Nonlinear Dimensionality Reduction via the ENH-LTSA Method for Hyperspectral Image Classification

The problems of neglecting spatial features in hyperspectral imagery (HSI) and the high complexity of Local Tangent Space Alignment (LTSA) still exist in the nonlinear dimensionality reduction with LTSA for classification. Therefore, this paper proposes an innovative ENH-LTSA (Enhanced-Local Tangent Space Alignment) method to solve the two problems. First, random projection is introduced to preliminarily reduce the dimension of HSI data. It aims to improve the speed of neighbor searching and the local tangent space construction. Then, the new method presents the similarity measure via the adaptive weighted summation kernel (AWSK) distance. The AWSK distance considers both spectral and spatial features in HSI data, and attempts to ameliorate the k-nearest neighbors (KNNs) of each pixel. Furthermore, the adaptive spatial window is proposed to automatically estimate the proper window size for the description of spatial features. After that, fast approximate KNNs graph construction via Recursive Lanczos Bisection is incorporated into the new method to reduce the complexity of KNNs searching. When finishing constructing each local tangent space, the new method uses a fast low-rank approximate singular value decomposition to speed up eigenvalue decomposition of the global alignment matrix that is constituted with local manifold coordinates. Five groups of experiments with two different HSI datasets are designed to completely analyze and testify the ENH-LTSA method. Experimental results show that ENH-LTSA outperforms LTSA, both in classification results and in computational speed.