Self-adaptive manifold discriminant analysis for feature extraction from hyperspectral imagery

•We propose a self-adaption optimization-based manifold learning method.•A two-stage projection matrix optimization model to optimize the projection matrix for FE.•Maximal manifold margin criterion is designed to quantify the similarity among embedded features.•Backward propagation strategy is introduced to minimize the loss value through iteration process.•Experiments validate the superior HSI classification performance. Traditional manifold learning methods generally include a single projection stage that maps high-dimensional data into lower-dimensional space. However, these methods cannot guarantee that the projection matrix is optimal for classification, which limits their practical application. To address this issue, we propose a two-stage projection matrix optimization model termed self-adaptive manifold discriminant analysis (SAMDA). In pre-training projection stage, SAMDA obtains an initial projection matrix by constructing an interclass graph and an intraclass graph under the graph embedding (GE) framework. In weight optimization stage, a maximal manifold margin criterion is developed to further optimize the weights of projection matrix by feature similarity. A self-adaptive optimization process is introduced to increase the margins among different manifolds in low-dimensional space and extract discriminant features that are beneficial to classification. Experimental results on PaviaU, Indian Pines and Heihe data sets demonstrate that the proposed SAMDA method can achieve better classification results than some state-of-the-art methods.