References

[1]L. Sorber, I. Domanov, M. Van Barel, and L. De Lathauwer. Exact line and plane search for tensor optimization. Computational Optimization and Applications, 63(1):121–142, 2015. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/sistakulak/reports/exact_line_and_plane_search_for_tensor_optimization.pdf, doi:10.1007/s10589-015-9761-5.
[2]L. Sorber, M. Van Barel, and L. De Lathauwer. Numerical solution of bivariate and polyanalytic polynomial systems. SIAM Journal on Numerical Analysis, 52(4):1551–1572, 2014. URL: ftp://ftp.esat.kuleuven.ac.be/SISTA/sistakulak/reports/numerical_solution_of_polynomial_systems.pdf, doi:10.1137/130932387.
[3]L. C. Dixon and G. P. Szegő. The global optimization problem: an introduction. Towards global optimisation II, pages 1–15, 1978.
[4]L. R. Tucker. Some mathematical notes on three-mode factor analysis. Psychometrika, 31(3):279–311, 1966. doi:10.1007/BF02289464.
[5]T. G. Kolda and B. W. Bader. Tensor decompositions and applications. SIAM Review, 51(3):455–500, September 2009. doi:10.1137/07070111X.
[6]A. Cichocki, D. Mandic, A. H. Phan, C. Caiafa, G. Zhou, Q. Zhao, and L. De Lathauwer. Tensor decompositions for signal processing applications: From two-way to multiway component analysis. IEEE Signal Processing Magazine, 32(2):145–163, 2015. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/delathauwer/reports/ldl-14-19.pdf, doi:10.1109/MSP.2013.2297439.
[7]L. Sorber, M. Van Barel, and L. De Lathauwer. Unconstrained optimization of real functions in complex variables. SIAM Journal on Optimization, 22(3):879–898, 2012. URL: ftp://ftp.esat.kuleuven.be/sista/delathauwer/reports/ldl-11-85.pdf, doi:10.1137/110832124.
[8]T. Adali and P. J. Schreier. Optimization and estimation of complex-valued signals: theory and applications in filtering and blind source separation. IEEE Signal Processing Magazine, 5(31):112–128, 2014. doi:10.1109/MSP.2013.2287951.
[9]W. Squire and G. Trapp. Using complex variables to estimate derivatives of real functions. SIAM Review, 10(1):110–112, March 1998. doi:10.1137/S003614459631241X.
[10]F. L. Hitchcock. The expression of a tensor or a polyadic as a sum of products. Journal of Mathematical Physics, 6(1):164–189, 1927. doi:10.1002/sapm192761164.
[11]F. L. Hitchcock. Multiple invariants and generalized rank of a $p$-way matrix or tensor. Journal of Mathematical Physics, 7(1):39–79, 1927. doi:10.1002/sapm19287139.
[12]J. D. Carroll and J.-J. Chang. Analysis of individual differences in multidimensional scaling via an $n$-way generalization of “Eckart–Young” decomposition. Psychometrika, 35(3):283–319, 1970. doi:10.1007/BF02310791.
[13]R. A. Harshman. Foundations of the PARAFAC procedure: models and conditions for an “explanatory” multi-modal factor analysis. UCLA Working Papers in Phonetics, 16(1):84–84, 1970.
[14]E. Sanchez and B. R. Kowalski. Tensorial resolution: a direct trilinear decomposition. Journal of Chemometrics, 4(1):29–45, 1990. doi:10.1002/cem.1180040105.
[15]N. Vervliet, O. Debals, L. Sorber, and L. De Lathauwer. Breaking the curse of dimensionality using decompositions of incomplete tensors: Tensor-based scientific computing in big data analysis. Signal Processing Magazine, IEEE, 31(5):71–79, September 2014. URL: ftp://ftp.esat.kuleuven.be/stadius/nvervliet/IEEE_SPM_Vervliet_Breaking2014.pdf, doi:10.1109/MSP.2014.2329429.
[16]R. Bro. Multi-way analysis in the food industry: models, algorithms, and applications. PhD thesis, University of Amsterdam, 1998.
[17]L. De Lathauwer, B. De Moor, and J. Vandewalle. A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications, 21(4):1253–1278, 2000. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/delathauwer/reports/ldl-94-31.pdf, doi:10.1137/S0895479896305696.
[18]N. Vervliet and L. De Lathauwer. A randomized block sampling approach to canonical polyadic decomposition of large-scale tensors. IEEE Journal of Selected Topics in Signal Processing, 10(2):284–295, March 2016. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/nvervliet/vervliet2015randomizedblocksampling.pdf, doi:10.1109/JSTSP.2015.2503260.
[19]L. De Lathauwer. A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization. SIAM Journal on Matrix Analysis and Applications, 28(3):642–666, 2006. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/delathauwer/reports/ldl-04-95.pdf, doi:10.1137/040608830.
[20]L. De Lathauwer, B. De Moor, and J. Vandewalle. Computation of the canonical decomposition by means of a simultaneous generalized Schur decomposition. SIAM Journal on Matrix Analysis and Applications, 26(2):295–327, 2004. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/ida/reports/11-116.pdf, doi:10.1137/S089547980139786X.
[21]X. Liu and N. D. Sidiropoulos. Cramér–Rao lower bounds for low-rank decomposition of multidimensional arrays. IEEE Transactions on Signal Processing, 49(9):2074–2086, Sept. 2001. doi:10.1109/78.942635.
[22]P. Tichavský, A.-H. Phan, and Z. Koldovský. Cramér–Rao-induced bounds for CANDECOMP/PARAFAC tensor decomposition. IEEE Transactions on Signal Processing, 61(8):1986–1997, Apr. 2013. doi:10.1109/TSP.2013.2245660.
[23]I. Oseledets. Tensor-train decomposition. SIAM Journal on Scientific Computing, 33(5):2295–2317, 2011. doi:10.1137/090752286.
[24]N. Vervliet, O. Debals, L. Sorber, M. Van Barel, and L. De Lathauwer. Tensorlab 3.0. Mar. 2016. Available online. URL: http://www.tensorlab.net.
[25]L. Sorber, M. Van Barel, and L. De Lathauwer. Optimization-based algorithms for tensor decompositions: canonical polyadic decomposition, decomposition in rank-$(L_r,L_r,1)$ terms and a new generalization. SIAM Journal on Optimization, 23(2):695–720, 2013. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/sistakulak/reports/algorithms_for_tensor_decompositions.pdf, doi:10.1137/120868323.
[26]L. De Lathauwer. Decompositions of a higher-order tensor in block terms — Part I: lemmas for partitioned matrices. SIAM Journal on Matrix Analysis and Applications, 30(3):1022–1032, 2008. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/delathauwer/reports/ldl-07-80.pdf, doi:10.1137/060661685.
[27]L. De Lathauwer. Decompositions of a higher-order tensor in block terms — Part II: definitions and uniqueness. SIAM Journal on Matrix Analysis and Applications, 30(3):1033–1066, 2008. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/delathauwer/reports/ldl-07-81.pdf, doi:10.1137/070690729.
[28]L. De Lathauwer. Blind separation of exponential polynomials and the decomposition of a tensor in rank-$(L_r,L_r,1)$ terms. SIAM Journal on Matrix Analysis and Applications, 32(4):1451–1474, 2011. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/delathauwer/reports/ldl-11-165.pdf, doi:10.1137/100805510.
[29]L. De Lathauwer, B. De Moor, and J. Vandewalle. On the best rank-1 and rank-$(R_1,R_2,…,R_n)$ approximation of higher-order tensors. SIAM Journal on Matrix Analysis and Applications, 21(4):1324–1342, 2000. URL: ftp://ftp.esat.kuleuven.be/pub/SISTA/ida/reports/97-75.pdf, doi:10.1137/S0895479898346995.
[30]C. F. Caiafa and A. Cichocki. Generalizing the column–row matrix decomposition to multi-way arrays. Linear Algebra and its Applications, 433(3):557–573, 2010. doi:10.1016/j.laa.2010.03.020.
[31]N. Vannieuwenhoven, R. Vandebril, and K. Meerbergen. A new truncation strategy for the higher-order singular value decomposition. SIAM Journal on Scientific Computing, 34(2):A1027–A1052, 2012. doi:10.1137/110836067.
[32]N. Halko, P. G. Martinsson, and J. A. Tropp. Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review, 53(2):217–288, 2011. doi:10.1137/090771806.
[33]P. M. Kroonenberg. Applied multiway data analysis. volume 702. Wiley-Interscience, 2008.
[34]M. Ishteva, L. De Lathauwer, P.-A. Absil, and S. Van Huffel. Differential-geometric Newton method for the best rank-$(R_1,R_2, R_3)$ approximation of tensors. Numerical Algorithms, 51(2):179–194, June 2009. URL: ftp://ftp.esat.kuleuven.ac.be/sista/mishteva/reports/SISTA-08-111.pdf, doi:10.1007/s11075-008-9251-2.
[35]M. Ishteva, P.-A. Absil, S. Van Huffel, and L. De Lathauwer. Best low multilinear rank approximation of higher-order tensors, based on the Riemannian trust-region scheme. SIAM Journal on Matrix Analysis and Applications, 32(1):115–135, 2011. URL: ftp://ftp.esat.kuleuven.be/sista/delathauwer/reports/ldl-09-142.pdf, doi:10.1137/090764827.
[36]L. Sorber, M. Van Barel, and L. De Lathauwer. Structured data fusion. IEEE Journal of Selected Topics in Signal Processing, 9(4):586–600, June 2015. URL: ftp://ftp.esat.kuleuven.be/stadius/lsorber/structured_data_fusion.pdf, doi:10.1109/JSTSP.2015.2400415.
[37]J.-P. Royer, N. Thirion-Moreau, and P. Comon. Computing the polyadic decomposition of nonnegative third order tensors. Signal Processing, 91(9):2159–2171, 2011. doi:10.1016/j.sigpro.2011.03.006.
[38]R. Cabral Farias, J.E. Cohen, and P. Comon. Exploring multimodal data fusion through joint decompositions with flexible couplings. Working paper or preprint, May 2015. URL: https://hal.archives-ouvertes.fr/hal-01158082.
[39]H. Mohimani, M. Babaie-Zadeh, and C. Jutten. A fast approach for overcomplete sparse decomposition based on smoothed $\ell ^0$ norm. IEEE Transactions on Signal Processing, 57(1):289–301, Jan 2009. doi:10.1109/TSP.2008.2007606.
[40]O. Debals and L. De Lathauwer. Stochastic and deterministic tensorization for blind signal separation. In Latent Variable Analysis and Signal Separation, volume 9237 of Lecture Notes in Computer Science, 3–13. Springer Berlin / Heidelberg, 2015. URL: ftp://ftp.esat.kuleuven.be/stadius/odebals/debals2015stochastic.pdf, doi:10.1007/978-3-319-22482-4_1.
[41]O. Debals, M. Van Barel, and L. De Lathauwer. Löwner-based blind signal separation of rational functions with applications. IEEE Transactions on Signal Processing, 64(8):1909–1918, April 2016. URL: ftp://ftp.esat.kuleuven.be/stadius/odebals/debals2015lowner.pdf, doi:10.1109/TSP.2015.2500179.
[42]C. L. Nikias and A. P. Petropulu. Higher-order spectra analysis: A nonlinear signal processing framework. PTR Prentice Hall, Englewood Cliffs, NJ, 1993.