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

Locality Preserving Projection (LPP) has shown great efficiency in feature extraction. LPP capturesthe locality by the K-nearest neighborhoods. However, recent progress has demonstrated the importanceof global geometric structure in discriminant analysis. Thus, both the locality and global geometricstructure are critical for dimension reduction. In this paper, a novel linear supervised dimensionalityreduction algorithm, called Locality and Global Geometric Structure Preserving (LGGSP)projection, is proposed for dimension reduction. LGGSP encodes not only the local structure informationinto 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 localintrinsic structure. Besides, a margin matrix is defined to capture the global structure of differentclasses. Finally, the three matrices are integrated into the framework of graph embedding for optimalsolution. The proposed scheme is illustrated using both simulated data points and the well-knownIndian Pines hyperspectral data set, and the experimental results are promising.