Bio-Computing Research Center, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, Guangdong, China; Shenzhen Medical Biometrics Perception and Analysis Engineering Laboratory, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, Guangdong, China.
Bio-Computing Research Center, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, Guangdong, China; Shenzhen Medical Biometrics Perception and Analysis Engineering Laboratory, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, Guangdong, China.
Neural Netw. 2018 Jun;102:36-47. doi: 10.1016/j.neunet.2018.02.002. Epub 2018 Feb 21.
Least square regression is a very popular supervised classification method. However, two main issues greatly limit its performance. The first one is that it only focuses on fitting the input features to the corresponding output labels while ignoring the correlations among samples. The second one is that the used label matrix, i.e., zero-one label matrix is inappropriate for classification. To solve these problems and improve the performance, this paper presents a novel method, i.e., inter-class sparsity based discriminative least square regression (ICS_DLSR), for multi-class classification. Different from other methods, the proposed method pursues that the transformed samples have a common sparsity structure in each class. For this goal, an inter-class sparsity constraint is introduced to the least square regression model such that the margins of samples from the same class can be greatly reduced while those of samples from different classes can be enlarged. In addition, an error term with row-sparsity constraint is introduced to relax the strict zero-one label matrix, which allows the method to be more flexible in learning the discriminative transformation matrix. These factors encourage the method to learn a more compact and discriminative transformation for regression and thus has the potential to perform better than other methods. Extensive experimental results show that the proposed method achieves the best performance in comparison with other methods for multi-class classification.
最小二乘回归是一种非常流行的监督分类方法。然而，有两个主要问题极大地限制了它的性能。第一个问题是，它只关注将输入特征拟合到相应的输出标签，而忽略了样本之间的相关性。第二个问题是，使用的标签矩阵，即零一标签矩阵，不适合分类。为了解决这些问题并提高性能，本文提出了一种新的方法，即基于类间稀疏性的判别最小二乘回归（ICS_DLSR），用于多类分类。与其他方法不同，所提出的方法追求变换后的样本在每个类中具有共同的稀疏结构。为此，在最小二乘回归模型中引入了类间稀疏性约束，使得来自同一类的样本的边缘可以大大减小，而来自不同类的样本的边缘可以增大。此外，引入了具有行稀疏性约束的误差项来放松严格的零一标签矩阵，这使得该方法在学习判别转换矩阵时更加灵活。这些因素鼓励该方法为回归学习更紧凑和更具判别性的转换，从而有可能比其他方法表现更好。广泛的实验结果表明，与其他多类分类方法相比，所提出的方法具有最佳的性能。
