Abstract 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.

中文翻译：

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从高光谱图像中提取特征的自适应流形判别分析

摘要 传统的流形学习方法通​​常包括将高维数据映射到低维空间的单个投影阶段。然而，这些方法不能保证投影矩阵对于分类是最优的，这限制了它们的实际应用。为了解决这个问题，我们提出了一种称为自适应流形判别分析（SAMDA）的两阶段投影矩阵优化模型。在预训练投影阶段，SAMDA通过在图嵌入（GE）框架下构建类间图和类内图来获得初始投影矩阵。在权重优化阶段，开发了最大流形边际准则，通过特征相似度进一步优化投影矩阵的权重。引入自适应优化过程，增加低维空间中不同流形之间的边际，提取有利于分类的判别特征。在 PaviaU、Indian Pines 和 Heihe 数据集上的实验结果表明，所提出的 SAMDA 方法比一些最先进的方法可以获得更好的分类结果。