IEEE Trans Neural Netw Learn Syst. 2016 Oct;27(10):2072-83. doi: 10.1109/TNNLS.2015.2477321. Epub 2015 Oct 27.
Human preferences are usually measured using ordinal variables. A system whose goal is to estimate the preferences of humans and their underlying decision mechanisms requires to learn the ordering of any given sample set. We consider the solution of this ordinal regression problem using a support vector machine algorithm. Specifically, the goal is to learn a set of classifiers with common direction vectors and different biases correctly separating the ordered classes. Current algorithms are either required to solve a quadratic optimization problem, which is computationally expensive, or based on maximizing the minimum margin (i.e., a fixed-margin strategy) between a set of hyperplanes, which biases the solution to the closest margin. Another drawback of these strategies is that they are limited to order the classes using a single ranking variable (e.g., perceived length). In this paper, we define a multiple ordinal regression algorithm based on maximizing the sum of the margins between every consecutive class with respect to one or more rankings (e.g., perceived length and weight). We provide derivations of an efficient, easy-to-implement iterative solution using a sequential minimal optimization procedure. We demonstrate the accuracy of our solutions in several data sets. In addition, we provide a key application of our algorithms in estimating human subjects' ordinal classification of attribute associations to object categories. We show that these ordinal associations perform better than the binary one typically employed in the literature.
人类的偏好通常使用序数变量来衡量。一个旨在估计人类偏好及其潜在决策机制的系统需要学习任何给定样本集的排序。我们使用支持向量机算法来解决这个有序回归问题。具体来说，目标是学习一组具有公共方向向量和不同偏差的分类器，正确分离有序的类别。当前的算法要么需要解决计算成本高昂的二次优化问题，要么基于最大化一组超平面之间的最小边际（即固定边际策略），这会使解决方案偏向于最近的边际。这些策略的另一个缺点是，它们仅限于使用单个排名变量（例如，感知长度）对类别进行排序。在本文中，我们定义了一种基于最大化每个连续类相对于一个或多个排名（例如，感知长度和重量）的边际之和的多元有序回归算法。我们提供了一种使用序列最小优化过程的高效、易于实现的迭代解决方案的推导。我们在几个数据集上证明了我们的解决方案的准确性。此外，我们还提供了我们的算法在估计人类主体对对象类别的属性关联的有序分类中的一个关键应用。我们表明，这些有序关联比文献中通常使用的二进制关联表现更好。
