Many methods based on matrix factorization have recently been proposed and achieve good performance in many practical applications. Latent low-rank representation (LatLRR) is a marvelous feature extraction method, and it has shown a powerful ability in extracting robust data features. However, LatLRR and the variants of LRR have some shortcomings as follows: (1) The label information of the original data are not considered, and they are usually unsupervised learning methods. (2) The local structure information is not preserved in the projected space. (3) The dimension of projection space is not reduced, and the extracted features do not have good and distinct interpretability. In order to solve the above problems, a new dimensionality reduction method based on low-rank representation termed robust sparse low-rank embedding (RSLRE) is proposed. Especially, by introducing the $L_{2,1}$ norm constraint into the projected matrix, RSLRE algorithm can adaptively select the most discriminative and robust data features. In addition, two different matrices are introduced to ensure that projected feature dimensions can be reduced, and the obtained features can simultaneously maintain most of the energy of the observed samples. A large number of experiments on five public image datasets show that the proposed method can achieve very encouraging results compared with some classical feature extraction methods.

最近提出了许多基于矩阵分解的方法，并在许多实际应用中取得了良好的性能。潜在低秩表示（LatLRR）是一种了不起的特征提取方法，它在提取鲁棒数据特征方面表现出了强大的能力。但是，LatLRR 和 LRR 的变体存在以下不足：（1）未考虑原始数据的标签信息，通常是无监督学习方法。(2) 局部结构信息不保留在投影空间中。(3)投影空间的维数没有降低，提取的特征没有很好的清晰的可解释性。为了解决上述问题，提出了一种新的基于低秩表示的降维方法，称为鲁棒稀疏低秩嵌入（RSLRE）。${升}_{2,1}$将范数约束引入到投影矩阵中，RSLRE 算法可以自适应地选择最具辨别力和鲁棒性的数据特征。此外，引入了两个不同的矩阵，以确保可以减少投影特征维度，并且获得的特征可以同时保持观察样本的大部分能量。在五个公共图像数据集上的大量实验表明，与一些经典的特征提取方法相比，所提出的方法可以取得非常令人鼓舞的结果。