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.

高光谱图像分类在远程图像分析的维护中起着重要的作用，已经引起了很多研究兴趣。尽管已经提出了包括无监督和有监督的方法在内的各种方法，但是获得令人满意的分类结果仍然是一个挑战。本文提出了一种基于变分非局域图理论的高效率转导学习方法，用于高光谱图像分类。首先，采用非局部矢量邻域相似度建立稀疏图表示。然后将变分分割框架扩展到标签空间，并构造矢量化非局部能量函数。接下来，设计了一种快速的综合交替最小化迭代算法来实现标签转换学习。同时，标记的样本约束通过单形投影得以确保加倍。最后，对六个广泛使用的高光谱图像数据集进行了实验，与其他最新的分类方法相比，分类结果表明该方法具有较高的分类性能。得益于图论和转导思想，所提出的分类方法可以传播标签，并在一定程度上克服了维数高和标签受限的问题。