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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 917259, 13 pages
Research Article

Local and Global Geometric Structure Preserving and Application to Hyperspectral Image Classification

1Department of Computer and Information Science, University of Macau, Avenida Padre Tomas Pereira, Taipa 1356, Macau
2Department of Mathematics and Computer Science, Guangxi Normal University of Nationalities, Chongzuo 532200, China

Received 15 December 2014; Revised 16 March 2015; Accepted 16 March 2015

Academic Editor: Hakim Naceur

Copyright © 2015 Huiwu Luo 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.


Locality Preserving Projection (LPP) has shown great efficiency in feature extraction. LPP captures the locality by the K-nearest neighborhoods. However, recent progress has demonstrated the importance of global geometric structure in discriminant analysis. Thus, both the locality and global geometric structure are critical for dimension reduction. In this paper, a novel linear supervised dimensionality reduction algorithm, called Locality and Global Geometric Structure Preserving (LGGSP) projection, is proposed for dimension reduction. LGGSP encodes not only the local structure information into the optimal objective functions, but also the global structure information. To be specific, two adjacent matrices, that is, similarity matrix and variance matrix, are constructed to detect the local intrinsic structure. Besides, a margin matrix is defined to capture the global structure of different classes. Finally, the three matrices are integrated into the framework of graph embedding for optimal solution. The proposed scheme is illustrated using both simulated data points and the well-known Indian Pines hyperspectral data set, and the experimental results are promising.