@article{77a37d175bc24cc4b43a3bd773b1d933,
title = "Perturbation LDA: Learning the difference between the class empirical mean and its expectation",
abstract = "Fisher's linear discriminant analysis (LDA) is popular for dimension reduction and extraction of discriminant features in many pattern recognition applications, especially biometric learning. In deriving the Fisher's LDA formulation, there is an assumption that the class empirical mean is equal to its expectation. However, this assumption may not be valid in practice. In this paper, from the {"}perturbation{"} perspective, we develop a new algorithm, called perturbation LDA (P-LDA), in which perturbation random vectors are introduced to learn the effect of the difference between the class empirical mean and its expectation in Fisher criterion. This perturbation learning in Fisher criterion would yield new forms of within-class and between-class covariance matrices integrated with some perturbation factors. Moreover, a method is proposed for estimation of the covariance matrices of perturbation random vectors for practical implementation. The proposed P-LDA is evaluated on both synthetic data sets and real face image data sets. Experimental results show that P-LDA outperforms the popular Fisher's LDA-based algorithms in the undersampled case.",
keywords = "Face recognition, Fisher criterion, Perturbation analysis",
author = "Zheng, {Wei Shi} and Lai, {J. H.} and YUEN, {Pong Chi} and Li, {Stan Z.}",
note = "Funding Information: This project was supported by the NSFC (60675016, 60633030), the 973 Program (2006CB303104), NSF of GuangDong (06023194, 2007B030603001) and Earmarked Research Grant HKBU2113/06E from Hong Kong Research Grant Council. The authors would also like to thank the great efforts made by (associate) editor and all reviewers for improvement of this paper. Funding Information: About the Author— J.H. LAI was born in 1964. He received the M.Sc. degree in applied mathematics in 1989 and the Ph.D. degree in mathematics in 1999 from Sun Yat-sen University, Guangzhou, China. He joined Sun Yat-sen University in 1989, where currently, he is a Professor with the Department of Electronics and Communication Engineering, School of Information Science and Technology. He has published over 50 papers in the international journals, book chapters, and conferences. His current research interests are in the areas of digital image processing, pattern recognition, multimedia communication, wavelets and their applications. Dr. Lai had successfully organized the International Conference on Advances in Biometric Personal Authentication{\textquoteright} 2004, which was also the Fifth Chinese Conference on Biometric Recognition (Sinobiometrics{\textquoteright}04), Guangzhou, in December 2004. He has taken charge of more than four research projects, including NSFC (number 60144001, 60 373 082, 60675016), the Key (Key grant) Project of Chinese Ministry of Education (number 105 134), and NSF of Guangdong, China (number 021 766, 06023194). Dr. Lai has published over 60 papers and he serves as a board member of the Image and Graphics Association of China and also serves as a board member and secretary-general of the Image and Graphics Association of Guangdong. ",
year = "2009",
month = may,
doi = "10.1016/j.patcog.2008.09.012",
language = "English",
volume = "42",
pages = "764--779",
journal = "Pattern Recognition",
issn = "0031-3203",
publisher = "Elsevier Ltd.",
number = "5",
}