The robustness to outliers, noises, and corruptions has been paid more attention recently to increase the performance in linear feature extraction and image classification. As one of the most effective subspace learning methods, low-rank representation (LRR) can improve the robustness of an algorithm by exploring the global representative structure information among the samples. However, the traditional LRR cannot project the training samples into low-dimensional subspace with supervised information. Thus, in this paper, we integrate the properties of LRR with supervised dimensionality reduction techniques to obtain optimal low-rank subspace and discriminative projection at the same time. To achieve this goal, we proposed a novel model named Discriminative Low-Rank Projection (DLRP). Furthermore, DLRP can break the limitation of the small class problem which means the number of projections is bound by the number of classes. Our model can be solved by alternatively linearized alternating direction method with adaptive penalty and the singular value decomposition. Besides, the analyses of differences between DLRP and previous related models are shown. Extensive experiments conducted on various contaminated databases have confirmed the superiority of the proposed method.

中文翻译：

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区分性低秩投影，用于强大的子空间学习

为了提高线性特征提取和图像分类的性能，最近更加关注了对异常值，噪声和损坏的鲁棒性。作为最有效的子空间学习方法之一，低秩表示（LRR）可以通过探索样本之间的全局代表结构信息来提高算法的鲁棒性。但是，传统的LRR无法将训练样本投射到具有监督信息的低维子空间中。因此，在本文中，我们将LRR的属性与监督降维技术相结合，以同时获得最佳的低秩子空间和判别投影。为了实现这一目标，我们提出了一种新的模型，称为区分低秩投影（DLRP）。此外，DLRP可以打破小类别问题的局限性，这意味着投影的数量受类别数量的限制。我们的模型可以通过具有自适应惩罚和奇异值分解的交替线性交替方向方法来求解。此外，还对DLRP与先前相关模型之间的差异进行了分析。在各种受污染数据库上进行的大量实验已经证实了该方法的优越性。