Generalized two dimensional principal component analysis by Lp-norm for image analysis.

Copyright (C) 2015 Jing Wang

Two demos:
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 $\times$ (height $\times$ width).
For 2D algorithms, the image data should be 3D matrix, height $\times$ width $\times$ 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 maximization,” 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 Transactions 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
wangjing0@seu.edu.cn
yuzhounh@163.com
2015-3-22 11:07:44