IEEE Trans Cybern. 2017 Dec;47(12):4250-4262. doi: 10.1109/TCYB.2016.2623638. Epub 2016 Nov 10.
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional subspace for supervised learning tasks, e.g., classification and regression. This paper aims to learn both the discriminant low-rank representation (LRR) and the robust projecting subspace in a supervised manner. To achieve this goal, we cast the problem into a constrained rank minimization framework by adopting the least squares regularization. Naturally, the data label structure tends to resemble that of the corresponding low-dimensional representation, which is derived from the robust subspace projection of clean data by low-rank learning. Moreover, the low-dimensional representation of original data can be paired with some informative structure by imposing an appropriate constraint, e.g., Laplacian regularizer. Therefore, we propose a novel constrained LRR method. The objective function is formulated as a constrained nuclear norm minimization problem, which can be solved by the inexact augmented Lagrange multiplier algorithm. Extensive experiments on image classification, human pose estimation, and robust face recovery have confirmed the superiority of our method.
低秩学习因其在各种实际任务中的有效性而受到广泛关注，例如子空间分割和图像分类。大多数低秩方法无法为监督学习任务（例如分类和回归）捕获低维子空间。本文旨在以监督的方式学习判别低秩表示（LRR）和稳健的投影子空间。为了实现这一目标，我们通过采用最小二乘正则化将问题转化为一个约束秩最小化框架。自然地，数据标签结构倾向于类似于由低秩学习从干净数据的稳健子空间投影得到的对应低维表示。此外，通过施加适当的约束（例如拉普拉斯正则化），原始数据的低维表示可以与一些信息结构相关联。因此，我们提出了一种新的约束 LRR 方法。目标函数被公式化为一个约束核范数最小化问题，可以通过近似增广拉格朗日乘子算法来解决。在图像分类、人体姿态估计和稳健人脸恢复方面的大量实验证实了我们方法的优越性。
