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Generalized two dimensional principal component analysis by Lp-norm for image analysis. 
Copyright (C) 2015 Jing Wang

See two demos in:
G2DPCA_demo_1, https://github.com/yuzhounh/G2DPCA_demo_1
G2DPCA_demo_2, https://github.com/yuzhounh/G2DPCA_demo_2
2018-6-13 22:58:14

For 1D algorithms, the image data should be 2D matrix, nSub*(height*width). 
For 2D algorithms, the image data should be 3D matrix, height*width*nSub. 
The images are listed in the subject-by-subject manner. Please refer to the 
manuscript for more information about the experiments, and refer to the 
2DPCAL1-S toolbox (https://github.com/yuzhounh/2DPCAL1-S) for the main 
script.


Variables:
database, ORL or FERET
x,   image data
lam, a tuning parameter in RSPCA or 2DPCAL1-S
s,   a tuning parameter in GPCA or G2DPCA
p,   a tuning parameter in GPCA or G2DPCA
nPV, number of projection vectors to be calculated
W,   projection vectors


Major references:
PCA
M. Turk and A. Pentland, “Eigenfaces for recognition,” Journal of
cognitive neuroscience, vol. 3, no. 1, pp. 71–86, 1991.

PCA-L1
N. Kwak, “Principal component analysis based on L1-norm maximiza-
tion,” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 30, no. 9, pp. 1672–1680, 2008.

RSPCA
D. Meng, Q. Zhao, and Z. Xu, “Improve robustness of sparse PCA by
L1-norm maximization,” Pattern Recognition, vol. 45, no. 1, pp. 487–
497, 2012.

GPCA
Z. Liang, S. Xia, Y. Zhou, L. Zhang, and Y. Li, “Feature extraction
based on Lp-norm generalized principal component analysis,” Pattern
Recognition Letters, vol. 34, no. 9, pp. 1037–1045, 2013.

2DPCA
J. Yang, D. Zhang, A. F. Frangi, and J.-Y. Yang, “Two-dimensional
PCA: a new approach to appearance-based face representation and
recognition,” IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 26, no. 1, pp. 131–137, 2004.

2DPCA-L1
X. Li, Y. Pang, and Y. Yuan, “L1-norm-based 2DPCA,” IEEE Transac-
tions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40,
no. 4, pp. 1170–1175, 2010.

2DPCAL1-S
H. Wang and J. Wang, “2DPCA with L1-norm for simultaneously robust
and sparse modelling,” Neural Networks, vol. 46, no. 0, pp. 190–198,
2013.

G2DPCA
J. Wang, “Generalized 2-D Principal Component Analysis by Lp-Norm for 
Image Analysis,” IEEE Transactions on Cybernetics, vol. 46, no. 3, 
pp. 792-803, 2016. 


Contact information:
Jing Wang
[email protected]
[email protected]

2015-3-22 11:07:44