Incremental Support Vector Learning for Ordinal Regression
Incremental Support Vector Learning for Ordinal Regression
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DOI：
10.1109/tnnls.2014.2342533
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发表时间：
2015-07-01
影响因子：
10.4
通讯作者：
Li, Shuo
中科院分区：
文献类型：
--
作者：
Gu, Bin;Sheng, Victor S.;Li, Shuo
支持向量有序回归（SVOR）是解决有序回归问题的一种流行方法。然而，到目前为止，还没有有效的算法提出来解决增量SVOR学习由于复杂的公式。最近，一个有趣的准确的在线算法被提出用于训练nu-支持向量分类（nu-SVC），它可以处理一个二次公式与一对等式约束。在本文中，我们首先提出了一个修改的SVOR制定的利润率总和的战略基础上。该公式具有多个约束，并且每个约束包括等式和不等式的混合。然后，我们扩展了精确的在线nu-SVC算法的修改配方，并提出了一个有效的增量SVOR算法。该算法可以处理具有多个约束的二次方程，其中每个约束由一个等式和一个不等式组成。更重要的是，它解决了平等和不平等约束之间的冲突。并给出了算法的有限收敛性分析。在多个基准数据集和真实数据集上的数值实验表明，增量式算法可以在有限步内收敛到最优解，并且比现有的批处理和增量式SVOR算法更快。同时，改进的公式具有更好的精度比现有的增量SVOR算法，是准确的基于利润率的Shashua和莱文的公式。
Support vector ordinal regression (SVOR) is a popular method to tackle ordinal regression problems. However, until now there were no effective algorithms proposed to address incremental SVOR learning due to the complicated formulations of SVOR. Recently, an interesting accurate on-line algorithm was proposed for training nu-support vector classification (nu-SVC), which can handle a quadratic formulation with a pair of equality constraints. In this paper, we first present a modified SVOR formulation based on a sum-of-margins strategy. The formulation has multiple constraints, and each constraint includes a mixture of an equality and an inequality. Then, we extend the accurate on-line nu-SVC algorithm to the modified formulation, and propose an effective incremental SVOR algorithm. The algorithm can handle a quadratic formulation with multiple constraints, where each constraint is constituted of an equality and an inequality. More importantly, it tackles the conflicts between the equality and inequality constraints. We also provide the finite convergence analysis for the algorithm. Numerical experiments on the several benchmark and real-world data sets show that the incremental algorithm can converge to the optimal solution in a finite number of steps, and is faster than the existing batch and incremental SVOR algorithms. Meanwhile, the modified formulation has better accuracy than the existing incremental SVOR algorithm, and is as accurate as the sum-of-margins based formulation of Shashua and Levin.