The global and local geometric structures of data play a key role in subspace learning. Although many manifold-based subspace learning methods have been proposed for preserving the local geometric structure of data, they usually use a predefined neighbor graph to characterize it. However, the predefined neighbor graph might be not optimal since it keeps fixed during the subsequent subspace learning process. Moreover, most manifold-based subspace learning methods ignore the global structure of data. To address these issues, we propose a low-rank discriminative adaptive graph preserving (LRDAGP) subspace learning method for image feature extraction and recognition by integrating the low-rank representation , adaptive manifold learning, and supervised regularizer into a unified framework. To capture the optimal local geometric structure of data for subspace learning, LRDAGP adopts an adaptive manifold learning strategy that the neighbor graph is adaptively updated during the subspace learning process. To capture the optimal global structure of data for subspace learning, LRDAGP also seeks the low-rank representations of data in a low-dimensional subspace during the subspace learning process. Moreover, for improving the discrimination ability of the learned subspace, a supervised regularizer is designed and incorporated into the LRDAGP model. Experimental results on several image datasets show that LRDAGP is effective for image feature extraction and recognition.

数据的全局和局部几何结构在子空间学习中起关键作用。尽管已提出了许多基于流形的子空间学习方法来保留数据的局部几何结构，但它们通常使用预定义的邻居图对其进行表征。但是，预定义的邻居图可能不是最佳的，因为它在后续子空间学习过程中保持固定。此外，大多数基于流形的子空间学习方法都忽略了数据的全局结构。为了解决这些问题，我们通过将低秩表示，自适应流形学习和监督正则化器集成到一个统一的框架中，提出了一种用于图像特征提取和识别的低秩判别自适应图保留（LRDAGP）子空间学习方法。为了捕获用于子空间学习的数据的最佳局部几何结构，LRDAGP采用了一种自适应流形学习策略，即在子空间学习过程中对邻居图进行自适应更新。为了捕获用于子空间学习的数据的最佳全局结构，LRDAGP还在子空间学习过程中寻求低维子空间中数据的低秩表示。此外，为了提高学习子空间的判别能力，设计了一个监督正则化器并将其并入LRDAGP模型。在多个图像数据集上的实验结果表明，LRDAGP对于图像特征提取和识别是有效的。为了捕获用于子空间学习的数据的最佳全局结构，LRDAGP还在子空间学习过程中寻求低维子空间中数据的低秩表示。此外，为了提高学习子空间的判别能力，设计了一个监督正则化器并将其并入LRDAGP模型。在多个图像数据集上的实验结果表明，LRDAGP对于图像特征提取和识别是有效的。为了捕获用于子空间学习的数据的最佳全局结构，LRDAGP还在子空间学习过程中寻求低维子空间中数据的低秩表示。此外，为了提高学习子空间的判别能力，设计了一个监督正则化器并将其并入LRDAGP模型。在多个图像数据集上的实验结果表明，LRDAGP对于图像特征提取和识别是有效的。