A closed-form solution for multilinear PARAFAC decompositions

SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop

Volumn , Issue , 2008, Pages 487-491

  Roemer, Florian ^a   Haardt, Martin ^a  

^a ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Array signal processing; Multidimensional signal processing; Parameter estimation

Indexed keywords

ACOUSTIC MICROSCOPES; AMPLITUDE MODULATION; CHEMICAL SENSORS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; DECOMPOSITION; ESTIMATION; MATRIX ALGEBRA; MISSILE BASES; SENSOR ARRAYS; SENSORS; SIGNAL PROCESSING; SOLUTIONS; TENSORS;

ARRAY SIGNAL PROCESSING; BEST ESTIMATE; CLOSED-FORM SOLUTIONS; COMPUTER SIMULATIONS; DIMENSIONAL PROBLEMS; IDENTIFIABILITY; ITERATIVE TECHNIQUES; MULTICHANNEL SIGNAL PROCESSING; MULTIDIMENSIONAL SIGNAL PROCESSING; PARAFAC; PARAFAC ANALYSIS; PARALLEL FACTOR ANALYSIS; PARAMETER ESTIMATION; SIMULTANEOUS MATRIX DIAGONALIZATION;

SIGNAL THEORY;

EID: 52949085885     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SAM.2008.4606918     Document Type: Conference Paper

References (15)

1. L. Albera, A. Ferréol, P. Comon, and P. Chevalier, "Blind identification of overcomplete mixtures of sources (BiOME)", Elsevier J. Linear Algebra Appl., vol. 391, pp. 3-30, Nov. 2004.
2. R. Bro, N. Sidiropoulos, and G. B. Giannakis, "A fast least squares algorithm for separating trilinear mixtures", in Proc. Int. Workshop on Independent Component Analysis for Blind Signal Separation (ICA 99), pp. 289-294, Jan. 1999.
3. R. B. Cattell, "Parallel proportional profiles and other principles for determining the choice of factors by rotation", Psychometrika, vol. 9, Dec. 1944.
4. J. P. C. L. da Costa, M. Haardt, and F. Roemer, "Robust methods based on HOSVD for estimating the number of components in PARAFAC models", in Proc. 5-th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2008), Darmstadt, Germany, July 2008.
5. L. de Lathauwer, "Parallel Factor Analysis by Means of Simultaneous Matrix Decompositions", in Proc. First IEEE Int. Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2005), pp. 125-128, Dec. 2005.
6. L. de Lathauwer, "A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization", SIAM J. Matrix Anal. Appl., vol. 28, no. 3, pp. 642-666, Dec. 2006.
7. L. de Lathauwer, B. de Moor, and J. Vanderwalle, "A multilinear singular value decomposition", SIAM J. Matrix Anal. Appl., vol. 21, no. 4, pp. 1253-1278, 2000.
8. L. de Lathauwer, B. de Moor, and J. Vanderwalle, "Independent componant analysis and (simultaneous) third-order tensor diagonalization", IEEE Trans. on Signal Processing, vol. 49, no. 10, Oct. 2001.
9. P. M. Kroonenberg and J. de Leeuw, "Principal component analysis of three-mode data by means of alternating least squares algorithms", Psychometrika, vol. 45, no. 1, pp. 69-97, Mar. 1980.
10. J. B. Kruskal, "Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics", Linear Algebra Applications, vol. 18, pp. 95-138, 1977.
11. N. Petrochilos and P. Comon, "Link between the Joint Diagonalisation of symmetrical cubes and PARAFAC: an application to Secondary Surveillance Radar", in Proc. of IEEE SAM 2006, Waltham (MA), 12-14 July 2006.
12. M. Rajih, Blind Identification of Underdetermined Mixtures Based on the Characteristic Function, PhD thesis, Université de Nice à Sophia Antipolis, Dec. 2006.
13. F. Roemer and M. Haardt, "A closed-form solution for Parallel Factor (PARAFAC) analysis", in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008), pp. 2365-2368, Las Vegas, NV, USA, Apr. 2008.
14. E. Sanchez and B. R. Kowalski, "Tensorial resolution: a direct trilinear decomposition", J. Chemom., vol. 4, pp. 29-45, 1990.
15. N. D. Sidiropoulos, G. B. Giannakis, and R. Bro, "Blind PARAFAC receivers for DS-CDMA Systems", IEEE Transactions Sig. Process., vol. 48, pp. 810-823, Mar. 2000.