Multilinear principal component analysis
Multilinear principal component analysis (MPCA) [1] is a multilinear extension of principal component analysis (PCA) and it is a classical algorithm in multilinear subspace learning.
The algorithm
MPCA performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variations. As in PCA, MPCA works on centered data. The MPCA solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems. Each subproblem is a classical PCA problem, which can be easily solved.
Extensions
- Uncorrelated MPCA (UMPCA) [2]
- Boosting+MPCA[3]
- Non-negative MPCA (NMPCA) [4]
- Robust MPCA (RMPCA) [5]
Resources
- ```Matlab implementation: MPCA.
- ^ H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, "MPCA: Multilinear principal component analysis of tensor objects," IEEE Trans. Neural Netw., vol. 19, no. 1, pp. 18–39, Jan. 2008.
- ^ H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, "Uncorrelated multilinear principal component analysis for unsupervised multilinear subspace learning," IEEE Trans. Neural Netw., vol. 20, no. 11, pp. 1820–1836, Nov. 2009.
- ^ H. Lu, K. N. Plataniotis and A. N. Venetsanopoulos, "Boosting Discriminant Learners for Gait Recognition using MPCA Features", EURASIP Journal on Image and Video Processing, Volume 2009, Article ID 713183, 11 pages, 2009. doi:10.1155/2009/713183.
- ^ Y. Panagakis, C. Kotropoulos, G. R. Arce, "Non-negative multilinear principal component analysis of auditory temporal modulations for music genre classification", IEEE Trans. on Audio, Speech, and Language Processing, vol. 18, no. 3, pp. 576–588, 2010.
- ^ K. Inoue, K. Hara, K. Urahama, "Robust multilinear principal component analysis", Proc. IEEE Conference on Computer Vision, 2009, pp. 591–597.