Incorporating local and global geometric structure for hyperspectral image classification

The highly correlated data structure makes the computational cost of hyperspectral image (HSI) much complex. The need of effective processing and analyzing of HSI has met many difficulties and become an open topic in the community of high dimensional data analysis. Local structure has shown great efficiency in feature extraction. Yet recent progress has also 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 discriminant information into the optimal objective functions, but also the global margin information. To be specific, two adjacent graph (viz., similarity matrix and variance matrix), are constructed to detect the local intrinsic structure, simultaneously, a graph matrix to capture the global margin of different classes. Experimental results on both benchmark data sets and the real hyperspectral image data set demonstrate the effectiveness and practicability of proposed scheme.