Abstract
Marginal Fisher analysis (MFA) not only aims to maintain the original relations of neighboring data points of the same class but also wants to keep away neighboring data points of the different classes. MFA can effectively overcome the limitation of linear discriminant analysis (LDA) due to data distribution assumption and available projection directions. However, MFA confronts the undersampled problems. Generalized marginal Fisher analysis (GMFA) based on a new optimization criterion is presented, which is applicable to the undersampled problems. The solutions to the proposed criterion for GMFA are derived, which can be characterized in a closed form. Among the solutions, two specific algorithms, namely, normal MFA (NMFA) and orthogonal MFA (OMFA), are studied, and the methods to implement NMFA and OMFA are proposed. A comparative study on the undersampled problem of face recognition is conducted to evaluate NMFA and OMFA in terms of classification accuracy, which demonstrates the effectiveness of the proposed algorithms.
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This work was supported by Science Foundation of the Fujian Province of China (No. 2010J05099)
Wu-Yi Yang received the Ph.D. degree from the Institute of Automation, Chinese Academy of Sciences, PRC in 2009. Currently, he is an assistant professor at the Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education and the College of Oceanography and Environmental Science, Xiamen University, PRC.
His research interests include communication signal processing, image processing, video processing, and machine learning.
Sheng-Xing Liu received the Ph.D. degree from Xiamen University, PRC in 2009. Currently, he is an associate professor at the Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education and the College of Oceanography and Environmental Science, Xiamen University.
His research interests include signal processing and machine learning.
Tai-Song Jin received the Ph.D. degree in computer science from Beijing Institute of Technology, PRC in 2007. now, he is an assistant professor at the School of Information Science and Technology, Xiamen University, PRC and working on developing new low-level vision algorithms for object recognition.
His research interests include computer vision and pattern recognition.
Xiao-Mei Xu received the B. Sc., M. Sc., and Ph. D. degrees in underwater acoustics from the Xiamen University, PRC in 1982, 1988, and 2002, respectively. She is currently a professor at the Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education and the College of Oceanography and Environmental Science, Xiamen University.
Her research interests include underwater acoustic data communication, and underwater acoustic detection and sensing.
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Yang, WY., Liu, SX., Jin, TS. et al. An optimization criterion for generalized marginal Fisher analysis on undersampled problems. Int. J. Autom. Comput. 8, 193–200 (2011). https://doi.org/10.1007/s11633-011-0573-5
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DOI: https://doi.org/10.1007/s11633-011-0573-5