IEEE Trans Pattern Anal Mach Intell. 2022 May;44(5):2438-2452. doi: 10.1109/TPAMI.2020.3033994. Epub 2022 Apr 1.
Regression analysis based methods have shown strong robustness and achieved great success in face recognition. In these methods, convex l-norm and nuclear norm are usually utilized to approximate the l-norm and rank function. However, such convex relaxations may introduce a bias and lead to a suboptimal solution. In this paper, we propose a novel Enhanced Group Sparse regularized Nonconvex Regression (EGSNR) method for robust face recognition. An upper bounded nonconvex function is introduced to replace l-norm for sparsity, which alleviates the bias problem and adverse effects caused by outliers. To capture the characteristics of complex errors, we propose a mixed model by combining γ-norm and matrix γ-norm induced from the nonconvex function. Furthermore, an l-norm based regularizer is designed to directly seek the interclass sparsity or group sparsity instead of traditional l-norm. The locality of data, i.e., the distance between the query sample and multi-subspaces, is also taken into consideration. This enhanced group sparse regularizer enables EGSNR to learn more discriminative representation coefficients. Comprehensive experiments on several popular face datasets demonstrate that the proposed EGSNR outperforms the state-of-the-art regression based methods for robust face recognition.
基于回归分析的方法在人脸识别中表现出了很强的鲁棒性，并取得了巨大的成功。在这些方法中，通常利用凸 l-范数和核范数来近似 l-范数和秩函数。然而，这种凸松弛可能会引入偏差，导致次优解。本文提出了一种新颖的增强群组稀疏正则化非凸回归（EGSNR）方法，用于鲁棒人脸识别。引入了一个有界的非凸函数来代替 l-范数进行稀疏化，从而缓解了偏差问题和异常值带来的不利影响。为了捕捉复杂误差的特征，我们通过结合γ-范数和由非凸函数诱导的矩阵γ-范数，提出了一种混合模型。此外，设计了一个基于 l-范数的正则项，直接寻求类间稀疏性或群组稀疏性，而不是传统的 l-范数。还考虑了数据的局部性，即查询样本与多个子空间之间的距离。这种增强的群组稀疏正则化使 EGSNR 能够学习更具判别力的表示系数。在几个流行的人脸数据集上的综合实验表明，所提出的 EGSNR 优于最新的基于回归的鲁棒人脸识别方法。
