DocumentCode :
2608078
Title :
1D-PCA, 2D-PCA to nD-PCA
Author :
Yu, Hongchuan ; Bennamoun, Mohammed
Author_Institution :
Sch. of Comput. Sci. & Software Eng., Western Australia Univ., Perth, WA
Volume :
4
fYear :
0
fDate :
0-0 0
Firstpage :
181
Lastpage :
184
Abstract :
In this paper, we first briefly reintroduce the 1D and 2D forms of the classical principal component analysis (PCA). Then, the PCA technique is further developed and extended to an arbitrary n-dimensional space. Analogous to 1D- and 2D-PCA, the new nD-PCA is applied directly to n-order tensors (n ges 3) rather than 1-order tensors (1D vectors) and 2-order tensors (2D matrices). In order to avoid the difficulties faced by tensors computations (such as the multiplication, general transpose and Hermitian symmetry of tensors), our proposed nD-PCA algorithm has to exploit a newly proposed higher-order singular value decomposition (HO-SVD). To evaluate the validity and performance of nD-PCA, a series of experiments are performed on the FRGC 3D scan facial database
Keywords :
principal component analysis; singular value decomposition; tensors; 1D-PCA; 2D-PCA; 3D scan facial database; high-order singular value decomposition; n-dimensional space; n-order tensor; nD-PCA; principal component analysis; tensor computation; Australia; Computer science; Covariance matrix; Face recognition; Matrix decomposition; Performance evaluation; Principal component analysis; Singular value decomposition; Software engineering; Tensile stress;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Pattern Recognition, 2006. ICPR 2006. 18th International Conference on
Conference_Location :
Hong Kong
ISSN :
1051-4651
Print_ISBN :
0-7695-2521-0
Type :
conf
DOI :
10.1109/ICPR.2006.19
Filename :
1699811
Link To Document :
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