One norm linear programming support vector regression
One norm linear programming support vector regression
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DOI：
10.1016/j.neucom.2015.09.024
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发表时间：
2016-01
期刊：
影响因子：
6
通讯作者：
M. Tanveer;Mohit Mangal;I. Ahmad;Y. Shao
中科院分区：
文献类型：
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作者：
M. Tanveer;Mohit Mangal;I. Ahmad;Y. Shao
本文提出了一种新的1-范数支持向量回归机（SVR）的线性规划公式，其解是通过在对偶空间中将外罚问题转化为无约束极小化问题，并利用牛顿法求解得到的。修正的无约束最小化问题的求解与SVR中的二次规划问题相比，简化为求解线性方程组，算法简单、快速。该算法从任何起点收敛，可以很容易地在MATLAB中实现，而无需使用任何优化包。所提出的方法的主要优点是，它导致了一个强大的和稀疏的模型表示，这意味着最优解向量的许多组件将成为零，因此，决策函数可以确定使用的支持向量的数量少得多相比，SVR，平滑SVR（SSVR）和加权SVR（WSVR）。为了证明其有效性，在知名的合成和真实世界的基准数据集上进行了实验。与SVR、SSVR和WSVR相比，该方法在较少的训练时间内具有相似或更好的泛化性能，表明了其适用性和实用性。
In this paper, a new linear programming formulation of a 1-norm support vector regression (SVR) is proposed whose solution is obtained by solving an exterior penalty problem in the dual space as an unconstrained minimization problem using Newton method. The solution of modified unconstrained minimization problem reduces to solving just system of linear equations as opposed to solving quadratic programming problem in SVR, which leads to extremely simple and fast algorithm. The algorithm converges from any starting point and can be easily implemented in MATLAB without using any optimization packages. The main advantage of the proposed approach is that it leads to a robust and sparse model representation meaning that many components of the optimal solution vector will become zero and therefore the decision function can be determined using much less number of support vectors in comparison to SVR, smooth SVR (SSVR) and weighted SVR (WSVR). To demonstrate its effectiveness, experiments were performed on well-known synthetic and real-world benchmark datasets. Similar or better generalization performance of the proposed method in less training time in comparison with SVR, SSVR and WSVR clearly exhibits its suitability and applicability.