It is very challenging to obtain sufficiently discriminative features from the original data in real-world applications. Despite the multiplicity of researches on the linear discriminative analysis, most of them are sensitive to noise, outliers and the distribution of data, especially in the low sample size context. In this paper, we propose a novel image classification method, namely Margin and Locality Discriminant Projection, which simultaneously considers the margin and locality structure information based on low-rank and sparse representation. Specifically, the proposed method integrates marginal fisher analysis and neighborhood preserving embedding so as to preserve the intrinsic structure as well as enhance the discriminative ability, on account of which a more robust and comprehensive graph can be constructed to obtain sufficiently discriminative features. Meanwhile, the low-rank and sparsity constraints are introduced to compensate the noise. The proposed model can be solved efficiently using the linear alternative direction method with adaptive penalty and eigen-decomposition. Extensive experiments are conducted on four databases and the results demonstrate that the proposed method can achieve superior performance than other state-of-the-art algorithms.

在实际应用中，要从原始数据中获得足够的区分性是非常具有挑战性的。尽管关于线性判别分析的研究很多，但大多数对噪声，离群值和数据分布敏感，尤其是在样本量较小的情况下。在本文中，我们提出了一种新的图像分类方法，即边缘和局部判别投影，它同时基于低秩和稀疏表示来考虑边缘和局部结构信息。具体而言，该方法将边际费舍尔分析与邻域保留嵌入相结合，以保留其固有结构并增强判别能力，因此，可以构建一个更强大，更全面的图形以获得足够的判别特征。同时，引入了低秩和稀疏约束来补偿噪声。使用具有自适应惩罚和特征分解的线性替代方向方法可以有效地解决所提出的模型。在四个数据库上进行了广泛的实验，结果表明，与其他最新算法相比，该方法具有更高的性能。