Ordinal-Class Core Vector Machine

Ordinal regression is one of the most important tasks of relation learning, and several techniques based on support vector machines (SVMs) have also been proposed for tackling it, but the scalability aspect of these approaches to handle large datasets still needs much of exploration. In this paper, we will extend the recent proposed algorithm Core Vector Machine (CVM) to the ordinal-class data, and propose a new algorithm named as Ordinal-Class Core Vector Machine (OCVM). Similar with CVM, its asymptotic time complexity is linear with the number of training samples, while the space complexity is independent with the number of training samples. We also give some analysis for OCVM, which mainly includes two parts, the first one shows that OCVM can guarantee that the biases are unique and properly ordered under some situation; the second one illustrates the approximate convergence of the solution from the viewpoints of objective function and KKT conditions. Experiments on several synthetic and real world datasets demonstrate that OCVM scales well with the size of the dataset and can achieve comparable generalization performance with existing SVM implementations.