tensor decompositions and applications," SIAM Review, vol. 51, no. 3, pp. 455–500, 2009.

Tucker Methods

  • HOSVD: L. De Lathauwer, B. De Moor, and J. Vandewalle, "A multilinear singular value decomposition," SIAM J. Matrix Anal. Appl., vol. 21, no. 4, pp. 1253–1278, 2000.
  • ST-HOSVD: N. Vannieuwenhoven, R. Vandebril, K. Meerbergen, "A new truncation strategy for the higher-order singular value decomposition," SIAM J. Sci. Comput., vol. 34, no. 2, pp. A1027–A1052, 2012.
  • HOOI: L. De Lathauwer, B. De Moor, and J. Vandewalle, "On the best rank-1 and rank-(R1,R2,...,R_N) approximation of higher-order tensors," SIAM J. Matrix Anal. Appl., vol. 21, no. 4, pp. 1324–1342, 2000.

Block and Structured Models (BTD / LL1)

  • Block-term decomposition (BTD): L. De Lathauwer, "Decompositions of a higher-order tensor in block terms—Part I: Lemmas for partitioned matrices," SIAM J. Matrix Anal. Appl., vol. 30, no. 3, pp. 1022–1032, 2008.
  • L. De Lathauwer, "Decompositions of a higher-order tensor in block terms—Part II: Definitions and uniqueness," SIAM J. Matrix Anal. Appl., vol. 30, no. 3, pp. 1033–1066, 2008.
  • BTD-ALS: L. De Lathauwer and D. Nion, "Decompositions of a higher-order tensor in block terms—Part III: Alternating least squares algorithms," SIAM Journal on Matrix Analysis and Applications, vol. 30, no. 3, pp. 1067–1083, 2008. PDF.

Join decompositions

  • Conditioning of join decompositions: P. Breiding and N. Vannieuwenhoven, "The condition number of join decompositions," SIAM Journal on Matrix Analysis and Applications, vol. 39, no. 1, pp. 287–309, 2018. arXiv:1611.08117 (PDF).

Riemannian Optimization and Julia Ecosystem

  • Riemannian trust-region / Gauss–Newton for canonical rank (CP) approximation: P. Breiding and N. Vannieuwenhoven, "A Riemannian Trust Region Method for the Canonical Tensor Rank Approximation Problem," SIAM Journal on Optimization, vol. 28, no. 3, pp. 2435–2465, 2018. arXiv:1709.00033 (PDF).
  • Riemannian optimization: P.-A. Absil, R. Mahony, and R. Sepulchre, Optimization Algorithms on Matrix Manifolds. Princeton University Press, 2008.
  • Julia manifold optimization ecosystem: R. Bergmann et al., ManifoldsBase.jl, Manifolds.jl, and Manopt.jl.