IEEE Trans Cybern. 2014 May;44(5):681-94. doi: 10.1109/TCYB.2013.2266336. Epub 2013 Jun 27.
The classification of patterns into naturally ordered labels is referred to as ordinal regression. This paper proposes an ensemble methodology specifically adapted to this type of problem, which is based on computing different classification tasks through the formulation of different order hypotheses. Every single model is trained in order to distinguish between one given class (k) and all the remaining ones, while grouping them in those classes with a rank lower than k , and those with a rank higher than k. Therefore, it can be considered as a reformulation of the well-known one-versus-all scheme. The base algorithm for the ensemble could be any threshold (or even probabilistic) method, such as the ones selected in this paper: kernel discriminant analysis, support vector machines and logistic regression (LR) (all reformulated to deal with ordinal regression problems). The method is seen to be competitive when compared with other state-of-the-art methodologies (both ordinal and nominal), by using six measures and a total of 15 ordinal datasets. Furthermore, an additional set of experiments is used to study the potential scalability and interpretability of the proposed method when using LR as base methodology for the ensemble.
模式到自然有序标签的分类被称为有序回归。本文提出了一种专门适用于这种类型问题的集成方法，该方法基于通过制定不同的有序假设来计算不同的分类任务。每个单独的模型都经过训练，以区分一个给定的类（k）和所有其他类，同时将它们分组为低于 k 的类和高于 k 的类。因此，它可以被认为是众所周知的一对一方案的重新表述。集成的基础算法可以是任何阈值（甚至是概率）方法，例如本文中选择的方法：核判别分析、支持向量机和逻辑回归（LR）（都重新制定以处理有序回归问题）。通过使用六个度量标准和总共 15 个有序数据集，与其他最先进的方法（有序和名义）相比，该方法具有竞争力。此外，还使用一组额外的实验来研究当使用 LR 作为集成的基础方法时，所提出的方法在可扩展性和可解释性方面的潜力。
