Low-rank 2D local discriminant graph embedding for robust image feature extraction

Abstract

As a popular feature extraction algorithm, the 2D local preserving projections (2DLPP) algorithm has been successfully applied in many fields. Using 2D image representation, the 2DLPP algorithm preserves the manifold attributes and retains the local information of high-dimensional space data. However, the 2DLPP algorithm may encounter some problems in real-world applications, such as a lack of discriminatory ability, singularity problems, and sensitivity to occlusion and noise in data. Therefore, this paper introduces low-rank into the 2DLPP algorithm and proposes a new feature extraction algorithm, which is the low-rank two-dimensional local discriminant graph embedding (LR-2DLDGE), to solve these problems. To improve the LR-2DLDGE algorithm robustness, we fuse the discriminant information in graph embedding and the low-rank properties of the data. The algorithm has three advantages: First, the algorithm uses a graph embedding (GE) framework to maintain the local neighbourhood discrimination information between data. Second, the LR-2DLDGE algorithm ensures that the data points are as independent as possible from different classes in the feature space. Finally, the algorithm uses the L1-norm as a constraint and reduces the influence of noise and corruption through low-rank learning. The theoretical computational complexity and convergence of the algorithm are explicated and proved. Extensive experimental results on three occluded and noisy image datasets confirm the effectively and robustness of LR-2DLDGE, respectively.