Low-Rank 2-D Neighborhood Preserving Projection for Enhanced Robust Image Representation
提出低秩二维邻域保持投影方法，将图像分解为低秩特征和稀疏噪声，再学习邻域图，并引入结构不连贯学习增强判别力，实验证明对噪声图像表示有效。
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> 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 (DLR2DNPP). 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.