Wang Changlin, Yang Zhixia, Ye Junyou, Yang Xue
College of Mathematics and Systems Science, Xinjiang University, Urumuqi 830046, China.
Institute of Mathematics and Physics, Xinjiang University, Urumuqi 830046, China.
Entropy (Basel). 2023 Jul 24;25(7):1103. doi: 10.3390/e25071103.
For multi-class classification problems, a new kernel-free nonlinear classifier is presented, called the hard quadratic surface least squares regression (HQSLSR). It combines the benefits of the least squares loss function and quadratic kernel-free trick. The optimization problem of HQSLSR is convex and unconstrained, making it easy to solve. Further, to improve the generalization ability of HQSLSR, a softened version (SQSLSR) is proposed by introducing an ε-dragging technique, which can enlarge the between-class distance. The optimization problem of SQSLSR is solved by designing an alteration iteration algorithm. The convergence, interpretability and computational complexity of our methods are addressed in a theoretical analysis. The visualization results on five artificial datasets demonstrate that the obtained regression function in each category has geometric diversity and the advantage of the ε-dragging technique. Furthermore, experimental results on benchmark datasets show that our methods perform comparably to some state-of-the-art classifiers.
针对多类分类问题，提出了一种新的无核非线性分类器，称为硬二次曲面最小二乘回归（HQSLSR）。它结合了最小二乘损失函数和无二次核技巧的优点。HQSLSR的优化问题是凸的且无约束的，易于求解。此外，为了提高HQSLSR的泛化能力，通过引入ε-拖动技术提出了一个软化版本（SQSLSR），该技术可以扩大类间距离。通过设计一种交替迭代算法来解决SQSLSR的优化问题。在理论分析中讨论了我们方法的收敛性、可解释性和计算复杂性。在五个人工数据集上的可视化结果表明，在每个类别中获得的回归函数具有几何多样性以及ε-拖动技术的优势。此外，在基准数据集上的实验结果表明我们的方法与一些最先进的分类器性能相当。
