Ramp-loss nonparallel support vector regression: Robust, sparse and scalable approximation
Ramp-loss nonparallel support vector regression: Robust, sparse and scalable approximation
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斜坡损失非并行支持向量回归：稳健、稀疏且可扩展的近似
DOI：
10.1016/j.knosys.2018.02.016
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发表时间：
2018-05
影响因子：
8.8
通讯作者：
Pardalos Panos M.
中科院分区：
文献类型：
--
作者：
Tang Long;Tian Yingjie;Yang Chunyan;Pardalos Panos M.
虽然双支持向量回归（TSVR）已经被广泛研究并且成功开发了各种变体，但是当涉及到离群点时，回归模型可能会被错误地驱动到离群点，从而产生极差的泛化性能。为了克服这一缺点，本文提出了一种斜坡损失非并行支持向量回归机（RL-NPSVR）。RL-NPSVR通过采用Ramp ε-不敏感损失函数和另一种Ramp型线性损失函数，不仅可以显式滤除噪声和抑制野值，而且具有良好的稀疏性。RL-NPSVR的非凸性问题用凹凸规划（CCCP）解决。CCCP严格遵循结构风险最小化（SRM）原则，在原问题中加入正则化项，实际上解决了一系列与标准SVR具有相同对偶问题形式的重构凸优化问题，从而避免了求逆矩阵，并可采用SMO型快速算法加速训练过程.在不同数据集上的数值实验验证了我们提出的RL-NPSVR在离群敏感性，泛化能力，稀疏性和可扩展性方面的有效性。
Although the twin support vector regression (TSVR) has been extensively studied and diverse variants are successfully developed, when it comes to outlier-involved training set, the regression model can be wrongly driven towards the outlier points, yielding extremely poor generalization performance. To overcome such shortcoming, a Ramp-loss nonparallel support vector regression (RL-NPSVR) is proposed in this work. By adopting Ramp ε-insensitive loss function and another Ramp-type linear loss function, RL-NPSVR can not only explicitly filter noise and outlier suppression but also have an excellent sparseness. The non- convexity of RL-NPSVR is solved by concave–convex programming (CCCP). Because a regularized term is added into each primal problem by rigidly following the structural risk minimization (SRM) principle, CCCP actually solves a series of reconstructed convex optimizations which have the same formulation of dual problem as the standard SVR, so that computing inverse matrix is avoided and SMO-type fast algorithm can be used to accelerate the training process. Numerical experiments on various datasets have verified the effectiveness of our proposed RL-NPSVR in terms of outlier sensitivity, generalization ability, sparseness and scalability.
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