As a famous multivariable analysis technique, regression methods, such as ridge regression, are widely used for image representation and dimensionality reduction. However, the metric of ridge regression and its variants is always the Frobenius norm (F-norm), which is sensitive to outliers and noise in data. At the same time, the performance of the ridge regression and its extensions is limited by the class number of the data. To address these problems, we propose a novel regression learning method which named low-rank discriminative regression learning (LDRL) for image representation. LDRL assumes that the input data is corrupted and thus the $L_1$ norm can be used as a sparse constraint on the noised matrix to recover the clean data for regression, which can improve the robustness of the algorithm. Due to learn a novel project matrix that is not limited by the number of classes, LDRL is suitable for classifying the data set no matter whether there is a small or large number of classes. The performance of the proposed LDRL is evaluated on six public image databases. The experimental results prove that LDRL obtains better performance than existing regression methods.

作为一种著名的多变量分析技术，诸如山脊回归之类的回归方法被广泛用于图像表示和降维。但是，岭回归及其变体的度量始终是Frobenius范数（F-norm），它对异常值和数据噪声敏感。同时，岭回归及其扩展的性能受数据的类数限制。为了解决这些问题，我们提出了一种新颖的回归学习方法，该方法称为低秩判别回归学习（LDRL）用于图像表示。LDRL假设输入数据已损坏，因此${\mathrm{大号}}_{\mathrm{1个}}$范数可以用作对噪声矩阵的稀疏约束，以恢复干净数据以进行回归，从而可以提高算法的鲁棒性。由于学习了不受类别数限制的新颖的项目矩阵，因此无论存在少量类别还是大量类别，LDRL都适用于对数据集进行分类。建议的LDRL的性能在六个公共图像数据库上进行了评估。实验结果证明，LDRL比现有的回归方法具有更好的性能。