Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 176058, 15 pages
Research Article

An Efficient Feature Extraction Method, Global Between Maximum and Local Within Minimum, and Its Applications

1School of Science, Xi'an Jiaotong University, Xi'an 710049, China
2State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, China

Received 28 March 2011; Revised 16 April 2011; Accepted 18 April 2011

Academic Editor: Jyh Horng Chou

Copyright © 2011 Lei Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Feature extraction plays an important role in preprocessing procedure in dealing with small sample size problems. Considering the fact that LDA, LPP, and many other existing methods are confined to one case of the data set. To solve this problem, we propose an efficient method in this paper, named global between maximum and local within minimum. It not only considers the global structure of the data set, but also makes the best of the local geometry of the data set through dividing the data set into four domains. This method preserves relations of the nearest neighborhood, as well as demonstrates an excellent performance in classification. Superiority of the proposed method in this paper is manifested in many experiments on data visualization, face representative, and face recognition.