366
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

The rank of a 2 × 2 × 2 tensor

Pages 943-950 | Received 19 May 2009, Accepted 05 Nov 2010, Published online: 14 Apr 2011

References

  • E. Acar, S.A. Çamtepe, M.S. Krishnamoorthy, and B. Yener, Modeling and multiway analysis of chatroom tensors, Proceedings of the IEEE International Conference on Intelligence and Security Informatics EMBS 2007, IEEE Computer Society, Convention Center, “Cité Internationale”, Lyon, France, 2005, pp. 256–268 (Lecture Notes in Computer Science, Vol. 3495).
  • Beckmann , C and Smith , S . 2005 . Tensorial extensions of the independent component analysis for multisubject FMRI analysis . NeuroImage , 25 : 294 – 311 .
  • Comon , P . 2002 . “ Tensor decompositions ” . In Mathematics in Signal Processing V , Edited by: McWhirter , JG and Proudler , IK . 1 – 24 . Oxford, , UK : Clarendon Press .
  • De Lathauwer , L and De Moor , B . 1998 . “ From matrix to tensor: Multilinear algebra and signal processing ” . In Mathematics in Signal Processing IV , Edited by: McWhirter , J and Proudler , I . 1 – 15 . Oxford, , UK : Clarendon Press .
  • Golub , G and Van Loan , C . 1996 . Matrix Computations, , 3rd edition , Baltimore : Johns Hopkins University Press .
  • Kiers , HAL . 2000 . Towards a standardized notation and terminology in multiway analysis . J. Chemometrics , 14 : 105 – 122 .
  • T.G. Kolda and B.W. Bader, Higher-order web link analysis using multilinear algebra, Proceedings of the 5th IEEE International Conference on Data Mining, ICDM 2005, IEEE Computer Society, InterContinental Houston, Houston, TX, 2005, pp. 242–249.
  • Kolda , TG and Bader , BW . 2009 . Tensor decompositions and applications . SIAM Rev. , 51 : 455 – 500 .
  • Kroonenberg , PM . 1983 . Three-mode Principal Component Analysis: Theory and Applications , Leiden : DSWO Press .
  • Kruskal , JB . 1989 . “ Rank, decomposition, and uniqueness for 3-way and n-way arrays ” . In Multiway Data Analysis , Edited by: Coppi , R and Bolasco , S . 7 – 18 . Amsterdam : Elsevier .
  • Martínez-Montes , E , Valdées-Sosa , PA , Miwakeichi , F , Goldman , RI and Cohen , MS . 2004 . Concurrent EEG/fmri analysis by multiway partial least squares . NeuroImage , 22 : 1023 – 1034 .
  • Miwakeichi , F , Martínez-Montes , E , Valdés-Sosa , PA , Nishiyama , N , Mizuhara , H and Yamaguchi , Y . 2004 . Decomposing EEG data into space-time-frequency components using parallel factor analysis . NeuroImage , 22 : 1035 – 1045 .
  • Martin , CDMoravitz and Loan , CFVan . A Jacobi-type method for computing orthogonal tensor decompositions, SIAM J. Matrix Anal. Appl. 30 (2008), pp. 1219–1232
  • Savas , B and Eldén , L . 2007 . Handwritten digit classification using higher order singular value decomposition . Pattern Recogn. , 40 : 993 – 1003 .
  • Sidiropoulos , N , Bro , R and Giannakis , G . 2000 . Parallel factor analysis in sensor array processing . IEEE Trans. Sig. Proc. , 48 : 2377 – 2388 .
  • Smilde , A , Bro , R and Geladi , P . 2004 . Multi-way Analysis: Applications in the Chemical Sciences , Chichester, , UK : Wiley .
  • Ten Berge , JMF . 1991 . Kruskal's polynomial for 2 × 2 × 2 arrays and a generalization to 2 × n × n arrays . Psychometrika , 56 : 631 – 636 .
  • M.A.O. Vasilescu and D. Terzopoulos, Multilinear analysis of image ensembles: Tensorfaces, Proceedings of the 7th European Conference on Computer Vision ECCV 2002, Springer, Palladium and Industriens Hus, Copenhagen, 2002, pp. 447–460 (Lecture Notes in Computer Science, Vol. 2350).
  • Vasilescu , MAO and Terzopoulos , D . Multilinear image analysis for face recognition . Proceedings of the International Conference on Pattern Recognition ICPR 2002 . 2002 . Vol. 2 , pp. 511 – 514 . Quebec City, , Canada
  • Vasilescu , MAO and Terzopoulos , D . Multilinear subspace analysis of image ensembles . Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition CVPR 2003 . 2003 . pp. 93 – 99 . Madison, Wisconsin : IEEE Computer Society, Monona Terrace Convention Center .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.