Least squares regression (LSR) is widely used for pattern classification. Some variants based on it try to enlarge the margin between different classes to achieve better performance. However, the large margin classifier doesn’t work well when it deals with the complex applications in the real world, such as face recognition, where images are captured with different facial expressions, lighting conditions or background. To address this problem, we propose a regularized negative label relaxation least squares regression method with the following characteristics. First, we introduce a negative \( \varepsilon \) dragging technique to relax the strict binary label matrix into a slack label matrix, which has more freedom to fit the labels and reduces the class margins at the same time. Second, we introduce manifold learning and class compactness graph to devise a regularization item to preserve the intrinsic structure of data and avoid the problem of overfitting. The class compactness graph can enable samples from the same class to be kept close together after they are transformed into the slack label space. The algorithm based on L2-norm loss function is devised. The experimental results show that our algorithm achieves better classification accuracy.

中文翻译：

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用于人脸识别的正则化负标签松弛最小二乘回归

最小二乘回归（LSR）被广泛用于模式分类。基于它的某些变体试图扩大不同类之间的余量，以获得更好的性能。但是，大边距分类器在处理现实世界中的复杂应用程序（例如人脸识别）时效果不佳，例如使用不同的面部表情，光照条件或背景来捕获图像。为了解决这个问题，我们提出一种具有以下特征的正则化负标签松弛最小二乘回归方法。首先，我们引入一个负数\（\ varepsilon \）拖动技术可将严格的二进制标签矩阵放宽为松弛的标签矩阵，从而具有更大的自由度来适合标签并同时减少类边距。其次，我们引入流形学习和类紧度图来设计一个正则化项，以保留数据的固有结构并避免过度拟合的问题。类紧密度图可以使来自同一类的样本在转换为松弛标签空间后可以保持紧密在一起。设计了基于L2-范数损失函数的算法。实验结果表明，该算法具有较好的分类精度。