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Historically, MPCA has been referred to as "M-mode PCA", a terminology which was coined by Peter Kroonenberg in 1980.<ref name="Kroonenberg1980"/> In 2005, [[M. Alex O. Vasilescu|Vasilescu]] and [[Demetri Terzopoulos|Terzopoulos]] introduced the Multilinear PCA<ref name="MPCA-MICA2005">M. A. O. Vasilescu, D. Terzopoulos (2005) [http://www.media.mit.edu/~maov/mica/mica05.pdf "Multilinear Independent Component Analysis"], "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR’05), San Diego, CA, June 2005, vol.1, 547-553."</ref> terminology as a way to better differentiate between linear and multilinear tensor decomposition, as well as, to better differentiate between the work<ref name="Vasilescu2002b"/><ref name="Vasilescu2002a"/><ref name="Vasilescu2003"/><ref name="Vasilescu2004"/> that computed 2nd order statistics associated with each data tensor mode(axis), and subsequent work on Multilinear Independent Component Analysis<ref name="MPCA-MICA2005"/> that computed higher order statistics associated with each tensor mode/axis.
Multilinear PCA may be applied to compute the causal factors of data formation, or as signal processing tool on data tensors whose individual observation have either been vectorized <ref name="Vasilescu2002b"/>
<ref name="Vasilescu2002a">M.A.O. Vasilescu, D. Terzopoulos (2002) [http://www.media.mit.edu/~maov/tensorfaces/eccv02_corrected.pdf "Multilinear Analysis of Image Ensembles: TensorFaces," Proc. 7th European Conference on Computer Vision (ECCV'02), Copenhagen, Denmark, May, 2002, in Computer Vision -- ECCV 2002, Lecture Notes in Computer Science, Vol. 2350, A. Heyden et al. (Eds.), Springer-Verlag, Berlin, 2002, 447-460. ]</ref>
<ref name="Vasilescu2003">M.A.O. Vasilescu, D. Terzopoulos (2003) [http://www.media.mit.edu/~maov/tensorfaces/cvpr03.pdf "Multilinear Subspace Analysis for Image Ensembles,'' M. A. O. Vasilescu, D. Terzopoulos, Proc. Computer Vision and Pattern Recognition Conf. (CVPR '03), Vol.2, Madison, WI, June, 2003, 93-99.]</ref>
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== Feature selection ==
MPCA features: Supervised MPCA feature selection is used in object recognition<ref name="MPCA">, M. A. O. Vasilescu, D. Terzopoulos (2003) [http://www.cs.toronto.edu/~maov/tensorfaces/cvpr03.pdf "Multilinear Subspace Analysis of Image Ensembles"], "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR’03), Madison, WI, June, 2003"</ref> while unsupervised MPCA feature selection is employed in visualization task.<ref>H. Lu, H.-L. Eng, M. Thida, and K.N. Plataniotis, "[http://www.dsp.utoronto.ca/~haiping/Publication/CrowdMPCA_CIKM2010.pdf Visualization and Clustering of Crowd Video Content in MPCA Subspace]," in Proceedings of the 19th ACM Conference on Information and Knowledge Management (CIKM 2010)
== Extensions ==
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