Nonlocal graph theory based transductive learning for hyperspectral image classification

• The NLM similarity feature with full dimensionality of HSI data is exploited. • A trunsductive variational model with nonlocal sparse graph expression is presented. • A fast transductive alternating minimization iteration algorithm is designed to solve the classification problem. • The classification results exhibit the excellent classification performance of the proposed method. The Overall Flowchart of Transductive Learning Method for HSI Classification using Nonlocal Graph Theory Hyperspectral Image classification plays an important role in the maintenance of remote image analysis, which has been attracting a lot of research interest. Although various approaches, including unsupervised and supervised methods, have been proposed, obtaining a satisfactory classification result is still a challenge. In this paper, an efficient transductive learning method using variational nonlocal graph theory for hyperspectral image classification is proposed. First, the nonlocal vector neighborhood similarity is employed to build sparse graph representation. Then the variational segmentation framework is extended to label space, and the vectorization nonlocal energy function is constructed. Next, a fast comprehensive alternating minimization iteration algorithm is designed to implement labels transductive learning. At the same time, the labeled sample constraints are doubled ensured with simplex projection. Finally, experiments on six widely used hyperspectral image datasets are implemented, compared with other state-of-the-art classification methods, the classification results demonstrate that the proposed method has higher classification performance. Benefiting from graph theory and transductive idea, the proposed classification method can propagate labels and overcome the very high dimensionality and limited labeling problem to some extent.