Abstract
We propose a new algorithm to impose independence constraints in one mode of the CP model, and show with simulations that it outperforms the existing algorithm.
This research is funded by a PhD grant of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen). Research supported by Research Council KUL: GOA-AMBioRICS, CoE EF/05/006 Optimization in Engineering, IDO 05/010 EEG-fMRI; Flemish Government: FWO: projects, G.0407.02 (support vector machines), G.0360.05 (EEG, Epileptic), G.0519.06 (Noninvasive brain oxygenation), FWO-G.0321.06 (Tensors/Spectral Analysis), G.0341.07 (Data fusion), research communities (ICCoS, ANMMM); IWT: PhD Grants; Belgian Federal Science Policy Office IUAP P6/04 (‘Dynamical systems, control and optimization’, 2007-2011); EU: BIOPATTERN (FP6-2002-IST 508803), ETUMOUR (FP6-2002-LIFESCIHEALTH 503094), Healthagents (IST-2004-27214), FAST (FP6-MC-RTN-035801); ESA: Cardiovascular Control (Prodex-8 C90242).
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References
Beckmann, C.F., Smith, S.M.: Tensorial extensions of independent component analysis for multisubject fmri analysis. Neuroimage 25, 294–311 (2005)
Cardoso, J.-F., Souloumiac, A.: Blind beamforming for non-gaussian signals. IEE Proc. F 140, 362–370 (1994)
Carroll, J.D., Chang, J.: Analysis of individual differences in multidimensional scaling via an n-way generalization of ’eckart-young’ decomposition. Psychometrika 35, 283–319 (1970)
Golub, G.H., Van Loan, C.F.: Matrix computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)
Harshman, R.A.: Foundations of the parafac procedure: models and conditions for an ’explanation’ multi-modal factor analysis. UCLA Working Papers in Phonetics, 16 (1970)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley & Sons, Chichester (2001)
Kruskal, J.B.: Three-way arrays: rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics. Psychometrika 18, 95–138 (1977)
De Lathauwer, L.: A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization. SIAM J. Matrix. Anal. Appl. 28, 642–666 (2006)
De Lathauwer, L., De Moor, B., Vandewalle, J.: An introduction to independent component analysis. J. Chemometrics 14, 123–149 (2000)
De Lathauwer, L., De Moor, B., Vandewalle, J.: On the best rank-1 and rank-{R 1,R 2, ...,R N } approximation of higher-order tensors. SIAM J. Matrix. Anal. Appl. 21, 1324–1342 (2000)
De Lathauwer, L., De Moor, B., Vandewalle, J.: Computation of the canonical decomposition by means of a simultaneous generalized schur decomposition. SIAM J. Matrix. Anal. Appl. 26, 295–327 (2004)
Leurgans, S.E., Ross, R.T., Abel, R.B.: A decomposition for three-way arrays. SIAM J Matrix. Anal. Appl. 14, 1064–1083 (1993)
Sanchez, E., Kowalski, B.R.: Tensorial resolution: a direct trilinear decomposition. J Chemometrics 4, 29–45 (1990)
Siridopoulos, N.D., Bro, R.: On the uniqueness of multilinear decomposition of n-way arrays. J Chemometrics 14, 229–239 (2000)
Smilde, A., Bro, R., Geladi, P.: Multi-way Analysis with applications in the Chemical Sciences. John Wiley & Sons, Chichester (2004)
Stegeman, A.: Comparing independent component analysis and the parafac model for artificial multi-subject fmri data. Technical Report, Heymans Institute, University of Groningen, the Netherlands (2007)
Van Der Veen, A.-J., Paulraj, A.: An analytical constant modulus algorithm. IEEE Trans. Signal Proc. 44, 1136–1155 (1996)
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De Vos, M., De Lathauwer, L., Van Huffel, S. (2007). Imposing Independence Constraints in the CP Model. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds) Independent Component Analysis and Signal Separation. ICA 2007. Lecture Notes in Computer Science, vol 4666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74494-8_5
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DOI: https://doi.org/10.1007/978-3-540-74494-8_5
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