Name
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 |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1109/ICPR.2006.19 | ICPR (4) |
Keywords | Field | DocType |
2d-pca,hermitian symmetry,3d scan facial database,arbitrary n-dimensional space,high-order singular value decomposition,new nd-pca,nd-pca,pca technique,tensor computation,proposed nd-pca algorithm,1-order tensors,2-order tensors,component analysis,n-order tensor,1d-pca,principal component analysis,n-dimensional space,tensors computation,singular value decomposition,tensors,higher-order singular value decomposition | Singular value decomposition,Invariants of tensors,Pattern recognition,Transpose,Tensor,Matrix (mathematics),Multiplication,Hermitian function,Artificial intelligence,Mathematics,Principal component analysis | Conference |
Volume | ISSN | ISBN |
4 | 1051-4651 | 0-7695-2521-0 |
Citations | PageRank | References |
20 | 0.93 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hongchuan Yu | 1 | 116 | 12.72 |
| Mohammed Bennamoun | 2 | 37 | 4.14 |