IEEE Trans Neural Netw Learn Syst. 2012 Nov;23(11):1738-54. doi: 10.1109/TNNLS.2012.2212721.
This paper presents a framework of discriminative least squares regression (LSR) for multiclass classification and feature selection. The core idea is to enlarge the distance between different classes under the conceptual framework of LSR. First, a technique called ε-dragging is introduced to force the regression targets of different classes moving along opposite directions such that the distances between classes can be enlarged. Then, the ε-draggings are integrated into the LSR model for multiclass classification. Our learning framework, referred to as discriminative LSR, has a compact model form, where there is no need to train two-class machines that are independent of each other. With its compact form, this model can be naturally extended for feature selection. This goal is achieved in terms of L2,1 norm of matrix, generating a sparse learning model for feature selection. The model for multiclass classification and its extension for feature selection are finally solved elegantly and efficiently. Experimental evaluation over a range of benchmark datasets indicates the validity of our method.
本文提出了一种用于多类分类和特征选择的判别最小二乘回归（LSR）框架。其核心思想是在 LSR 的概念框架下扩大不同类之间的距离。首先，引入了一种称为 ε-dragging 的技术，迫使不同类别的回归目标沿相反方向移动，从而扩大类之间的距离。然后，将 ε-draggings 集成到用于多类分类的 LSR 模型中。我们的学习框架，称为判别式 LSR，具有简洁的模型形式，其中不需要训练相互独立的二类机器。由于其简洁的形式，该模型可以自然地扩展到特征选择中。通过矩阵的 L2,1 范数实现了这一目标，为特征选择生成了一个稀疏学习模型。最后，优雅而有效地解决了多类分类模型及其特征选择扩展的问题。在一系列基准数据集上的实验评估表明了我们方法的有效性。
