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}}</ref> and Peter Kroonenberg's "M-mode PCA/3-mode PCA" work.<ref name="Kroonenberg1980">P. M. Kroonenberg and J. de Leeuw, [http://www.springerlink.com/content/c8551t1p31236776/ Principal component analysis of three-mode data by means of alternating least squares algorithms], Psychometrika, 45 (1980), pp. 69–97.</ref> In 2000, De Lathauwer etal. restated Tucker and Kroonenberg's work in clear and concise numerical computational terms in their SIAM paper entitled [[Multilinear Singular Value Decomposition]],<ref name="DeLathauwer2000a">L.D. Lathauwer, B.D. Moor, J. Vandewalle (2000) [http://portal.acm.org/citation.cfm?id=354398 "A multilinear singular value decomposition"], ''SIAM Journal of Matrix Analysis and Applications'', 21 (4), 1253–1278</ref> (HOSVD) and in their paper "On the Best Rank-1 and Rank-(R<sub>1</sub>, R<sub>2</sub>, ..., R<sub>N</sub> ) Approximation of Higher-order Tensors".<ref name=DeLathauwer2000b>L. D. Lathauwer, B. D. Moor, J. Vandewalle (2000) [http://portal.acm.org/citation.cfm?id=354405 "On the best rank-1 and rank-(R1, R2, ..., RN ) approximation of higher-order tensors"], ''SIAM Journal of Matrix Analysis and Applications'' 21 (4), 1324–1342.</ref>
Circa 2001, Vasilescu reframed the data analysis, recognition and synthesis problems as multilinear tensor problems based on the insight that most observed data are the compositional consequence of several causal factors of data formation, and are well suited for multi-modal data tensor analysis. The power of the tensor framework was showcased by analyzing human motion joint
<ref name="Vasilescu2002b">M. A. O. Vasilescu (2002) [http://www.media.mit.edu/~maov/motionsignatures/hms_icpr02_corrected.pdf "Human Motion Signatures: Analysis, Synthesis, Recognition," Proceedings of International Conference on Pattern Recognition (ICPR 2002), Vol. 3, Quebec City, Canada, Aug, 2002, 456-460.]</ref>
(CVPR 2001, ICPR 2002), face recognition - [[TensorFaces]],
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