This paper proposes a method to solve ordinal regression problems, namely the non-parallel hyperplanes ordinal regression machine (NPHORM). The goal of this approach is to find $K$ different hyperplanes for the $K$ classes with ordinal information, so that each class is as close as possible to the corresponding hyperplane while as far as possible from the adjacent to the left and right classes. The more flexible separate hyperplanes are preferred using the order information of the data. As a result, this approach only needs to solve $K$ quadratic programming problems independently. Our approach NPHORM is validated on 2 artificial datasets, 16 discretised regression datasets and 17 real ordinal regression datasets and compared with 8 outstanding SVM-based ordinal regression approaches. The results show that our approach NPHORM is comparable with the other SVM-based approaches, especially in real ordinal regression datasets. In addition, our NPHORM is also carried out on the historical color image dataset to compare the performance of deep learning method. Experimental results demonstrate that the performance of our NPHORM outperforms the deep learning methods on MAE.

本文提出了一种解决序数回归问题的方法，即非平行超平面序数回归机（NPHORM）。这种方法的目标是发现$ķ$ 不同的超平面 $ķ$具有序数信息的类别，以便每个类别都尽可能靠近相应的超平面，而尽可能远离相邻的左侧和右侧类别。使用数据的顺序信息来选择更灵活的独立超平面。结果，这种方法只需要解决$ķ$二次编程问题独立。我们的方法NPHORM在2个人工数据集，16个离散回归数据集和17个真实序数回归数据集上得到了验证，并与8种基于SVM的出色序数回归方法进行了比较。结果表明，我们的方法NPHORM与其他基于SVM的方法具有可比性，尤其是在实际有序回归数据集中。此外，我们还对历史彩色图像数据集进行了NPHORM，以比较深度学习方法的性能。实验结果表明，我们的NPHORM的性能优于MAE上的深度学习方法。