IEEE Trans Cybern. 2019 May;49(5):1859-1872. doi: 10.1109/TCYB.2018.2815559. Epub 2018 Mar 27.
2-D neighborhood preserving projection (2DNPP) uses 2-D images as feature input instead of 1-D vectors used by neighborhood preserving projection (NPP). 2DNPP requires less computation time than NPP. However, both NPP and 2DNPP use the L norm as a metric, which is sensitive to noise in data. In this paper, we proposed a novel NPP method called low-rank 2DNPP (LR-2DNPP). This method divided the input data into a component part that encoded low-rank features, and an error part that ensured the noise was sparse. Then, a nearest neighbor graph was learned from the clean data using the same procedure as 2DNPP. To ensure that the features learned by LR-2DNPP were optimal for classification, we combined the structurally incoherent learning and low-rank learning with NPP to form a unified model called discriminative LR-2DNPP (DLR-2DNPP). By encoding the structural incoherence of the learned clean data, DLR-2DNPP could enhance the discriminative ability for feature extraction. Theoretical analyses on the convergence and computational complexity of LR-2DNPP and DLR-2DNPP were presented in details. We used seven public image databases to verify the performance of the proposed methods. The experimental results showed the effectiveness of our methods for robust image representation.
二维邻域保持投影（2DNPP）使用二维图像作为特征输入，而不是邻域保持投影（NPP）使用的一维向量。2DNPP 比 NPP 所需的计算时间更少。然而，NPP 和 2DNPP 都使用 L 范数作为度量，这对数据中的噪声很敏感。在本文中，我们提出了一种新的 NPP 方法，称为低秩 2DNPP（LR-2DNPP）。该方法将输入数据分为两个部分：一部分编码低秩特征，另一部分确保噪声是稀疏的。然后，使用与 2DNPP 相同的过程从干净数据中学习最近邻图。为了确保 LR-2DNPP 学习到的特征最适合分类，我们将结构不一致学习和低秩学习与 NPP 相结合，形成一个称为判别式低秩 2DNPP（DLR-2DNPP）的统一模型。通过对学习到的干净数据的结构不和谐进行编码，DLR-2DNPP 可以增强特征提取的判别能力。详细介绍了 LR-2DNPP 和 DLR-2DNPP 的收敛性和计算复杂性的理论分析。我们使用七个公共图像数据库来验证所提出方法的性能。实验结果表明，我们的方法对于稳健的图像表示是有效的。
