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Laplacian Regularized Spatial-Aware Collaborative Graph for Discriminant Analysis of Hyperspectral Imagery

Dimensionality Reduction (DR) models are of significance to extract low-dimensional features for Hyperspectral Images (HSIs) data analysis where there exist lots of noisy and redundant spectral features. Among many DR techniques, the Graph-Embedding Discriminant Analysis framework has demonstrated its effectiveness for HSI feature reduction. Based on this framework, many representation based models are developed to learn the similarity graphs, but most of these methods ignore the spatial information, resulting in unsatisfactory performance of DR models. In this paper, we firstly propose a novel supervised DR algorithm termed Spatial-aware Collaborative Graph for Discriminant Analysis (SaCGDA) by introducing a simple but efficient spatial constraint into Collaborative Graph-based Discriminate Analysis (CGDA) which is inspired by recently developed Spatial-aware Collaborative Representation (SaCR). In order to make the representation of samples on the data manifold smoother, i.e., similar pixels share similar representations, we further add the spectral Laplacian regularization and propose the Laplacian regularized SaCGDA (LapSaCGDA), where the two spectral and spatial constraints can exploit the intrinsic geometric structures embedded in HSIs efficiently. Experiments on three HSIs data sets verify that the proposed SaCGDA and LapSaCGDA outperform other state-of-the-art methods.