Laplacian Regularized Collaborative Graph for Discriminant Analysis of Hyperspectral Imagery

Collaborative graph-based discriminant analysis (CGDA) has been recently proposed for dimensionality reduction and classification of hyperspectral imagery, offering superior performance. In CGDA, a graph is constructed by ℓ2- norm minimization-based representation using available labeled samples. Different from sparse graph-based discriminant analysis (SGDA) where a graph is built by ℓ1- norm minimization, CGDA benefits from within-class sample collaboration and computational efficiency. However, CGDA does not consider data manifold structure reflecting geometric information. To improve CGDA in this regard, a Laplacian regularized CGDA (LapCGDA) framework is proposed, where a Laplacian graph of data manifold is incorporated into the CGDA. By taking advantage of the graph regularizer, the proposed method not only can offer collaborative representation but also can exploit the intrinsic geometric information. Moreover, both CGDA and LapCGDA are extended into kernel versions to further improve the performance. Experimental results on several different multiple-class hyperspectral classification tasks demonstrate the effectiveness of the proposed LapCGDA.